<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Diferentes tecnologias e a forma como enfatizam a relevância de diferentes domínios do conhecimento profissional do professor</style></title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A interdisciplinaridade em contexto de integração da tecnologia: o conhecimento profissional de professores de Matemática e de Físico-Química</style></title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Teixeira</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">C. Martins</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Desenvolvimento profissional do professor de matemática através de uma formação em STEAM – Mathematics Teacher Professional Development through STEAM Training</style></title><secondary-title><style face="normal" font="default" size="100%">EIEM 2025</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">In Press</style></year></dates><pub-location><style face="normal" font="default" size="100%">Lisboa</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Exploring mathematics teachers' knowledge: an analysis based on the KTMT model and the use of different models of graphing calculators</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Haspekian, M.</style></author><author><style face="normal" font="default" size="100%">Tabach, M.</style></author><author><style face="normal" font="default" size="100%">J. Trgalova</style></author><author><style face="normal" font="default" size="100%">H-G. Weigand</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Rethinking Knowledge for Teaching Mathematics with Technology: Tensions, Extensions and Future Agenda</style></title><secondary-title><style face="normal" font="default" size="100%">PME 49</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><publisher><style face="normal" font="default" size="100%">IGPME</style></publisher><pub-location><style face="normal" font="default" size="100%">Helsinky, Finland</style></pub-location><pages><style face="normal" font="default" size="100%">248-275</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The integration of digital technology to promote mathematical learning remains challenging for teachers. The continuous difficulty in fully achieving technology’s potential highlights the need to further examine and develop models addressing teachers’ knowledge in relation to technology. In this Research Forum, we analyse existing technology-related knowledge models, exploring similarities and differences. We also consider how these models have been used in research, highlighting tensions driven by emerging technologies, and resulting extensions of the models. Finally, we discuss possible integrations across frameworks and the potential to include dimensions beyond knowledge. This discussion aims to deepen understanding of current models and suggest directions and a research agenda for future development.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bernardi, M.L.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers' knowledge in GAI-supported mathematics education</style></title><secondary-title><style face="normal" font="default" size="100%">PME 49</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><publisher><style face="normal" font="default" size="100%">IGPME</style></publisher><pub-location><style face="normal" font="default" size="100%">Helsinky, Finland</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Teixeira</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">C. Martins</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers' perceptions of teaching practices, the STEAM approach, and collaborative work</style></title><secondary-title><style face="normal" font="default" size="100%">Perspectives and Trends in Education and Technology</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">560-569</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Menezes, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ knowledge and technology in the teaching of functions: A view from Portugal and Brazil</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Mathematical Behavior</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.jmathb.2025.101301</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">81</style></volume><pages><style face="normal" font="default" size="100%">1-17</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Technology integration although highly recommended has proved to be complex. This study aims to characterize the perceptions of secondary mathematics teachers (grades 7th to 12th), from Portugal (Braga region) and Brazil (Campinas region), regarding the teaching of Functions and the use of technology. We also intend to consider the context of the two countries, reflecting on justifications for the differences identified (if any). The study adopts a mixed methodology based on a questionnaire applied to 129 Portuguese teachers in Braga region and 136 Brazilian teachers in Campinas region (quantitative dimension) and on an interview to six Portuguese teachers and six Brazilian teachers (qualitative dimension). The results point to similarities between teachers from Portugal and Brazil, but also to some differences. Technology potential is recognized by teacher from both countries, however teachers from Brazil tend to assume a more traditional use of technology, based on showing and more teacher-centered. This difference can be related to the Portuguese curriculum, valuing a relevant use of technology for more than three decades.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Technological integration and interdisciplinarity: The role of teachers' professional knowledge</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Teixeira</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">C. Martins</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Challenges and potential in implementing STE(A)M in teachers' practices: a systematic review</style></title><secondary-title><style face="normal" font="default" size="100%">International Journal of Mathematical Education in Science and Technology</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1080/0020739X.2025.2496701</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">56</style></volume><pages><style face="normal" font="default" size="100%">1384-1400</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The potential of STE(A)M has been widely recognised in recent years; however, challenges have also been identified in the implementation of this approach, making it important to deepen research into teachers’ practices. In this study, we conducted a systematic review focused on teaching practices within a STE(A)M approach, to understand what challenges and limitations teachers encounter, as well as the possibilities authors suggest to overcome them. The research question is: What are the challenges and potentialities of implementing the STE(A)M approach in teachers’ practices? This review analysed articles indexed in the Web of Science and Scopus databases over the last eight years, following the PRISMA scheme. The 26 articles examined highlight challenges such as time management, lack of resources and funding, limited guidance, gaps in teacher training, difficulty integrating subject areas, issues implementing new technologies and obstacles imposed by school structures. In light of these, the following proposals were suggested: placing greater emphasis on STE(A)M in initial and continuing teacher education, increasing support from schools and government bodies, encouraging collaborative work between teachers from different areas, adopting innovative strategies and methodologies and offering a clearer conceptualisation of STE(A)M.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">8</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Spagnolo, C.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ChatGPT e o ensino da Matemática: alguns exemplos para refletir sobre desafios e oportunidades</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://em.apm.pt/index.php/em/article/view/3056</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">176</style></volume><pages><style face="normal" font="default" size="100%">46-50</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bernardi, M.L.</style></author><author><style face="normal" font="default" size="100%">Capone, R.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Generative AI in mathematics education: pre-service teachers’ knowledge and implications for their professional development</style></title><secondary-title><style face="normal" font="default" size="100%">International Journal of Mathematical Education in Science and Technology</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1080/0020739X.2025.2490104</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">56</style></volume><pages><style face="normal" font="default" size="100%">1513-1530</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Incorporating technologies with Generative Artificial Intelligence (GenAI) into education requires a shift in teaching methodologies. However, little is known about how pre-service teachers perceive the relevance and challenges of this incorporation, particularly in mathematics education. This study investigates pre-service teachers’ interactions with GenAI, addressing the relevance and challenges of integrating it in mathematics teaching and discussing possible implications for their knowledge and professional development. Specifically, it intends to understand: How does the pre-service teachers’ interaction with GenAI during the design and implementation of teaching activities relate to their professional knowledge? And how does this relation impact the relevance they ascribe to GenAI? In this qualitative and interpretative study, involving seven pre-service mathematics teachers, we analyse the interplay between participants’ knowledge and use of a GenAI (in this case, ChatGPT), guided by KTMT – Knowledge for Teaching Mathematics with Technology model. The main conclusions revealed a landscape characterised by promise and challenge, where GenAI can be a valuable educational&lt;br /&gt;
tool when used to facilitate discussion and promote critical thinking, highlighting the relevance and development of KTMT. The ability to evaluate and reflect on AI-generated responses can promote professional development, preparing pre-service teachers for an increasing presence of technology in educational environments.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">8</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Knowledge to teach Mathematics with technology: the Global Model</style></title><secondary-title><style face="normal" font="default" size="100%">International Journal of Mathematical Education in Science and Technology</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1080/0020739X.2025.2483488</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">56</style></volume><pages><style face="normal" font="default" size="100%">1494-1512</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The teacher’s central role in technology integration and the challenges of that integration emphasise the need for a deeper understanding about the teacher’s knowledge required to teach with technology. Based on previous work and a systematic literature review, we identified three knowledge models often used: TPACK, KTMT and&lt;br /&gt;
PTK. The goal of this paper is to discuss the similarities and differences between these knowledge models and present a Global Model. This Global Model is not a new model. On the contrary, it is a model developed based on the existing models and intending to integrate in a single model the knowledge domains considered in the different existing models. The Global Model highlights the common domains considered and the common roots for the three models, but it also makes explicit the differences, mostly related to the understanding of the domains or even to the domains considered, and also to the way how the knowledge’s development is conceived.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">8</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The role of professional knowledge in teachers' responses to technological hiccups in mathematics and physics classrooms</style></title><secondary-title><style face="normal" font="default" size="100%">School Sciences and Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://doi.org/10.1111/ssm.18369</style></url></web-urls></urls></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ knowledge and technology: the global model</style></title><secondary-title><style face="normal" font="default" size="100%">CERME</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Bolzano, Italy</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The teachers’ central role in technology integration and the challenges of that integration emphasize the need for a deeper understanding about the teachers’ knowledge required to teach with technology. Based on previous work and a systematic literature review, we identified three knowledge models often used: TPACK, KTMT and PTK. The goal of this paper is to discuss the similarities and differences between these knowledge models and present a Global Model. This Global Model is not a new model. On the contrary, it is a model developed based on the existing models and intending to integrate in a single model the knowledge domains considered in the different existing models. The Global Model highlights the common domains considered and the common roots for the three models, but it also makes explicit the differences, mostly related to the understanding of the domains or even to the domains considered, and also to the way how the knowledge’s development is conceived.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Jacinto, H.</style></author><author><style face="normal" font="default" size="100%">J. Matos</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Moral-Sánchez, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Tecnologias emergentes no ensino e aprendizagem da matemática: Que desafios para a investigação em Educação Matemática?</style></title><secondary-title><style face="normal" font="default" size="100%">EIEM 2025</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><pub-location><style face="normal" font="default" size="100%">Lisboa</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Characterizing the knowledge mobilized by mathematics teachers: A case study with different technologies - Caracterização do conhecimento mobilizado por professores de matemática: Um estudo de caso com diferentes tecnologias</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM 2024</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/siem2024_cb_hr.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Caldas da Rainha</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Forging interdisciplinary paths: Teachers' professional knowledge on disciplinary articulation - Trilhando caminhos interdisciplinares: Conhecimento profissional dos professores sobre a articulação disciplinar</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM 2024</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2024_siem_coelho_rocha.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Caldas da Rainha</style></pub-location><pages><style face="normal" font="default" size="100%">1-12</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The challenges of disciplinary integration in teaching practice, especially in the implementation of tasks that promote interdisciplinary approaches, highlight the importance of teachers' professional knowledge in this process. Using a naturalistic approach, this study aims to characterize the professional knowledge of a physics teacher when adopting an interdisciplinary approach using technology. The results of the research revealed that the teacher mobilizes different types of knowledge, showing a differentiated knowledge of the most appropriate mathematical application to teach a given piece of content, and knowledge of how pedagogical strategies can be aided through different applications using technology.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Interdisciplinary professional knowledge: divergences and convergences of two models – Conhecimento profissional interdisciplinar: divergências e convergências de dois modelos</style></title><secondary-title><style face="normal" font="default" size="100%">Iberian Journal of Information Systems and Technologies</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.risti.xyz/issues/ristie71.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">E71</style></volume><pages><style face="normal" font="default" size="100%">316-328</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Giglione, S.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Investigating the impact of technology integration on Italian and Portuguese teachers’ perspectives concerning standardized assessment</style></title><secondary-title><style face="normal" font="default" size="100%">MEDA – Mathematics Education at the Digital Age</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://community.ict.uniba.it/comunicazionedigitale/it/fuori-collana/meda4-proceedings-30.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Bari, Italy</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O conhecimento profissional do professor na mobilização de diferentes representações com diferentes tecnologias</style></title><secondary-title><style face="normal" font="default" size="100%">Iberian Journal of Information Systems and Technologies</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.risti.xyz/issues/ristie71.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">E71</style></volume><pages><style face="normal" font="default" size="100%">486-499</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Sacristán, A.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Santacruz-Rodríguez, M.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Policies and implementations for technology use in mathematics education: perspectives from around the world</style></title><secondary-title><style face="normal" font="default" size="100%">Handbook of digital resources in mathematics education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/978-3-030-95060-6_52-1</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">1-35</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this chapter, we examine the role of policies and other factors affecting digital technology (DT) integration in mathematics education. In particular, we develop a cross-national analysis of the impact on DT implementation in four countries: two countries in Europe (Italy and Portugal) and two countries in Latin America (Colombia and Mexico). We analyze the role that policies, political changes, reforms, curricula, educational organization and systems, sociocultural aspects, and teachers’ training, knowledge, and beliefs play toward possible DT implementations. We observe that there is a discourse in policies to promote digital technologies’ use, but in practice the availability and integration of such resources in mathematics classrooms is still scarce. We also note that the efforts done during the pandemic did not change this, promoting general ICT use, rather than DT resources that might enhance mathematics teaching and learning.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Matos, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Problem solving in a real-life context: an approach during the learning of inequalities</style></title><secondary-title><style face="normal" font="default" size="100%">European Journal of Science and Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.scimath.net/article/problem-solving-in-a-real-life-context-an-approach-during-the-learning-of-inequalities-13828</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study was conducted while 9th grade students learn to solve inequalities and seeks to understand their approach to solving problems with a real-life context. Specifically, the aim is to understand: (1) What are the main characteristics of the students’ approaches to the proposed problems? (2) What is the impact of the real context on the students’ resolutions? A qualitative and interpretative methodology is adopted, based on case studies, with data collected through documentary collection and audio recording of discussions between a pair of students while solving problems. The main conclusions suggest a trend to approach problems without establishing immediate connections with what was being done in the classroom, with students’ decisions being essentially guided by criteria of simplicity. The real context of the problems seems to have the potential to develop in students a more integrated mathematics, focused on understanding and not so much on the repetition of mechanical and meaning-independent procedures. The students’ familiarization with the context in question is one of the aspects highlighted by this study.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Babo, A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Problem-solving and mathematical competence: a look to the relation during the study of Linear Programming</style></title><secondary-title><style face="normal" font="default" size="100%">Thinking Skills and Creativity</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.sciencedirect.com/science/article/pii/S1871187123002286</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">51</style></volume><pages><style face="normal" font="default" size="100%">1-14</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study seeks reflection on the approaches of 11th grade students to Linear Programming problems, discussing the approaches taken at different moments of the teaching process. It aims to analyze:&lt;br /&gt;
How is the students’ mathematical competence characterized in relation to problemsolving;&lt;br /&gt;
What differences can be identified in the resolutions at different moments of the teaching and learning process.&lt;br /&gt;
We adopt a qualitative and interpretative methodology, analyzing the approaches of two pairs of students with different mathematical backgrounds. The analysis is guided by P´olya’s stages of solving a problem and aspects of the understanding of mathematical competence. The results show different approaches to the problems depending on the teaching moment and different competences. The mathematical background impacts the students’ success when they implement routine procedures, however it does not seem to determine the students’ competence to reason about a problem.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The role of teachers’ knowledge and the use of different technologies in the classroom</style></title><secondary-title><style face="normal" font="default" size="100%">MEDA – Mathematics Education at the Digital Age</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://community.ict.uniba.it/comunicazionedigitale/it/fuori-collana/meda4-proceedings-30.pdf</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2024_meda_botelho_rocha.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Bari, Italy</style></pub-location><pages><style face="normal" font="default" size="100%">121-128</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The potential of technology to enhance the learning of mathematics is widely acknowledged. However, realizing this potential requires teachers to possess the knowledge to effectively integrate it into their teaching practices. This study aims to characterize the mathematics teacher's knowledge when using different technologies in teaching and learning. It also aims to study the existence of relationships between the specific domains of the Knowledge for Teaching Mathematics with Technology – KTMT and the integration of graphing calculator and Excel. The methodology adopted is qualitative with an interpretative approach, using a case study of Mathematics teacher in the 11th grade (16-17 years old) with extensive experience in the use of technology. This study shows that different KTMT knowledge is mobilized, according to the technology chosen and the specific characteristics of each of the technologies used influenced the teacher's pedagogical choices.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teaching Mathematics with technology: a preliminary version of the Global Knowledge model - Ensinar Matemática com tecnologia: uma versão preliminar do modelo Global do Conhecimento</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM 2024</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/siem2024_hr.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Caldas da Rainha</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study aims to discuss similarities and differences between knowledge models focusing on technology, developing the Global Model. This is not a new model, but rather a contribution to the articulation between different conceptual frameworks.&lt;/p&gt;
&lt;p&gt;Este estudo visa discutir semelhanças e diferenças entre modelos de conhecimento com foco na tecnologia, desenvolvendo a partir destes o Modelo Global. Este não é um novo modelo, mas antes um contributo para a articulação entre diferentes quadros conceptuais.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The use of the TPACK framework on research about teachers’ knowledge to teach with digital technology</style></title><secondary-title><style face="normal" font="default" size="100%">MEDA – Mathematics Education at the Digital Age</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://community.ict.uniba.it/comunicazionedigitale/it/fuori-collana/meda4-proceedings-30.pdf</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2024_meda_rocha.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Bari, Italy</style></pub-location><pages><style face="normal" font="default" size="100%">359-366</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The potential of digital technologies for teaching and learning mathematics is widely recognized and teachers’ knowledge is one of the elements impacting their integration. Several authors have intended to characterize the teachers’ knowledge required and developed several models, being TPACK one of these models. In this study, we seek to conduct a systematic review of the research on the integration of digital technologies by mathematics teachers based on the TPACK model. Specifically, we intend to answer the following research questions: (1) What are the main methodological options adopted? (2) How is the framework operationalized/used in the studies? The review was based on a search in the Scopus database and resulted in the identification of 10 relevant documents. The analysis suggests a prevalence of qualitative approaches, but a strong use of questionnaires; and an integration of the model with other frameworks, namely the developmental model of TPACK.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Sacristán, A.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Santacruz-Rodríguez, M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Addressing the congruence and similarity of figures with technology: A cross-national comparison</style></title><secondary-title><style face="normal" font="default" size="100%">ICTMT</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Analyzing teachers’ knowledge based on their approach to the information provided by technology</style></title><secondary-title><style face="normal" font="default" size="100%">European Journal of Science and Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.30935/scimath/12522</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">132-145</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Teachers’ knowledge plays a central role in technology integration. In this study we analyze situations, where there is some divergence between the mathematical results and the information offered by the graphing calculator (lack of mathematical fidelity), putting the focus in the teachers and in their approaches. The goal of this study is to analyze, in the light of knowledge for teaching mathematics with technology (KTMT) model, the teachers’ professional knowledge, assuming the situations of lack of mathematical fidelity as having the potential to reveal some characteristics of their knowledge. Specifically, considering the teaching of functions at 10th grade (age 16), we intend to analyze: (1) What knowledge do the teachers have of technology and of its mathematical fidelity? (2) What can the teachers’ options related to situations of lack of mathematical fidelity tell us about their knowledge in other KTMT domains? The study adopts a qualitative and interpretative approach based on the case studies of two teachers. Data were collected by interviews and class observation, being the analysis guided by the KTMT model. The main result points to the relevance of the mathematics and technology knowledge. However, there is evidence of some difficulties to integrate the information provided by the technology with the mathematics, and also of some interference of the teaching and learning and technology knowledge, and specifically of the knowledge related to the students. This suggests that the analysis of the teachers’ actions in relation to situations of lack of mathematical fidelity, can be useful to characterize their KTMT.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ferreira, G.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">A. Rodrigues</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">As conexões matemáticas na resolução de problemas</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do EIEM 2023 - Encontro em Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Aveiro</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Conhecimento profissional do professor: a influência das perturbações tecnológicas no ensino de Matemática e Física - Teacher's professional knowledge: The influence of technological disruptions in the teaching of Mathematics and Physics</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XXXIII SIEM – Seminário de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Barcelos</style></pub-location><pages><style face="normal" font="default" size="100%">1-10</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">M. Botelho</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A fluência representacional num contexto de uso de tecnologia em Matemática e Física e Química</style></title><secondary-title><style face="normal" font="default" size="100%">INCTE</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Fluência representacional: a Matemática na resolução de problemas de Física</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do EIEM 2023 – Encontro em Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Aveiro</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Martins, R.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Functional Thinking: A Study with 10th-Grade Students</style></title><secondary-title><style face="normal" font="default" size="100%">Education Sciences</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.3390/educsci13040335</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">13</style></volume><pages><style face="normal" font="default" size="100%">1-22</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study aims to understand the functional thinking of 10th-grade students while studying functions. Specifically, we intend to answer the following research questions: what are the functional thinking processes used by 10th-grade students when studying functions? What difficulties do students present while learning functions? In view of the nature of this research objective, we adopted a qualitative and interpretative approach. In order to answer these questions, data were collected from the written records produced by the students while solving the proposed tasks, from records of the oral interactions during discussions and from a questionnaire. The results show that functional thinking processes were implicit in the resolution of the tasks proposed to the students. The students expressed an understanding of how the variables were related, presenting evidence of their functional thinking while working on the new concepts represented by the functions addressed in the proposed tasks. Some students expressed difficulties in interpreting the different types of representations associated with the functions, in retaining the necessary information from a graphical representation that would help them to draw conclusions and establish correspondences, in explaining functional relationships, and in interpreting the information provided by algebraic expressions. These difficulties can reduce the recognition of the relationships between variables and their behavior in the different representations, becoming an obstacle to learning for some students.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">How the use of different technologies mobilises different domains of professional knowledge</style></title><secondary-title><style face="normal" font="default" size="100%">Cerme 13</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><pub-location><style face="normal" font="default" size="100%">Budapest, Hungary</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The impact of teachers' knowledge on the connection between technology supported exploration and mathematical proof</style></title><secondary-title><style face="normal" font="default" size="100%">European Journal of Science and Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.30935/scimath/13285</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">635-649</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Technology is recognized for its potential to implement exploration tasks. The ease and speed with which it becomes possible to observe many cases of a situation, allows the development of conjectures and brings conviction about their veracity. Mathematical proof, assumed as the essence of Mathematics, tends to appear to the students as something dispensable. Based on KTMT – Knowledge for Teaching Mathematics with Technology model, this study intends to understand the impact of the teachers’ knowledge on mathematical proof in a context of technology integration. The study adopts a qualitative and interpretative methodology, based on case study, analyzing the practice of one teacher. The conclusions emphasize the relevance of the teacher’s MTK – Mathematics and Technology Knowledge, and TLTK – Teaching and Learning and Technology Knowledge. The teacher's MTK guides her decisions, leading her to focus on helping students understand the meaning of conjecture and proof, valuing, at the same time, the relevance of algebraic manipulations. However, the teacher’s TLTK guides her practice, where the knowledge about the students is determinant. The study provides evidence about the difficulty of articulating proof and technology, but it also clarifies the relevance of this articulation and of how the teacher’s KTMT can impact the teacher’s decisions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Impacto do uso de diferentes representações sobre a aprendizagem de funções</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2023_em170.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">170</style></volume><pages><style face="normal" font="default" size="100%">43-46</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Models on teachers’ knowledge to teach with digital technology: a systematic review</style></title><secondary-title><style face="normal" font="default" size="100%">Cerme 13</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><pub-location><style face="normal" font="default" size="100%">Budapest, Hungary</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Teixeira</style></author><author><style face="normal" font="default" size="100%">C. Martins</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Abordagem STEAM: articulação disciplinar e práticas letivas de professores</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Contribution of the analysis of the mathematical concordance to understand the teachers’ KTMT</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Curriculum and Teaching</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.sciedupress.com/journal/index.php/jct/article/view/22486</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">412-422</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Technology is recognized by its potential to promote mathematical learning. However, achieving this potential&lt;br /&gt;
requires the teachers to have the knowledge to integrate it properly into their practices. Several authors have intended to characterize the teachers’ knowledge and developed several models, but this approach has often been criticized by its static approach, not attending neither valuing the teachers’ practice. In this study we adopt the KTMT – Knowledge for Teaching Mathematics with Technology model, assuming the teachers’ practice as the main scenario of analysis. We focus on the options guiding the teachers’ decisions when confronted with a situation of lack of mathematical concordance while teaching functions. The situations of lack of mathematical concordance (i.e., situations where the mathematics addressed by the students is different from the one intended by the teacher) are assumed as rich and encapsulating the potential to reveal significant aspects of the teachers’ KTMT. The main goal of the study is to understand what domains of the teachers’ KTMT are highlighted in these circumstances. A qualitative methodology is adopted and one episode of one 10th grade teacher’s practice is analyzed, based on the KTMT model. The conclusions reached show the relevance of different knowledge domains, but emphasize the Mathematics and Technology Knowledge (MTK). They also raise questions about the impact of the specific technology being used on the teachers’ KTMT.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">8</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Silva, A.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Martins, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The graphical representation in the learning of functions by 10th grade students</style></title><secondary-title><style face="normal" font="default" size="100%">Educación Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.revista-educacion-matematica.org.mx/descargas/vol34/1/07_REM_34-1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">34</style></volume><pages><style face="normal" font="default" size="100%">186-213</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A exploração de diferentes representações promove a compreensão dos tópicos de funções. Partindo deste pressuposto, com este estudo pretende-se analisar o contributo da representação gráfica na aprendizagem da noção de função inversa e da paridade de uma função por alunos do 10.º ano de escolaridade e identificar dificuldades na exploração dessa representação. Na procura de responder a este objetivo, adotou-se uma abordagem qualitativa e interpretativa para compreender as ações dos alunos na resolução das tarefas&lt;br /&gt;
propostas. A análise das resoluções mostra que a representação gráfica serviu de suporte para a instituição das definições dos tópicos em estudo. E isto apesar de alguns alunos revelarem dificuldades ao interpretar e ao construir gráficos; ao identificar imagens e imagens inversas em gráficos de funções; ao representar determinadas características gráficas associadas a alguns conceitos, como é o caso da relação entre a paridade de uma função e a simetria na sua representação gráfica (confundindo eixo de simetria e de reflexão). Globalmente, este estudo mostra como a abordagem de conceitos a partir da representação gráfica pode contribuir para a sua compreensão.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A interdisciplinaridade em contexto de integração da tecnologia: o conhecimento profissional de professores de Matemática e de Físico-Química</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Moving from one representation to another: different ways of doing it, different mathematical learning</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics in School</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><volume><style face="normal" font="default" size="100%">51</style></volume><issue><style face="normal" font="default" size="100%">4</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O conhecimento do professor de matemática e a integração das tecnologias na sua prática</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O conhecimento profissional do professor de matemática na integração de diferentes tecnologias</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XXXII Seminário de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Setúbal</style></pub-location><pages><style face="normal" font="default" size="100%">158-161</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O conhecimento profissional do professor e a interdisciplinaridade em contexto de integração com a tecnologia</style></title><secondary-title><style face="normal" font="default" size="100%">XXXII Seminário de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Setúbal</style></pub-location><pages><style face="normal" font="default" size="100%">162-165</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Costa, M.C.</style></author><author><style face="normal" font="default" size="100%">Jacinto, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O desenvolvimento curricular e a formação de professores</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pages><style face="normal" font="default" size="100%">267-276</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Pre-service teachers’ knowledge and the use of different technologies to teach Mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">Perspectives and Trends in Education and Technology</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">505-515</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Teachers are central to the choice of tasks proposed to the students. And the teachers’ knowledge is one of the important elements guiding these choices. Despite the different models that conceptualize the teachers’ knowledge to integrate technology in their practices, research has focused essentially on the integration of a single technology. Little is known about how the work with different technologies can contribute to promote the development of the professional knowledge of pre-service teachers (PTs) or how the use of different technologies mobilizes different domains of the PTs’ knowledge. The main goal of this study is to deepen the understanding about the relation between the PTs’ Knowledge for Teaching Mathematics with Technology (KTMT) and their choice of tasks. The study adopts a qualitative and in-terpretative methodology based on one case study. The main conclusions suggest a strong impact of the PTs’ Learning and Teaching Technology Knowledge (a knowledge related to the impact of technology on the teaching and learning process) and a not so strong impact of their Mathematical and Technological Knowledge (a knowledge related to the impact of technology on the mathematical knowledge). The conclusions also point to the potential of the work with different technologies to deepen the PTs reflections and analysis of tasks.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Monteiro, J.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Rethinking digital technology versus paper and pencil in 3D Geometry</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Learning for Development</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://jl4d.org/index.php/ejl4d/article/view/645/798</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">267-278</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Recognising the relevance of learning Geometry, and in particular 3D Geometry, this study aims to discuss the contributions that digital technology and paper and pencil approaches can bring to students’ learning. We seek, therefore, to identify the differences between the two approaches, and specifically: What factors are relevant in one and the other approach? What does one approach facilitate over the other? A quantitative and a qualitative and interpretive methodology was adopted, and based on a didactic intervention, the students' resolutions of the proposed tasks were analysed. The results obtained show that the experience and prior knowledge of the students with each of the solids involved seems to be decisive in the approach with paper and pencil. However, technology emerges as an enhancing resource when prior knowledge is more fragile. The study also shows differences between the representations supported by the two resources, suggesting the mobilisation of different knowledge by the students in relation to each of the resources.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Teixeira</style></author><author><style face="normal" font="default" size="100%">C. Martins</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STE(A)M approach: Distinguishing and discussing meanings</style></title><secondary-title><style face="normal" font="default" size="100%">EduLearn</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://library.iated.org/view/TEIXEIRA2022STE</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">IATED</style></publisher><pub-location><style face="normal" font="default" size="100%">Spain</style></pub-location><pages><style face="normal" font="default" size="100%">9842-9847</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The STE(A)M approach has been recognized by several authors for its potential in assisting teaching and learning, and several curriculum standards already value its application in the classroom. This approach is based on the articulation between different areas, the clarification, and the deepening of the concepts being studied. Although there are different approaches, according to the fields involved, STEM and STEAM are two among the most often mentioned in the literature. STEM is based on learning that integrates the following areas of knowledge: Science, Technology, Engineering, and Mathematics. The conceptualization of the STE(A)M approach is not consensual and uniform. There are different models focusing on problem-solving based learning, project-based-learning, design-based learning, and engineering models. Still, different authors present different conceptualizations of this approach. In this paper, we relied on the existing literature to discuss the different understandings of the STE(A)M approach. We will also pay attention to mathematics and how different authors see the disciplines’ role within a STE(A)M approach and discuss the evolution of the mentioned authors’ positions throughout time. Thus, methodologically, we undertook the following steps: (i) literature search based on the selected keywords; (ii) selection of the texts, considering the authors and time gap, in order to analyze the evolution of the research and (iii) collection and organization of the relevant topics for the study. This study aims to present the meanings, conceptualizations, and possible influences present in different models and for understand the evolution of the STEM and STEAM approaches over time. The main findings suggest a focus on the interdisciplinary or transdisciplinary approach as opposed to the primeval years of investigations in STEM and STEAM when many authors advocated a multidisciplinary approach. This change in thinking is due to the need to train students in an integral and holistic manner, developing citizens with transversal knowledge and skills prepared for the current societal challenges.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, T</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">As características do jogo e o conhecimento profissional do professor: que pontos de contacto?</style></title><secondary-title><style face="normal" font="default" size="100%">XVI Congresso Internacional Galego-Portugués de Psicopedagogia</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://congreso-xvigp.asocip.com/images/PDF/ATAS_XVI_CIGPP-2021.pdf</style></url></web-urls></urls><pub-location><style face="normal" font="default" size="100%">Braga, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">1117-1129</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For most teachers, the use of games is not a common practice. This limited professional experience forces the teacher to reflect on the use of games, on how to integrate them into class work, and on how to enhance the development of learning based on them. Our objective is to analyse a set of game scenarios and study aspects that characterise each of them, relating these characteristics to aspects of the professional knowledge to teach with technology. The study adopts an interpretative and qualitative methodology that seeks to understand the relationship between teachers' choices and their professional knowledge. The main findings suggest that the different characteristics of the game scenarios imply the creation of different working environments in the classroom; enhance the emergence of different student difficulties, requiring different ways to support their work; allowing/promoting different conceptual approaches; and the work with different representations. These differences between the game scenarios point to different emphases on the teaching and learning knowledge and the chemistry knowledge, suggesting different mobilizations of the teacher's professional knowledge.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Botelho, M. C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Conceptualizações do conhecimento do professor para a integração da tecnologia no ensino da matemática</style></title><secondary-title><style face="normal" font="default" size="100%">XVI Congresso Internacional Galego-Portugués de Psicopedagogia</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://congreso-xvigp.asocip.com/images/PDF/ATAS_XVI_CIGPP-2021.pdf</style></url></web-urls></urls><pub-location><style face="normal" font="default" size="100%">Braga, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">1413-1425</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The potential of technology for teaching and learning mathematics has been widely recognized. However, research has shown that the integration of technology into teaching practice has proved to be difficult, with teachers' knowledge and professional development being identified as a determinant factor.  Although there tends to be a focus on the teacher's knowledge of technology, the literature suggests that attention needs to be given to how to integrate technology into teaching practice, thereby involving other types of knowledge. This awareness has led several authors, inspired by Shulman's work, to develop models or conceptualizations of the knowledge required for effective integration of technology.&lt;br /&gt;
This study is based on a literature review of the research conducted on the models TPACK - Technological Pedagogical and Content Knowledge, KTMT - Knowledge for Teaching Mathematics with Technology, and PTK/MPTK - Mathematical Pedagogical Technology Knowledge and aims to carry out an analysis of the similarities and differences between the models considered. The main conclusions reached suggest the existence of a common basis for the models considered, but also point to several differences between them, with some highlighting the role of technology and its impact on the teaching and learning process, while others aim to integrate into the model elements based on research on technology or theories related to technology integration, such as instrumental genesis.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Palhares, P.</style></author><author><style face="normal" font="default" size="100%">M. Botelho</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">From classroom teaching to distance learning: the experience of Portuguese mathematics teachers</style></title><secondary-title><style face="normal" font="default" size="100%">INTED - 15th annual International Technology, Education and Development Conference</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://library.iated.org/view/ROCHA2021FRO</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">IATED</style></publisher><pages><style face="normal" font="default" size="100%">8961-8968</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Mathematical knowledge for teaching with technology: episodes of one teacher’s practice - Conhecimento matemático para ensinar com tecnologia: episódios da prática de uma professora</style></title><secondary-title><style face="normal" font="default" size="100%">Educação Matemática Debate</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.periodicos.unimontes.br/index.php/emd/article/view/4434/4779</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">5</style></volume><pages><style face="normal" font="default" size="100%">1-22</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Research has highlighted the potential of technology to transform the teaching of Mathematics, but also the relevance of teachers and their professional knowledge. In this article, a qualitative methodology is adopted and two episodes of the practice of one teacher are analyzed in the scope of the study of functions in the 10th grade, based on the model of Knowledge for Teaching Mathematics with Technology (KTMT). The goal is to characterize the teacher's knowledge from her practice, simultaneously understanding how this contributes to promoting the development of the teacher's knowledge. The conclusions reached show the importance of including in the KTMT conception aspects highlighted by the research on technology integration. These aspects are determinant to characterize the teacher's knowledge. They also show the relevance of the practice for the development of the teacher's knowledge and the dynamic character of the vision of knowledge offered by KTMT.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">11</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Sacristan, A.</style></author><author><style face="normal" font="default" size="100%">Santacruz-Rodríguez, M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Professional development for the integration of technology in the teaching of Mathematics: in search of pragmatic theories - Desenvolvimento profissional para a integração da tecnologia no ensino da Matemática: em busca de teorias pragmáticas</style></title><secondary-title><style face="normal" font="default" size="100%">XXXI Seminário de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/siem_2021.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Santarém</style></pub-location><pages><style face="normal" font="default" size="100%">1-10</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper presents part of a study that aimed to make more explicit the pragmatic theories that inform the design of professional development programs with an emphasis on the integration of digital technologies in the practices of mathematics teachers. The analysis carried out was based on a set of projects considered representative and implemented in four countries – Colombia, Italy, Mexico and Portugal. Based on this analysis, we identify relevant elements (e.g., similarities and differences, barriers and opportunities) and develop recommendations to be taken into account in the design of future professional development programs. In this process, we identified a set of aspects and sub-aspects, as well as several interconnections between them, which emerged in relation to five main themes and allowed us to reveal our pragmatic theories. Thus, this work provides a framework to support the design of future projects for the professional development of mathematics teachers regarding the use of digital technology.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">M. Botelho</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ knowledge for teaching Mathematics with technology: an analysis of different frameworks</style></title><secondary-title><style face="normal" font="default" size="100%">INTED - 15th annual International Technology, Education and Development Conference</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://library.iated.org/view/ROCHA2021TEA</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">IATED</style></publisher><pages><style face="normal" font="default" size="100%">8954-8960</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Teacher education is central to promote the development of the professional knowledge of teachers, and&lt;br /&gt;
to help them achieve an appropriate integration of digital technologies, an issue that has proved to be a&lt;br /&gt;
difficult one. Several authors refer difficulties in the integration of the technology, emphasizing the central&lt;br /&gt;
role played by the teachers’ knowledge in classroom use. In this paper we discuss three models (TPACK&lt;br /&gt;
– Technological Pedagogical and Content Knowledge, KTMT – Knowledge for Teaching Mathematics with&lt;br /&gt;
Technology, PTK / MPTK - Mathematical Pedagogical Technology Knowledge), intending to identify the&lt;br /&gt;
main contributions of each model to a deeper understanding of how to promote the teachers’ integration&lt;br /&gt;
of technology in the teaching of Mathematics. The study is based on a literature review and on an analysis&lt;br /&gt;
of the similarities and differences among the models and its use. On this analysis we identify common&lt;br /&gt;
influences among the models as well as influences from other research areas. The main conclusions&lt;br /&gt;
achieved point to a common base to all the models considered, but also to several differences among&lt;br /&gt;
them, being that some of the models emphasize the role of technology and its impact on Mathematics&lt;br /&gt;
learning, but others go further, intending to integrate in the model elements based on the research on&lt;br /&gt;
technology or even other theories such as the one on instrumental genesis.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Palha, S.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">A. Richit</style></author><author><style face="normal" font="default" size="100%">Oliveira, H</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">A tecnologia na formação inicial de professores de Matemática – um olhar sobre duas realidades</style></title><secondary-title><style face="normal" font="default" size="100%">Formação de professores e tecnologias digitais</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><publisher><style face="normal" font="default" size="100%">LF Editorial</style></publisher><pub-location><style face="normal" font="default" size="100%">São Paulo, Brasil</style></pub-location><pages><style face="normal" font="default" size="100%">1-34</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Perante as conhecidas dificuldades em alcançar uma adequada integração da tecnologia no processo de ensino e aprendizagem da Matemática, este estudo pretende, apoiando-se na formação ao nível da tecnologia ministrada em duas instituições europeias, identificar aspetos com potencial para promover a formação inicial, no âmbito da tecnologia, de professores de Matemática. Adota-se uma metodologia de índole qualitativa e interpretativa, sendo os dados recolhidos de natureza documental ou relativos a trabalhos de análise e reflexão crítica realizados por dois futuros professores (um de cada instituição). As principais conclusões alcançadas apontam para grandes diferenças entre os contextos de formação, com uma das instituições a valorizar de forma mais significativa a formação na área. Ainda assim, os futuros professores de ambas as instituições mostram alguma tendência para escolher tarefas onde a exploração que é feita da tecnologia fica aquém do seu potencial, onde o recurso ao papel e lápis está sempre presente, e onde a reflexão em torno das características das tarefas e da sua implementação parece ser algo superficial. Apesar da complexidade do processo de integração da tecnologia nas práticas, os aspetos referidos parecem-nos ser dignos de atenção em qualquer programa de formação inicial de professores de Matemática.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Sacristan, A.</style></author><author><style face="normal" font="default" size="100%">Santacruz-Rodríguez, M.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">A. Donevska-Todorova</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">J. Trgalova</style></author><author><style face="normal" font="default" size="100%">H-G. Weigand</style></author><author><style face="normal" font="default" size="100%">A. Clark-Wilson</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Towards pragmatic theories to underpin the design of teacher professional development concerning technology use in school mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics Education in the Digital Age: Learning, Practice and Theory </style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.routledge.com/Mathematics-Education-in-the-Digital-Age-Learning-Practice-and-Theory/Clark-Wilson-Donevska-Todorova-Faggiano-Trgalova-Weigand/p/book/9780367684525</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Routledge</style></publisher><pages><style face="normal" font="default" size="100%">42-68</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This chapter aims to make more explicit the grounded or ‘pragmatic theories’ that inform the design of mathematics teachers’ professional development (PD) to exploit technological affordances. It uses aspects of some representative projects that took place in four countries (Colombia, Italy, Mexico, and Portugal) to illustrate lessons learned (e.g., similarities and differences, barriers and opportunities) and provide important insights to inform future PD implementations. To do this, we have identified a set of aspects (and sub-aspects) that emerged in relation to five major themes and reveal our ‘pragmatic theories’ alongside a consideration of the interconnections between these aspects. Our contribution offers a methodological frame to support future PD designs for teachers of mathematics concerning digital technology uses.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Morais, C.</style></author><author><style face="normal" font="default" size="100%">Terroso, J.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">E de repente tudo mudou… - Editorial</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.apm.pt/portal/em.php?id=233955&amp;rid=233953</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">155</style></volume><pages><style face="normal" font="default" size="100%">1</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Graphical representation of functions using technology: a window to teacher knowledge</style></title><secondary-title><style face="normal" font="default" size="100%">Teaching Mathematics and its Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://academic.oup.com/teamat/article-abstract/39/2/105/5618956?redirectedFrom=fulltext</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">39</style></volume><pages><style face="normal" font="default" size="100%">105-126</style></pages><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">L. Leite</style></author><author><style face="normal" font="default" size="100%">E. Oldham</style></author><author><style face="normal" font="default" size="100%">A. Afonso</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">L. Dourado</style></author><author><style face="normal" font="default" size="100%">Martinho, H.</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Interdisciplinary technological approaches from a mathematics education point of view</style></title><secondary-title><style face="normal" font="default" size="100%">Science and mathematics education for 21st century citizens: challenges and ways forward</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://novapublishers.com/shop/science-and-mathematics-education-for-21st-century-citizens-challenges-and-ways-forwards/</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Nova Science Publishers</style></publisher><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Mathematics has a strong presence in the school curriculum, often justified by its usefulness in social life, in the world of work and by its connections with other sciences. This interdisciplinary connection, in particular when it requires constructing and refining mathematical models and discussing their applications to solve problems of other sciences, can assist students to understand why mathematics is so important in school. In the development of interdisciplinary activities, the characteristics of the tasks emerge as an important aspect. The emphasis is on the use of technological materials and the way they can support the development of concepts, provide different representations and support deeper understandings, and offer a multifaceted support to collect data and simulate experiences. Based on these assumptions, the aim of this chapter is to present, analyse and discuss tasks that promote interdisciplinary technological approaches from a mathematical point of view. In this chapter we assume interdisciplinarity as a complex construct, and in order to clarify its meaning we will discuss several types of conceptions, from multidisciplinary, to interdisciplinary, and to transdisciplinary. We will then address related concepts, such as modelling and STEM, highlighting similarities and differences between them, to reach an understanding of interdisciplinarity. In the process of the interdiciplinary approach, digital technologies arise as a central element. Based on a set of tasks on mathematics and on different sciences, we discuss what can change on an interdisciplinary approach to the teaching and learning of mathematical content and on the articulation between subjects.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Oitavem, I.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Palha, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Reinvenção do ensino a distância: a inovação ao ritmo de cada professor</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.apm.pt/portal/em.php?rid=233953&amp;id=19480</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">155</style></volume><pages><style face="normal" font="default" size="100%">16-20</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A suspensão das aulas presenciais na sequência da pandemia que estamos a atravessar trouxe para primeiro plano o ensino a distância. Neste artigo partilhamos algumas ideias e conceptualizações relativas a este tipo de ensino, abordamos aquilo que alguns autores que se têm dedicado à temática apontam como importantes desafios e oportunidades que se lhe encontram associados e, por fim, partilhamos algumas possíveis opções e recursos que pensamos poderem ser úteis para todos os professores que estão a viver a sua primeira experiência de ensino a distância.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Faggiano, E.</style></author><author><style face="normal" font="default" size="100%">Mennuni, F.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers as task designers in the digital age: Teaching using technology</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 10th ERME Topic Conference - MEDA 2020</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://drive.google.com/file/d/1onuTtshYC9SzkaswGT4twtM2QE0yWpsX/view</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2020_meda_rocha_faggiano_mennuni.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Linz (Austria)</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The aim of the paper is to present and analyse the case of one teacher attempting to introduce his students to fractals using digital technology. His task design process has been made explicit through the writing of a storyboard. It has been analysed in order to focus on the stages of the process, identifying prominent elements in it by using the knowledge quartet framework. Results can be useful to inform teacher educators about his needs with respect to the development of his ability in task design. The importance of this aspect, particularly worth of note in the digital age in which teachers have many opportunities to access teaching resources online, has been amplified by the constraints to which educational systems have been subjected during the Covid-19 pandemic emergency.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s11858-020-01195-1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">52</style></volume><pages><style face="normal" font="default" size="100%">1381-1396</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Teacher education is central to the development of the professional knowledge of pre-service teachers. The main goal of this paper is to refect on the development that the analysis (done by a group of pre-service secondary teachers) of a set of tasks, based on elements related to domains of KTMT—Knowledge for Teaching Mathematics with Technology—can bring to the knowledge of pre-service teachers of mathematics. Specifcally, the goal was to investigate the following questions: (1) What are the factors that guide the pre-service teachers’ task discussion? (2) Which KTMT domains are emphasized by pre-service teachers during task discussion? The elements taken into account are the characteristics of the tasks (focus on cognitive level, structuring level and technology role), the use of representations (focus on balance and articulation of representations), and the equilibrium between experimentation (focus on digital technology afordances) and justifcation (focus on argumentation and proof). The methodology of this case study involves a qualitative approach. The main conclusions suggest that infuences in the pre-service teachers’ discussion of tasks fell into the following categories: the potentialities of technology, the type of tasks, and the prospective teachers’ experience with a set of tasks, and analysis of some real students’ reports. With regard to KTMT, although it was possible to identify some global development, Teaching and Learning and Technology Knowledge was the domain in which stronger development took place.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">7</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">As diferentes representações de funções e a compreensão de alunos do ensino secundário num contexto de integração da tecnologia</style></title><secondary-title><style face="normal" font="default" size="100%">XV Congresso Internacional Galego-Portugués de Psicopedagogia</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://hdl.handle.net/2183/23486</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Asociación Científica Internacional de Psicopedagogía</style></publisher><pub-location><style face="normal" font="default" size="100%">Corunha, Espanha</style></pub-location><pages><style face="normal" font="default" size="100%">4148-4158</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The different representations of functions are assumed as central on the development of the concept of function. Being widely recognized the complexity of this concept, the different representations allow the student to understand in a representation what could not be understood in another representation. And the integration of technology into the teaching and learning process provides an easy and quick way to access different representations. This study intends to analyse the understanding of upper secondary students about the information transmitted by each of the representations of functions usually available on technology. Specifically, it intends to understand which transitions between representations are more easily understood by the students and which ones are more difficult to perform. It also intended to identify some aspects that may contribute to this. This study adopts a quantitative methodology in which the answers given by a class to a test focused on the transition from one representation to another are analysed; and a qualitative methodology based on interviews to three of the students in the class, as a way of seeking comprehension about their answers. The results achieved suggest a greater ease of understanding associated to the graphical representation and a greater difficulty associated to the tabular representation. The reasons for this seem to be related to the specific characteristics of each representation, but fundamentally with aspects related to the experiences lived by the students on the mathematics classes, being the integration of technology an influence not to neglect.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Oitavem, I.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Barcodes: The Mathematics of everyday life</style></title><secondary-title><style face="normal" font="default" size="100%">The Scottish Mathematical Council Journal</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://drive.google.com/file/d/1IdP9ZS431llwA6efOBQfcgPyTv8v68zv/view</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">49</style></volume></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Desenvolver o conhecimento de futuros professores sobre as características das tarefas e o papel que a tecnologia pode assumir nestas</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Castelo Branco, Portugal</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The main goal of this work is to characterize how the knowledge of pre-service teachers about the characteristics of the tasks and the role of technology evolves. Based on a case study carried out around a pair of pre-service teachers, the main conclusions point to the contribution of the reflection around a set of six tasks on Functions selected by the pre-service teachers. Central to this reflection was an analyze of the role technology can play in tasks, the comments made by the colleagues to their tasks and some experiences on modeling and open-ended tasks. These elements provided the development of a greater awareness regarding aspects such as the level of structuring of the task and its degree of challenge. And this was determinant for an appropriation of the different characteristics of the tasks and to the development of the pre-service teachers’ knowledge.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The impact of technology on the teachers’ use of different representations</style></title><secondary-title><style face="normal" font="default" size="100%">CERME</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://hal.archives-ouvertes.fr/hal-02417077/document</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Utrecht, Holanda</style></pub-location><pages><style face="normal" font="default" size="100%">2731-2738</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The potential of using different representations is widely recognized, but not much is known about how teachers use them nor about the impact of the technology on such use. The goal of this study is to characterize the teachers’ representational fluency when teaching functions at high school level, discussing, at the same time, the impact in the use of representations resulting from the use of technology. Adopting a qualitative approach, I analyze one teacher’s practice. The results suggest that algebraic and graphical representations are seen as more important, that tabular representation is assumed as irrelevant and that the access to technology impacts the learning, the representations used and how they are used.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">L. Leite</style></author><author><style face="normal" font="default" size="100%">et al</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Interdisciplinary tasks: pre-service teachers’ choice and approach</style></title><secondary-title><style face="normal" font="default" size="100%">Science and mathematics education in the 21st century</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/rocha_2019_sciencematheduc.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ATEE and CIEd</style></publisher><pub-location><style face="normal" font="default" size="100%">Brussels</style></pub-location><pages><style face="normal" font="default" size="100%">82-93</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study focusses on the criteria used by pre-service teachers of Mathematics to choose interdisciplinary tasks. The pre-service teachers’ knowledge is assumed as the basis of the actions taken and used as the origin of the choices and approaches observed. The study adopts a qualitative and interpretative methodology and the data were collected using class observation and interviews. The analysis is guided by the Application and Pedagogical Content Knowledge, a model inspired on TPACK (from Mishra and Koehler) and MKT (from Ball and colleagues). The conclusions point to an appreciation of the mathematical part of the tasks and to a devaluation of the remaining components. This suggests difficulty in articulating and integrating different domains of knowledge and points to a fragmented view of the potential of using mathematical applications.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Mathematical proof: from mathematics to school mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">Philosophical Transactions of the Royal Society A</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://royalsocietypublishing.org/doi/10.1098/rsta.2018.0045</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">377</style></volume><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Proof plays a central role in developing, establishing, and communicating mathematical knowledge. Nevertheless it is not such a central element in school mathematics. This article discusses some issues involving mathematical proof in school, intending to characterize the understanding of mathematical proof in school, its function and the meaning and relevance attributed to the notion of simple proof. The main conclusions suggest that the idea of addressing mathematical proof at all levels of school is a recent idea that is not yet fully implemented in schools. It requires an adaptation of the understanding of proof to the age of the students, reducing the level of formality, and allowing the students to experience the different functions of proof and not only the function of verification. Among the different functions of proof, the function of explanation deserves special attention due to the illumination and empowerment that it can bring to the students and their learning. The way this function of proof relates to the notion of simple proof (and the related aesthetic issues) seems relevant enough to make it, in the future, a focus of attention for the teachers who address mathematical proof in the classroom.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2140</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">P. Mendes</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The notion of function by basic education preservice teachers</style></title><secondary-title><style face="normal" font="default" size="100%">ATEE Winter Conference ‘Science and mathematics education in the 21st century</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><publisher><style face="normal" font="default" size="100%">ATEE and CIEd</style></publisher><pub-location><style face="normal" font="default" size="100%">Brussels</style></pub-location><pages><style face="normal" font="default" size="100%">120-130</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The current curricular guidelines for mathematics education in Portugal emphasize the relevance of working with different representations of functions to promote understanding. Given this relevance, we seek understanding about the notion of function held by 37 basic education pre-service teachers in their first year of a master’s course. Data were collected through a task focusing on identifying functions in situations based on different representations. The content analysis technique was then adopted in the search for an understanding of the justifications given by the participants. The results achieved suggest it is easier for the pre-service teachers to identify examples that are not functions than examples that are functions. There is also a tendency for greater accuracy in the identification of examples expressed by tables than by algebraic expressions. The justifications presented show a notion of function as a relation between values of two non-empty sets, but without guaranteeing that this relation is single-valued.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Caneco, R.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O uso de exemplos na demonstração: um estudo com alunos do 11.º ano</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Castelo Branco, Portugal</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article focuses the choice and use of examples by two students of the 11th grade to prove or refute a set of statements. The use of representations of sequences and functions is also considered. The study adopts a qualitative approach and data were collected by interviews and documental gathering. The conclusions suggest most of the examples used were well-known sequences or functions. However, the students sought different purposes for the use of examples, such as understanding the conjecture, demonstrate the falsity or truthfulness of the statement and conveying a general argument. The students made a satisfactory articulation between the various types of representations but relied mostly in the cartesian graph.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A perspectiva de futuros professores sobre a demonstração matemática</style></title><secondary-title><style face="normal" font="default" size="100%">XV Congresso Internacional Galego-Portugués de Psicopedagogia</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://congreso-xvgp.asocip.com/index.php/es/programacion/actas-del-congreso</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Asociación Científica Internacional de Psicopedagogía</style></publisher><pub-location><style face="normal" font="default" size="100%">Corunha, Espanha</style></pub-location><pages><style face="normal" font="default" size="100%">2203-2214</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The mathematical proof is assumed as a central element in the development of Mathematics. However, proof is conceived in different ways and assumed as having different functions in Mathematics. And when we move from mathematics to its teaching, the multiplicity of perspectives becomes even more significant. This diversity can have an impact on the students and on the relationship they establish with Mathematics. In these circumstances, this study seeks knowledge over the perspectives of future teachers regarding the mathematical demonstration. Specifically, it intends to achieve a deeper knowledge over the future teachers’ perspectives about what is a mathematical proof and about its functions. The study adopts a qualitative approach and uses interviews to collect data. The conclusions reached point to a traditional perspective of mathematical proof, closely tied to mathematical formalism and the validation function, where the teaching context introduces some changes, adjusting the formalism to the level of the students and highlighting the understanding function of proof, but maintaining the dominant character of the algebraic language.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">L. Leite</style></author><author><style face="normal" font="default" size="100%">et al</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Pre-service teachers’ knowledge: impact on the integration of mathematical applications on the teaching of mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">Science and mathematics education in the 21st century</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://hdl.handle.net/2183/23486</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ATEE and CIEd</style></publisher><pub-location><style face="normal" font="default" size="100%">Brussels</style></pub-location><pages><style face="normal" font="default" size="100%">26-37</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Mathematics is present everywhere. However, uncovering the relevance of Mathematics requires, from the teachers, a special kind of knowledge. This study tries to characterize the knowledge used by pre-service teachers when developing a mathematical task intending to promote the students’ exploration of barcodes. The study adopts a qualitative and interpretative methodology and the data were collected using class observation and interviews. The analysis is guided by the Application and Pedagogical Content Knowledge, a model inspired on TPACK (from Mishra and Koehler) and MKT (from Ball and colleagues). The conclusions point to some difficulties to see the potential of the situation to promote mathematical learning. The knowledge on the mathematical content seems to be dominant on the options assumed and operated in a rigid way that prevent the pre-service teachers from exploring the richness of the situation on the tasks they developed.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Roque, C.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Avaliação formativa com recurso à tecnologia [Formative assessment using technology]</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://domitila.edu.pt/ProfMat2018/docs/Atas%20SIEM2018.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Almada, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">53-69</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The present study aims to understand the potentialities and implications,&lt;br /&gt;
to the teacher and her practice, of the use of formative assessment with the support&lt;br /&gt;
of educational technology.&lt;br /&gt;
Regarding the research methodology, this study is part of the research on own&lt;br /&gt;
practice. The participants were the teacher, who was simultaneously a researcher,&lt;br /&gt;
and the students of a 9th grade class.&lt;br /&gt;
In the course of this experience it was found that the use of formative assessment&lt;br /&gt;
allows, on the one hand, the student to realize what he manages to understand, and&lt;br /&gt;
what he has to do to overcome what are less consolidated parts of the content in&lt;br /&gt;
study; and, on the other, the teacher to detect in a timely manner the difficulties of&lt;br /&gt;
the student and to change strategies to allow the student to overcome his difficulties.&lt;br /&gt;
The lack of time, the difficulties in managing the curriculum and the existence of&lt;br /&gt;
national exams are three of the main obstacles mentioned by the teachers for the&lt;br /&gt;
non-realization of formative assessment. In this experience it was found that the use&lt;br /&gt;
of new technologies turns possible to overcome these limitations.&lt;br /&gt;
This type of assessment had a very positive impact on teacher’s practice and in the&lt;br /&gt;
learning of the students.&lt;br /&gt;
Keywords: assessment; formative assessment; new technologies.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Demonstração matemática versus demonstração no ensino da Matemática – a perspetiva de professores [Mathematical proof versus proof on mathematics teaching – the teachers’ point of view]</style></title><secondary-title><style face="normal" font="default" size="100%">SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://domitila.edu.pt/ProfMat2018/docs/Atas%20SIEM2018.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Almada, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">70-82</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study intends to analyze the perspectives of teachers of different levels regarding proof and its functions in Mathematics and Mathematics teaching. Adopting a methodology of a qualitative nature, and based on interviews, the perspectives of teachers of upper secondary, higher education and training teachers of Mathematics were collected. The conclusions reached suggest that teachers seem to share a formal conception of mathematical proof, recognizing the need to introduce some simplification when considering proof in Mathematics teaching as well as the importance of their functions of validation, contribution to learning and even a cultural function.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Martinho, H.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A escrita matemática e a intuição em Geometria [Mathematical writting and intuition in geometry]</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.apm.pt/portal/em.php</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">149-150</style></volume><pages><style face="normal" font="default" size="100%">34-38</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O ensino de Funções no 3.º ciclo e no ensino secundário: que diferenças? [Teaching Functions at lower and upper secondary: what is different?]</style></title><secondary-title><style face="normal" font="default" size="100%">EIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://drive.google.com/open?id=1bXIGZHoCA8jw1khZlXhRfbbo_mxHRO3t</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Coimbra</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Neste estudo analisamos as perceções que professores do 3.º ciclo e do ensino secundário têm da sua prática no âmbito do ensino de Funções, com o objetivo de as caracterizar e de identificar as diferenças existentes entre estes dois grupos de professores. Um aspeto particularmente relevante se tivermos em conta que se tratam de dois grupos de professores com formações iniciais idênticas. Adotamos uma metodologia mista, com uma vertente quantitativa apoiada na aplicação de questionários e uma vertente qualitativa baseada na realização de entrevistas. As principais conclusões alcançadas apontam para semelhanças nas perceções dos professores, mas também para algumas diferenças em função do ciclo de ensino. Na planificação das aulas os manuais são amplamente utilizados, mas de forma diferente consoante o ciclo de ensino do professor. Os professores de ambos os ciclos de ensino estabelecem conexões entre diferentes representações, mas valorizam de diferentes formas as representações disponíveis. O envolvimento dos alunos nas atividades da aula é outro aspeto destacado pelos professores, mas uma vez mais existem diferenças. Na avaliação o recurso ao teste é enfatizado pelos dois grupos de professores, mas já existem diferenças quanto à importância atribuída ao trabalho de grupo.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">P. Teixeira</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O professor e a aula de Matemática [The teacher and the Mathematics class]</style></title><secondary-title><style face="normal" font="default" size="100%">EIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://drive.google.com/open?id=1bXIGZHoCA8jw1khZlXhRfbbo_mxHRO3t</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Coimbra</style></pub-location><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A formação e o desenvolvimento profissional do professor são determinantes para as opções que este assume na sala de aula. É o seu conhecimento, aquilo que valoriza e o contexto onde se encontra inserido que determinam as experiências de aprendizagem que proporciona aos seus alunos. Mas esse conhecimento profissional envolve uma multiplicidade de dimensões que decorrem da sua formação inicial e contínua, mas também das experiências que teve ocasião de vivenciar e de processos de socialização, onde a interação com os pares e as oportunidades de desenvolver trabalho colaborativo são elementos importantes. A aula de matemática surge assim como o campo aglutinador do trabalho do professor numa dupla vertente que se une num ciclo único: por um lado a aula de Matemática é o foco do trabalho do professor, onde as opções previamente assumidas são implementadas; e, por outro lado, é um ponto de partida para a reflexão e o desenvolvimento profissional do professor.&lt;/p&gt;
&lt;p&gt;Da planificação da aula, onde a escolha das tarefas e a forma de as implementar são aspetos centrais e onde a vertente histórica não deixará de estar presente; à sua implementação, operacionalizando diferentes recursos (nomeadamente os tecnológicos) e assumindo dinâmicas de aula diferenciadas; até à fase de reflexão entre pares, que termina e reinicia um novo ciclo – estas são as grandes etapas em torno das quais este texto se organiza e onde a formação inicial e contínua não deixarão de estar presentes.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Perceptions of mathematics teachers on the teaching of functions and on the use of technological materials - Perceções de professores de matemática sobre o ensino de funções e sobre o uso de materiais tecnológicos</style></title><secondary-title><style face="normal" font="default" size="100%">Educação Matemática Pesquisa</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://revistas.pucsp.br/emp/article/view/36538</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">113-139</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study intends to understand the perceptions of mathematics teachers from lower and upper secondary regarding the teaching of Functions and the use of technological materials. For that, a mixed methodology was adopted, and the perceptions of 129 teachers were collected through a questionnaire and four teachers through an interview. The main conclusions point to similarities in teachers' perceptions, but also to some differences related to the teaching level of lower or upper secondary. In the teaching of Functions, textbooks are widely used, but differently depending on the level being taught. The same happens with the representations and with the use that is made of the technologies. Involvement of students in work is another aspect considered important, but again there are differences. The assessment also has similarities, but differs in the valuation ascribed to group work.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ perspectives on the use of technology to teach Functions at lower and upper secondary</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 5th ERME Topic Conference - MEDA 2018</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.math.ku.dk/english/research/conferences/2018/meda/proceedings/papers/rocha_p_217.pdf</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/meda_rocha_2018.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Copenhagen, Denmark</style></pub-location><pages><style face="normal" font="default" size="100%">217-224</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study aims to understand the perceptions of lower and upper secondary age teachers of mathematics regarding the use of technology to teach functions. For that, a mixed methodology was adopted, and the perceptions of 129 teachers were collected through a questionnaire (quantitative section) and four teachers through an interview (qualitative section). The main conclusions point to similarities in teachers' perceptions, but also to some differences related to the level that they taught. Teachers show conviction about their knowledge on technology and about the potential of technology in what concerns their teaching and the students’ learning. However, they are not so clear about the best way to articulate technology and paper-and-pencil methods, nor about the use of technology in assessment.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Analyzing the teacher’s knowledge for teaching mathematics with technology</style></title><secondary-title><style face="normal" font="default" size="100%">ICTMT</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://ictmt13.sciencesconf.org/data/pages/proceedings_compressed_1.pdf</style></url></web-urls></urls><pub-location><style face="normal" font="default" size="100%">Lyon, France</style></pub-location><pages><style face="normal" font="default" size="100%">256-265</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The teacher’s knowledge has long been viewed as a strong influence on the students’ learning. Several authors have sought to develop procedures to assess this knowledge, but this has proved to be a complex task. In this paper I present an outline of a conceptualization to analyze the teacher's knowledge, based on the model of the Knowledge for Teaching Mathematics with Technology (KTMT) and a set of tasks. These tasks are chosen by the teacher taking into account the potential of the tasks to take advantage of the technology’s potential. The analysis of the teacher’s KTMT is based on the characteristics of the tasks chosen by the teacher; the balance established between the representations provided by the technology that the tasks advocate; the way how the tasks pay attention to the new issue of seeking for a suitable viewing window; and also the way how the tasks take into account the expectable difficulties of the students in the process of looking for the window.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Martinho, H.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A escrita matemática na resolução de um problema de geometria por alunos de licenciatura em Educação Básica [Mathematical writing in solving a geometry problem by undergraduate students in Basic Education]</style></title><secondary-title><style face="normal" font="default" size="100%">EIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Lisboa, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">163-178</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Apesar da escrita ter, habitualmente, uma maior expressão no ensino da Matemática que a própria oralidade, os alunos não estão habituados a explicitar raciocínios e a utilizar linguagem matemática apropriada. A comunicação matemática escrita tem algumas particularidades que podem ser diretamente trabalhadas com os alunos. Por exemplo, a escrita ajuda os alunos a dar sentido à Matemática e a melhorar o próprio discurso. As produções dos alunos transportam informações para o professor contribuindo para a planificação e concretização da sua prática profissional. Assim, e apesar de frequentemente ser descurada, a escrita matemática pode ser trabalhada na sala de aula, em particular, com futuros professores. Este artigo reporta parte de uma experiência realizada com uma turma da Licenciatura em Educação Básica, tendo por base a resolução em grupo de um problema de Geometria e o registo escrito do processo de resolução elaborado pelos alunos. Pretendeu-se desta forma caraterizar a comunicação escrita dos alunos e identificar contributos desta para a compreensão por parte do professor dos conhecimentos dos alunos. A análise da escrita matemática dos alunos, tendo por base um conjunto de critérios previamente definidos, permitiu identificar a preferência destes pelo recurso à representação verbal, dificuldades em fundamentar adequadamente as respostas apresentadas e uma forte tendência para desvalorizar as abordagens prévias que não conduziram à resposta ao problema. Permitiu ainda identificar uma tendência para não explicitar o entendimento das questões que lhes eram colocadas. A forma como os conceitos matemáticos surgem nas repostas escritas permite identificar aspetos relevantes do conhecimento dos alunos.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Moving from one representation to another: different ways of doing it, different mathematical learning</style></title><secondary-title><style face="normal" font="default" size="100%">The Scottish Mathematical Council Journal</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://drive.google.com/file/d/105peUCd3f60J0HN3d3CuRu6hIx_bjNAf/view</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">47</style></volume><pages><style face="normal" font="default" size="100%">40-48</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O professor e a fidelidade matemática da calculadora gráfica no estudo de Funções [The teacher and the mathematical fidelity of the graphing calculator in the study of Functions]</style></title><secondary-title><style face="normal" font="default" size="100%">XXVIII SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Viseu, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">116-128</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The teacher's knowledge of the mathematical fidelity of technology and the impact it has on the teacher’s practice is the focus of this article. Based on the conceptualization of Knowledge for Teaching Mathematics with Technology (KTMT), and involving the teaching of Functions at the 10th grade, we analyze: the situations of lack of mathematical fidelity considered by the teacher in the classes, the way how the teacher manages students' contact with this kind of situations, and how the teacher supports students when they are faced with a lack of mathematical fidelity. The conclusions reached point to: some devaluation of the situations of lack of mathematical fidelity, with only one type of situation being explicitly addressed; a careful selection of tasks, in order to ensure that these situations do not occur too soon; a focus on the identification by the students of this type of situation, suggesting what they can do to confirm the suspicion but without effective implementation of the process. As a consequence, knowledge of mathematical fidelity does not necessarily have a relevant impact on teacher’s practice and it is not easily transformed into a deep teacher’s KTMT.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Babo, A.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Problem solving in linear programming: a study in a vocational course - Resolução de problemas de Programação Linear: um estudo no ensino profissional</style></title><secondary-title><style face="normal" font="default" size="100%">Revista de Estudios e Investigación en Psicología y Educación</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><volume><style face="normal" font="default" size="100%">E</style></volume><pages><style face="normal" font="default" size="100%">41-46</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The development of meaningful learning becomes possible when students are actively involved in solving real problems. Thus, this study intends to investigate how students of the 11th grade of a vocational course solve problems of Linear Programming, using the graphing calculator. The conclusions reached indicate that: the interpretation of the conditions of the problems is the most delicate point; the graphical approach using technology is dominant; and the difficulties raised by the problem as well as the need to discuss the results achieved are the basis for the interactions both among the students and between them and the teacher.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Some factors impacting the teachers' assessment practices - Influências sobre as práticas de avaliação do professor</style></title><secondary-title><style face="normal" font="default" size="100%">REIPE</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://revistas.udc.es/index.php/reipe/article/view/reipe.2017.0.10.2465</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">E</style></volume><pages><style face="normal" font="default" size="100%">30-35</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The assessment and the role it should be assumed by the summative and formative component are often a reason for discussion. It is therefore important to understand how the teacher assessment practices are characterized and what influences them. That is, identify aspects taken into account when planning assessment; the (dis)continuities between assessment and learning; the divergences/consonances between assessment planned and implemented. The conclusions reached point to a strong influence of peers, to the assessment criteria of the school and to the students’ characteristics, in a scenario where the test is the dominant element in assessment.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">10</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teacher knowledge and the teaching of statistics using a graphing calculator -  Conhecimento profissional e ensino de estatística com recurso à calculadora gráfica</style></title><secondary-title><style face="normal" font="default" size="100%">REIPE</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://revistas.udc.es/index.php/reipe/article/view/reipe.2017.0.06.2307</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">E</style></volume><pages><style face="normal" font="default" size="100%">96-100</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Teaching statistics is often based on an approach focused on teaching theoretical aspects, disconnected from&lt;br /&gt;
practical relevance and from interpretation of results, and where the use of technology lies behind its potential. In&lt;br /&gt;
this context, it is important to analyze how the teachers’ knowledge is characterized and to identify aspects of this&lt;br /&gt;
knowledge that mark the professional practice. The conclusions reached emphasize the impact of content&lt;br /&gt;
knowledge and its influence on knowledge of content and teaching. Knowledge of curriculum is also relevant, as&lt;br /&gt;
well as the way how it seems to prevent the development of other types of knowledge.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">6</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Lopes</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O jogo como promotor da comunicação e aprendizagem matemática [Games to promote communication and mathematical learning]</style></title><secondary-title><style face="normal" font="default" size="100%">XXVII SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Porto, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">149-162</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Games are commonly appointed as a methodological tool capable of promoting students’ effective learning. In this context, this study intends to analyze the impact of mathematical discussions developed while&lt;br /&gt;
playing a polynomial game. Namely it intends to analyze the impact on the consolidation of mathematical concepts previously worked in the classroom and on the communications skills. Two case studies where developed involving 10th grade students. Data gathering was based on direct observation and an inquiry. The main conclusions suggest that the game encouraged the discussion about the mathematical contents and therefore promoted the development of the mathematical discourse. Besides that, it allowed a deeper apprehension of mathematical concepts, and the overcome of some difficulties.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Coelho, E.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O raciocínio dedutivo de alunos do 10.º ano de escolaridade [The deductive reasoning of students in the 10th grade]</style></title><secondary-title><style face="normal" font="default" size="100%">XXVII SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Porto, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">275-291</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Deductive reasoning, being central in mathematics, is also usually a source of difficulties for students, more used to the empirical approaches. In this study we focus on mathematical proof and we try to give attention to how this kind of reasoning is envisaged by the students, to the options they assume when asked to develop a deductive reasoning and to the factors affecting the implementation of this kind of reasoning. The study follows a qualitative and interpretative methodological approach, including the completion of two case studies of students of the 10th grade. Data were collected in work sessions and through interviews. The main findings point to a devaluation of mathematical proof and a strong preference for empirical approaches. Yet students show ability to develop different approaches. The preference for the mathematical subject and the attention given in class to the deduction work, appears to be relevant factors when considering the students' ability to develop a deductive reasoning when involved on a mathematical proof.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ use of the different representations in a context of technology integration</style></title><secondary-title><style face="normal" font="default" size="100%">Proceddings of 13th International Congress on Mathematical Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">ICME</style></publisher><pub-location><style face="normal" font="default" size="100%">Hamburg, Germany</style></pub-location><pages><style face="normal" font="default" size="100%">1-4</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study focus on the different representations provided by graphing calculators, intending to characterize how the teacher uses and integrates them on the process of teaching and learning functions at the secondary level. The methodology adopted is qualitative and interpretative, undertaking two case studies. The main conclusions point to different levels of flexibility in the use of the different representations depending on the teacher, but suggest a strong preference for the graphical and the algebraic representations, a use of the numerical representation based on the graph of the function and a total lack of use of the tabular representation.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teacher’s representational fluency in a context of technology use</style></title><secondary-title><style face="normal" font="default" size="100%">Teaching Mathematics and its Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://teamat.oxfordjournals.org/content/early/2016/04/28/teamat.hrw005.short?rss=1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">35</style></volume><pages><style face="normal" font="default" size="100%">53-64</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study focuses on teacher’s Knowledge for Teaching Mathematics with Technology (KTMT), paying a special attention to teacher’s representational fluency. It intends to characterize how the teacher uses and integrates the different representations provided by the graphing calculator on the process of teaching and learning functions at the high school level. Specifically, it intends to understand the balance established between the use of the different representations, and the way these representations are articulated. The study adopts a qualitative approach undertaking one teacher case study. Data were collected for two school years, at 10th and 11th grades, and included class observation, semi-structured interviews and documents gathering. Data analysis was mainly descriptive and interpretive in nature, considering the problem under study. The conclusions reached reveal an active use of the graphical and algebraic representations and a scarce use of the tabular representation. The lack of balance on the use of representations also includes the work within a representation. In this case the graphical representation is the only one that was explored. The conclusions also indicate a flexible articulation between the two representations usually used. It was possible to identify different patterns on the use of the representations and a frequent use of an interactive approach, marked by repeated alternations between representations. Globally, this study emphasizes teacher’s KTMT and raises questions about the impact of technology on teacher´s representational fluency and about the difference between a numerical and a tabular representation.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uma proposta para análise do Conhecimento para Ensinar Matemática com a Tecnologia [A proposal to analyze the teacher's Knowledge for Teaching Mathematics with Technology]</style></title><secondary-title><style face="normal" font="default" size="100%">XXVII SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Porto, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">427-441</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The teacher’s knowledge has long been viewed as a strong influence on the students’ learning. Several authors have sought to develop procedures to assess this knowledge, but this has proved to be a complex task. In this paper I present an outline of a conceptualization to analyze the teacher's knowledge, based on the model of the Knowledge for Teaching Mathematics with Technology (KTMT) and a set of tasks. These tasks are chosen by the teacher among the ones he prepared for his students taking into account the potential of the tasks to take advantage of the technology’s potential. The analyze of the teacher’s KTMT is based on the characteristics of the tasks chosen by the teacher; the balance established between the representations provided by the technology that the tasks advocate; the way how the tasks pay attention to the new issue of seeking for a suitable viewing window; and also the way how the tasks take into account the expectable difficulties of the students in the process of looking for the window.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Campos, S.</style></author><author><style face="normal" font="default" size="100%">Fernandes, J.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The use of graphing calculator in the exploration of nonlinear continuous models</style></title><secondary-title><style face="normal" font="default" size="100%">Revemat</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://periodicos.ufsc.br/index.php/revemat/article/view/1981-1322.2016v11n2p79/33629</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">79-98</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The integration of the graphing calculator in mathematical activity encourages students to express many of their processes and ways of thinking. Since some of the activities at the high school level are carried out with the graphing calculator, we intend to investigate the contribution of this resource to promote the learning of nonlinear continuous models in the 11th grade. By adopting a qualitative methodology, we collected and analysed the students‟ writing productions. At first, students used to present the information given by the calculator with no justification. As they acquire skills in the use of this resource, they usually set up the viewing window in order to visualize the graphical representations of functions that model the problem situation they are working on and also relate the different existing menus in the study of those functions characteristics. Such procedures make students to present the data collected in the calculator with a justification of their arguments and a validation of their conjectures.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. Botelho</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Aspectos da comunicação matemática na resolução de problemas</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XXVI SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">www.apm.pt/files/_XXVISIEM_Atas_prov_551361d5</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Évora, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">232-247</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The influence of mathematical communication over the students’ learning led to this research, whose main goal is to understand the impact on problem solving of the students’ communication difficulties. The study adopts a qualitative and interpretative methodology, undertaking two case studies of 10th grade students. The reached conclusions point to the students’ difficulties at the interpretation of the problem, namely at the interpretation of figures, and at the interpretation of the available data, especially when part of them is irrelevant to the problem. Some difficulties were also identified at the communication level, in relation to the arguments used by the students to support their ideas, where a clear preference to restrict them to mathematic calculations was identified.&lt;/p&gt;
&lt;p&gt;Resumo&lt;br /&gt;
A importância da comunicação matemática sobre a aprendizagem dos alunos, levou à realização desta investigação que pretendeu compreender o impacto sobre a resolução de problemas das dificuldades de comunicação evidenciadas pelos alunos. Optou-se por uma metodologia de natureza qualitativa e interpretativa e pela realização de estudos de caso envolvendo dois alunos do 10.º ano. As conclusões alcançadas apontam para dificuldades na interpretação do enunciado, nomeadamente relativamente às figuras e a dados em quantidade superior ao necessário. Também ao nível da comunicação da resolução foram identificadas dificuldades em fundamentar ideias, evidenciando uma preferência pelo recurso ao cálculo. &lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. Botelho</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A comunicação matemática na avaliação da resolução de problemas</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do ProfMat 2015</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2015_profmat_carmo.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Évora, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">74-89</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A aprendizagem dos nossos alunos é fortemente influenciada pelas caraterísticas das tarefas que lhes propomos e a resolução de problemas é frequentemente apontada como uma das tarefas com mais potencial para promover aprendizagens ricas. Mas aprender implica ser capaz de desenvolver raciocínios, de comunicar as nossas ideias e de compreender as dos outros num processo argumentativo e reflexivo. A avaliação das aprendizagens num contexto de resolução de problemas envolve assim, necessariamente como parte importante do processo, uma análise da comunicação que se estabelece entre todos os envolvidos.&lt;br /&gt;
Nesta comunicação iremos focar-nos precisamente na comunicação que se estabelece durante a resolução de problemas, abordando as dificuldades dos alunos e dando atenção à interpretação que fazem do enunciado, à compreensão que manifestam das figuras apresentadas, à relação que conseguem estabelecer entre a situação em causa e a informação disponibilizada através de um gráfico, à forma como conseguem explicitar o seu raciocínio e à linguagem matemática que utilizam no decurso do processo de argumentação. Para tal vamos basear-nos num conjunto de problemas propostos a alunos do 10.º ano de escolaridade no decorrer do estudo de funções.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Moreira</style></author><author><style face="normal" font="default" size="100%">S. Lopes</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Dos jogos à aprendizagem</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do ProfMat 2015</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2015_profmat_carolina_silvia.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Évora, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">142-159</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Neste texto apresentamos os jogos no ensino da matemática como uma forma de aprendizagem de conteúdos e não apenas como um recurso que cada professor pode usar nas suas aulas para tornar a aula diferente. Analisamos dois jogos desenvolvidos por nós e que utilizámos com alunos dos 7.º e 10.º anos de escolaridade, procurando não só apresentar os jogos, mas também aspetos da sua implementação em sala de aula, ponderando o contributo que trouxeram à aprendizagem dos alunos.&lt;br /&gt;
Aprender matemática depende de um grande número de variáveis, o que torna o ensino um processo complexo, pois é necessário que se desenvolva o raciocínio lógico, além de estimular o desenvolvimento das mais variadas capacidades transversais, tais como o pensamento autónomo, a criatividade, o sentido de estratégia e a capacidade de resolver problemas.&lt;br /&gt;
Duas das dificuldades frequentemente encontradas pelos professores passam pela falta de motivação para a aprendizagem e pelo desinteresse pela Matemática. A solução para estes problemas pode passar pela utilização de jogos para complementar o estudo, mas também para a aquisição de novos conteúdos. No entanto, apenas a implementação dos jogos não basta. O papel do professor é de extrema importância e a planificação e orientação da aula são fundamentais para que se alcancem os objetivos pretendidos.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Campos, S.</style></author><author><style face="normal" font="default" size="100%">Viseu, F.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Fernandes, J. A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The graphing calculator in the promotion of mathematical writing</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 12th International Conference onTechnology in Mathematics Teaching</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://hdl.handle.net/10400.1/6081</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Universidade do Algarve</style></publisher><pub-location><style face="normal" font="default" size="100%">Faro, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">590-598</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Through writing, students express many of their processes and ways of thinking. Since at high school level some of the activities are carried out with the graphing calculator, we intend to investigate the contribution of this resource to promote the mathematical writing in the learning of continuous nonlinear models at 11th grade. Adopting a qualitative methodology, we collected and analyzed the students’ writing productions. What they write when using the calculator gives evidence about the information valued (when they sketch graphics without any justification); about the strategies used (when they define the viewing window and relate different menus on the graphing calculator); and about the reasoning developed (when they justify the information given by the calculator and the formulation of generalizations and conjectures validation).&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The impact of technologies on the teacher's use of different representations</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 12th International Conference onTechnology in Mathematics Teaching</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://hdl.handle.net/10400.1/6081</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Universidade do Algarve</style></publisher><pub-location><style face="normal" font="default" size="100%">Faro</style></pub-location><pages><style face="normal" font="default" size="100%">304-311</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This study intends to characterize how the teacher uses and integrates the different representations provided by the graphing calculator on the process of teaching and learning functions at the secondary level. Specifically, it intends to understand the balance established between the use of the different representations, and the way these representations are articulated. The conclusions reached point to an active use of the graphic and algebraic representations and to a scarce use of the tabular representation. The conclusions also point to a flexible articulation between the two representations usual used, assuming different forms and frequently an interactive approach, repeatedly switching between representations.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The impact of the cultural context on the professional practice of the teacher</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 8th Annual International Conference of Education, Research and Innovation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2015IMP</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ICERI</style></publisher><pub-location><style face="normal" font="default" size="100%">Seville, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">659-668</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;THE IMPACT OF THE CULTURAL CONTEXT ON THE PROFESSIONAL PRACTICE OF THE TEACHER&lt;/p&gt;
&lt;p&gt;H. Rocha&lt;/p&gt;
&lt;p&gt;Universidade NOVA de Lisboa, Faculdade de Ciências e Tecnologia (PORTUGAL)&lt;/p&gt;
&lt;p&gt;The professional knowledge is a key element of the teacher’s practice. This knowledge is naturally influenced by the teacher’s beliefs and conceptions and by his training, but the context where he develops his practice is perhaps the most decisive influence. At this level, the school where the teacher works and his colleagues are a powerful influence, but the characteristics of his students are even a stronger influence. The cultural diversity of the students and specifically the linguistic diversity are highly relevant elements. A classroom where different languages converge is always a complex context which requires a deeper professional knowledge with inevitable repercussions over the teacher’s practice. &lt;/p&gt;
&lt;p&gt;This study focuses on a teacher working with a mathematics’ class of foreign students with heavy linguistic limitations on the language of instruction and it intends to analyze the impact of this context on the teacher’s practice. In particular, it intends to analyze how this context interferes with the characteristics of the tasks proposed by the teacher and with the way how mathematical concepts are presented to the students.&lt;/p&gt;
&lt;p&gt;The study adopts a qualitative and interpretative methodological approach, undertaking one teacher case study. Data were collected during one school year by semi-structured interviews, class observation, and documental data gathering. All interviews and classes observed were audio taped and transcribed. Data analysis was conducted in an interpretative way.&lt;/p&gt;
&lt;p&gt;The conclusions reached point to an increase on the appreciation of mechanization, to a large reduction in the use of problematic situations and to a presentation of Mathematics as calculation, disconnected from any application, and where reasoning appears as a marginal element or is even missing. The use of several examples becomes a key element of the practice of this teacher. The main finding of this study suggests that language limitations caused a strong impact on the practice of a teacher who considers the understanding and the development of reasoning from the discussion around mathematical ideas as central to the teaching of this subject. It was also possible to identify that the need to find a way to communicate reinforced the formalism of the mathematical language, placing it in the center of the learning process.&lt;/p&gt;
&lt;p&gt;Keywords: cultural context, teacher’s practice, mathematics.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Knowledge for teaching mathematics with technology and the search for a suitable viewing window to represent functions</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of Cerme 9</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://hal.archives-ouvertes.fr/CERME9</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Prague, Czech Republic</style></pub-location><pages><style face="normal" font="default" size="100%">2403-2409</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The usual difficulties of students regarding the choice of an appropriate window when using the graphing calculator in the study of functions and the importance of the teachers’ knowledge to overcoming them, led to this study. The main goal was to characterize the way teachers address the viewing window in the classroom, trying to infer aspects of the Knowledge for Teaching Mathematics with Technology that can justify that practice. The conclusions reached point to the importance of a set of specific knowledge where I highlight the knowledge of the students’ difficulties, the knowledge of mathematical content necessary to understand the impact of the viewing window on the graphic, and the knowledge of teaching strategies that address both the students’ difficulties and the relevant mathematical knowledge.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Múltiplas abordagens, múltiplas representações: um contributo para incrementar a relevância da representação algébrica [Multiple approaches, multiple representations: a contribute to increase the relevance of algebraic representation]</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.spiem.pt/publicacoes/arquivo/</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Bragança, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">327-339</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A tecnologia e o impacto que esta pode ter sobre as diferentes representações utilizadas e, em particular, sobre a representação algébrica são o foco deste artigo. Procura-se assim compreender como é que o professor enquadra a representação algébrica no trabalho em sala de aula e como a procura tornar relevante para os alunos num contexto de utilização da tecnologia. As conclusões alcançadas apontam para a opção por uma estreita articulação entre as representações algébrica e gráfica e para uma criteriosa escolha de tarefas, envolvendo múltiplas abordagens, onde a representação algébrica vem disponibilizar informação fundamental e tendencialmente inacessível a partir de outras representações.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O formal da matemática e o intuitivo da tecnologia: que articulação?</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do ProfMat 2015</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2015_profmat.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Évora, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">120-130</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A tecnologia é cada vez mais indispensável no dia-a-dia, rodeando-nos constantemente. Para os nossos alunos é uma realidade que conhecem desde sempre e que tendem a encarar com uma naturalidade descontraída e intuitiva. A facilidade de acesso à tecnologia e o modo como esta tende a enfatizar o intuitivo e a relegar para segundo plano o formal e a demonstração matemática são o foco deste artigo. Partindo da análise de uma proposta de trabalho onde alunos de 10.º ano começam por uma abordagem intuitiva apoiada na calculadora gráfica e terminam a realizar uma demonstração da conjectura que formularam, procuro discutir a problemática. As conclusões alcançadas sugerem que é possível colocar aos alunos situações onde estes se podem aperceber da vantagem de recorrer tanto a abordagens mais formais como a abordagens mais intuitivas e isto mesmo quando a tecnologia é uma realidade em sala de aula. Sugere ainda que a realização de demonstrações pode, entre outros aspectos já identificados na literatura, dar um contributo importante para a compreensão de aspectos basilares da Matemática.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O formalismo matemático num contexto de utilização da tecnologia [Mathematical proof in a context of technology integration]</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XXVI SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">www.apm.pt/files/_XXVISIEM_Atas_prov_551361d576189.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Évora</style></pub-location><pages><style face="normal" font="default" size="100%">22-35</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The technology and how it tends to emphasize the intuitive and overshadow calculus and mathematical proof are the focus of this paper. The conclusions reached suggest that tasks where students might realize the usefulness of calculus as well as of more intuitive approaches are possible even when the technology is a reality in the classroom. They also suggest that proof may, among other things already identified in the literature, make an important contribution to the students’ understanding of fundamental aspects of mathematics.&lt;/p&gt;
&lt;p&gt;A tecnologia e a forma como esta tende a enfatizar o intuitivo e a relegar para segundo plano o formal e a demonstração matemática são o foco deste artigo. As conclusões alcançadas sugerem que é possível colocar aos alunos situações onde estes se possam aperceber da vantagem de recorrer tanto a abordagens mais formais como a abordagens mais intuitivas e isto mesmo quando a tecnologia é uma realidade em sala de aula. Sugere ainda que a realização de demonstrações pode, entre outros aspectos já identificados na literatura, dar um contributo importante para a compreensão de aspectos basilares da Matemática.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Students' conceptions about the use of graphing calculators on tests</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 8th Annual International Conference of Education, Research and Innovation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2015STU</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">ICERI</style></publisher><pub-location><style face="normal" font="default" size="100%">Seville, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">3452-3459</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;STUDENTS’ CONCEPTIONS ABOUT THE USE OF GRAPHING CALCULATORS ON TESTS&lt;/p&gt;
&lt;p&gt;H. Rocha&lt;/p&gt;
&lt;p&gt;Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa (PORTUGAL)&lt;/p&gt;
&lt;p&gt;The assessment is considered a key element of the teaching and learning process and is often divided into two types: formative and summative. The distinction between these two types of assessment is usually made based on the moments in which it occurs and the objectives it has. Nevertheless, there are some continuities between these two types of assessment, and this leads some authors to question whether these two types of assessment should be seen as fully disjoint. Despite this, the prevailing understanding of summative assessment is that it takes place at the end of the learning process and that it is intended to classify the students.&lt;/p&gt;
&lt;p&gt;The technology and, in particular, the graphing calculator is recognized for the impact it may have on the students’ approaches to solve mathematical questions. When technology is available, several studies point to an higher relevance of the understanding of the mathematical concepts, to an increase in graphical approaches to mathematical questions and to an increment in the use of exploratory approaches to solve the problems that are posed. Of course, all these changes will have its impact also on summative assessment moments, and specifically in testing.&lt;/p&gt;
&lt;p&gt;Students’ conceptions about the use of technology have a deep impact on how they actually use the technology. The relevance usually attributed to tests, makes it important to understand what determines the performance of students in these moments.&lt;/p&gt;
&lt;p&gt;This study focuses on the use of the graphing calculator at assessment moments such as tests, intending to understand the students’ conceptions related to that use. Namely it intends to analyze the impact of the students’ conceptions about Mathematics, about the use of technology to learn, and about teachers’ perspectives.&lt;/p&gt;
&lt;p&gt;The study adopts a qualitative and interpretative methodological approach, undertaking two students’ case studies. Data were collected during one school year by semi-structured interviews, students’ observation at testing moments, and documental data gathering. All interviews were audio recorded and transcribed and the students’ observation was video recorded. Data analysis was conducted in an interpretative way.&lt;/p&gt;
&lt;p&gt;The conclusions reached suggest that students welcome the possibility of using the graphing calculator during testing. The way this technology allows them to avoid errors, both in the calculations and in the formulas to be used, is the main reason advanced by the students. The speed of resolution, which they consider very important during testing, is another of the valued aspects. The idea of Mathematics as something that you need to understand and where knowing the right formula is not enough to achieve the right answer is pointed as the main justification for the use of this technology in tests. Nevertheless, the idea that technology should not be used seems to be always present. The impact of family ideas and, in particular, the idea that one can become dependent of the graphing calculator, seems to have some influence over the students conceptions about the use of this technology. However, the one that is undoubtedly the decisive reason for this conception is what they consider to be the opinion of a teacher. For the students, a teacher cannot agree with the use of graphing calculators in tests. And the reason given for this is related to the idea that a teacher will not be able to actually understand the students’ mathematical knowledge if he uses the graphing calculator.&lt;/p&gt;
&lt;p&gt;Keywords: summative assessment, students’ conceptions, technology, mathematics.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Consensos e dilemas no ensino de matemática a alunos de um curso de Decoração e Pintura Cerâmica</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do VI Seminário Luso-Brasileiro Educação, Trabalho e Movimentos Sociais</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2013_lusobrasileiro.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">IE-UL</style></publisher><pub-location><style face="normal" font="default" size="100%">Lisboa, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">502-511</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A Matemática é uma das áreas que integra o plano curricular dos Cursos de Educação e Formação (CEF), pelo contributo para o exercício da cidadania em sociedades democráticas e tecnologicamente avançadas, mas esta é, também, frequentemente fonte de exclusão. O programa reconhece-o e enfatiza uma aprendizagem mais ligada ao concreto e à realidade. Mas reconhece também que é ao professor que compete gerir a sua implementação, dando forma às situações de aprendizagem e integrando-as de forma coerente e articulada no curso específico que os alunos frequentam. O estudo que aqui se apresenta teve como principal objectivo analisar e compreender as opções efectuadas pelo professor no decorrer das diferentes etapas da sua prática, dando atenção aos dilemas que enfrentou e às razões que valorizou na tomada de decisões. A abordagem metodológica adoptada é de natureza qualitativa e interpretativa, com a realização dum estudo de caso do professor de Matemática Aplicada dum CEF de Decoração e Pintura Cerâmica. A recolha de dados foi concretizada através de entrevistas, observação de aulas e recolha documental, sendo a análise de dados orientada pelo quadro teórico, conciliado com a interpretação destes. Nas conclusões do estudo a redução dos pré-requisitos, a preocupação em partir dos interesses dos alunos e a intenção de alargar a cultura dos alunos surgem como centrais na selecção das tarefas; enquanto o envolvimento activo dos alunos caracteriza a implementação das aulas. Os dilemas centram-se fundamentalmente na valorização relativa e aprofundamento a atribuir a cada conteúdo e na articulação entre formal e intuitivo.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Different representations in mathematics teaching with technology</style></title><secondary-title><style face="normal" font="default" size="100%"> Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><pub-location><style face="normal" font="default" size="100%">Vancouver, Canada</style></pub-location><pages><style face="normal" font="default" size="100%">6-384</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The main focus of this paper is the teacher’s representational fluency in a context of graphing calculator use. The conclusions reached point to a more intensive use of some representations over the others, suggesting that technology turns numerical or tabular representation into two different representations.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Games and the learning of mathematics outside the classroom</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the International Conference on Education and New Learning Technologies</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2014GAM</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">EduLearn</style></publisher><pub-location><style face="normal" font="default" size="100%">Barcelona, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">1781-1790</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;GAMES AND THE LEARNING OF MATHEMATICS OUTSIDE THE CLASSROOM&lt;br /&gt;
H. Rocha&lt;/p&gt;
&lt;p&gt;Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia (PORTUGAL)&lt;/p&gt;
&lt;p&gt;Playing games is a recreational activity that is also highly recognized as a potentially rich activity for the teaching and learning. It is an activity that involves the recognition and observance of rules, as well as the development of strategies to achieve victory. It is thus an activity that encourages compliance with rules but also the development of learning and therefore has a socializing character while stimulating critical thinking and analysis of situations. This is why many authors think about playing games as a problem-solving activity with great potential for the learning of mathematics. However, a review of the literature suggests that mathematical learning does not always occur, pointing to the relevance of the specific features of the game and the circumstances in which it is used. Looking to contribute to a better understanding of these issues, the project that was the basis of this study focuses on the use of games by middle school students, intending to promote their mathematical learning in a voluntary and informal context, outside the classroom. The games were available in MatLab, a room of the school supervised by mathematics teachers, which students could visit in their leisure time. In this communication I intend to analyze how the visits to MatLab contributed to the mathematical learning of students, considering the influence of specific characteristics of the games and the atmosphere created in MatLab, given the students’ previous mathematical knowledge.&lt;/p&gt;
&lt;p&gt;The study adopts a qualitative and interpretative methodological approach, undertaking two student case studies. Data collection was completed over three months and included observation of twenty visits of these students to MatLab. Data collection was made through the development of a logbook, audio record of the students’ visits and two interviews to the students and to their teacher. Data analysis was based on the evidence gathered in the light of the problem under study.&lt;/p&gt;
&lt;p&gt;The conclusions reached stress the importance of certain features of the games to promote student engagement, leading to a desire for self-improvement, very important for the development of sustained learning. Computer games have proven to have a stronger potential to engage students than board games. Nevertheless, the most important characteristics of a game seem to be related to the possibility of playing at different mathematical levels (without getting blocked by lack of knowledge) and to the possibility of keep getting better marks (without the existence of a maximum level from which evolution is not possible). In what concerns to achievement in mathematics’ classes, the students’ teacher reports an improvement in mathematics knowledge (more evident in the average achiever student) as well as an increase in students’ involvement in class work (more evident in the low achiever student).&lt;/p&gt;
&lt;p&gt;keywords: game-based learning, mathematics, informal learning.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Slides available at&lt;br /&gt;
&lt;a href=&quot;http://iated.org/presentations/pv_37880.pdf&quot; rel=&quot;nofollow&quot;&gt;http://iated.org/presentations/pv_37880.pdf&lt;/a&gt;&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The influence of teacher’s knowledge for teaching mathematics with technology on the implementation of investigation tasks</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 8th International Technology, Education and Development Conference</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2014INF</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">INTED</style></publisher><pub-location><style face="normal" font="default" size="100%">Valencia, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">494-503</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Mathematics teaching in Education and Training Courses</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the International Conference on Education and New Learning Technologies</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2014MAM</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">EduLearn</style></publisher><pub-location><style face="normal" font="default" size="100%">Barcelona, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">1866-1873</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;MATHEMATICS TEACHING IN EDUCATION AND TRAINING COURSES&lt;br /&gt;
H. Rocha&lt;/p&gt;
&lt;p&gt;Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia (PORTUGAL)&lt;/p&gt;
&lt;p&gt;Education and Training Courses have been specifically designed to the high number of young people in a situation of school dropout and in transition to working life, particularly those who enter the labor market early with insufficient levels of schooling and professional training. Mathematics is one of the curriculum components of these courses, for its contribution to the exercise of citizenship in a democratic society. Being an important part of the cultural legacy of our society is too often seen by students as a source of exclusion. It is known that young people who enter these courses often had an experience of underachievement in the discipline, what justifies that motivating students is at once the great challenge faced by the teacher. The program suggests taking a more concrete and linked to reality approach, allowing students to learn to recognize the mathematics in the world around them and using technology to promote that learning. However, it is the teacher who is responsible for managing its implementation, shaping the learning situations and integrating them in a coherent and articulated way in the specific course that students attend. In what concerns to assessment, the program also takes into account the usual characteristics of the students. Thus, the assessment includes a strong appreciation of students’ work, its presentation and discussion and further improvement of that work. The directions given to the teacher diverge from the traditional option of the evaluation test, providing guidelines to the form that each evaluation can take depending on the contents in study. However, once again, the teacher's role in curriculum management is not neglected, being valued the adequacy of proposals to the characteristics of the students.&lt;br /&gt;
The study presented here had as its main goal to analyze and understand the choices made by the teacher during the different stages of his practice, giving attention to the dilemmas he faced and to the reasons he took into account when making decisions.&lt;/p&gt;
&lt;p&gt;The study adopts a qualitative and interpretative methodological approach, undertaking one teacher case study. Data collection included semi-structured interviews, classroom observation and document collection. Data analysis was based on the evidence gathered in the light of the problem under study.&lt;/p&gt;
&lt;p&gt;The conclusions of the study point to the important role of technology and suggest that the reduction of prerequisites, the intention of taking into account the students’ interests and the desire of improving students culture is central in what concerns to task selection; while the active involvement of students characterized the implementation of the classes. The dilemmas faced by the teacher focus mainly on the relative importance and on the demanding level that he should give to each content, as well as the articulation that he should promote between formal and intuitive knowledge. In what concerns to assessment, the results achieved highlight the impact that students ideas can have on teacher’s practice, conducting to the inclusion of tests as an assessment element, against the teacher’s intentions. &lt;/p&gt;
&lt;p&gt;keywords: education and training courses, mathematics, innovation, technology.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Slides available at&lt;br /&gt;
&lt;a href=&quot;http://iated.org/presentations/pv_37897.pdf&quot;&gt;http://iated.org/presentations/pv_37897.pdf&lt;/a&gt;&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. Kahle</style></author><author><style face="normal" font="default" size="100%">Oitavem, I.</style></author><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Os problemas de Hilbert</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.apm.pt/portal/em.php?id=215499&amp;rid=209893&amp;search=words=Hilbert,author=,seccao=,ano=,_SEARCH_DONE=1&amp;page=1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">130</style></volume><pages><style face="normal" font="default" size="100%">23-27</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Práticas de avaliação sumativa na disciplina de Matemática Aplicada de um Curso de Educação e Formação</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do VI Seminário Luso-Brasileiro Educação, Trabalho e Movimentos Sociais</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/lusobrasileiro.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">IE-UL</style></publisher><pub-location><style face="normal" font="default" size="100%">Lisboa, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">643-653</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Os Cursos de Educação e Formação (CEF) foram concebidos tendo presente o elevado número de jovens em situação de abandono escolar, alunos usualmente marcados por experiências de insucesso, em particular a Matemática. O programa de Matemática Aplicada tem em conta esta realidade, tanto ao nível das aprendizagens como das metodologias e das características da avaliação a implementar. Relativamente à avaliação sumativa, é valorizado o trabalho desenvolvido pelo aluno, a sua apresentação, discussão e melhoria. As indicações dadas ao professor afastam-se da opção tradicional do teste de avaliação. O papel do professor na gestão curricular não é contudo negligenciado, sendo valorizada a adequação das propostas às características dos alunos. Este estudo pretende analisar as concepções de alunos e professores relativamente à avaliação sumativa, procurando compreender a forma como se influenciam mutuamente e como afectam a prática de avaliação do professor. Foram realizados três estudos de caso, incidindo sobre alunos e respectivo professor. Os dados foram recolhidos através de entrevistas, observação de aulas e recolha documental. Os resultados alcançados sugerem uma forte valorização dos testes por parte dos alunos, sendo notória a influência sobre as opções assumidas pelo professor. Determinantes parecem ser as concepções dos alunos relativamente ao papel de alunos e professores no que à avaliação respeita.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Processos de mudança associados às práticas de avaliação nos Cursos de Educação e Formação de Adultos</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XII Congresso da SPCE</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://xiicongressospce2014.utad.pt/?page_id=797</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2014_spce_b.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">UTAD e SPCE</style></publisher><pub-location><style face="normal" font="default" size="100%">Vila Real, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">2977-2985</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Os cursos de Educação e Formação de Adultos prevêem uma avaliação que se afasta do tradicionalmente implementado nas escolas, propiciando o emergir de processos de mudança. Neste estudo analisa-se a forma como um formador concretiza a avaliação, ponderando continuidades e descontinuidades relativamente a práticas anteriores, com a intenção de caracterizar o inerente processo de mudança e os factores que o influenciam.&lt;br /&gt;
As conclusões obtidas sugerem um processo de mudança complexo, cuja necessidade não é verdadeiramente reconhecida, e onde parece ser determinante a reflexão do formador sobre os formandos, o contexto existente e algumas opções ao nível local da escola.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The teacher and the integration of the graphing calculator viewing window in the teaching of mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 8th International Technology, Education and Development Conference</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://library.iated.org/view/ROCHA2014TEA</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">INTED</style></publisher><pub-location><style face="normal" font="default" size="100%">Valencia, Spain</style></pub-location><pages><style face="normal" font="default" size="100%">483-492</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uma caracterização dos jogos com maior potencial para estimular a aprendizagem matemática</style></title><secondary-title><style face="normal" font="default" size="100%">Atas do XII Congresso da SPCE</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://xiicongressospce2014.utad.pt/?page_id=797</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/hcr/files/2014_spce.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">UTAD e SPCE</style></publisher><pub-location><style face="normal" font="default" size="100%">Vila Real, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">1244-1253</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Reconhecendo o potencial do jogo para a aprendizagem matemática, este estudo pretende analisar o envolvimento e as aprendizagens dos alunos, com o objectivo de caracterizar os jogos com maior potencial para os promover.&lt;br /&gt;
Adoptando uma metodologia de índole qualitativa e envolvendo a realização de estudos de caso sobre alunos do 7.ºano, as conclusões alcançadas sugerem que os jogos de computador são particularmente apelativos para os alunos. Contudo, as características determinantes para o envolvimento dos alunos e consequente promoção da aprendizagem prendem-se com a possibilidade de jogar com diferentes níveis de conhecimento e com a obtenção de bons resultados no jogo.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Utilização, uso ou integração da tecnologia: contributo para a clarificação de um conceito</style></title><secondary-title><style face="normal" font="default" size="100%">Actas do XXV SIEM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.apm.pt/files/_ActasXXVSIEM_53435d9edc873.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Braga</style></pub-location><pages><style face="normal" font="default" size="100%">141-153</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Abstract. The recognition of the potential of technology for the teaching&lt;br /&gt;
and learning of mathematics has encouraged many studies around&lt;br /&gt;
technology. In all these studies, the integration, the utilization or the use of&lt;br /&gt;
technology is (or should be) necessarily an important element. In this paper&lt;br /&gt;
I consider the most common terminologies present in research and the&lt;br /&gt;
meaning assigned to them, based on a research review and on the analysis&lt;br /&gt;
of the studies presented in SIEM over the last five years. The conclusions&lt;br /&gt;
reached suggest a diversity of understandings and a lack of explicitness of&lt;br /&gt;
these understandings. However, different types of technology use seem to be&lt;br /&gt;
recognized, usually associated with continuity or change of practices. The&lt;br /&gt;
teacher's role and a more directive or more student-centered approach,&lt;br /&gt;
associated with a change in the proposed tasks, are also mentioned. In what&lt;br /&gt;
concerns to the terminology adopted, there is great diversity, with cases of&lt;br /&gt;
differentiation in terms of some of the elements listed and cases of adoption&lt;br /&gt;
of multiple terms with apparently identical meanings.&lt;/p&gt;
&lt;p&gt;Resumo. O reconhecimento das potencialidades da tecnologia para o&lt;br /&gt;
ensino e aprendizagem da Matemática tem motivado diversos estudos em&lt;br /&gt;
torno da tecnologia. Em todos eles a integração, a utilização ou o uso que é&lt;br /&gt;
feito da tecnologia é (ou deveria ser) necessariamente um elemento&lt;br /&gt;
importante. Neste artigo procuro ponderar as terminologias mais comuns&lt;br /&gt;
na investigação e o significado que lhes é atribuído, partindo de uma&lt;br /&gt;
revisão de literatura e analisando os estudos apresentados no SIEM nos&lt;br /&gt;
últimos cinco anos. As conclusões alcançadas apontam para uma&lt;br /&gt;
diversidade de entendimentos e para uma ausência de explicitação desses&lt;br /&gt;
entendimentos. Ainda assim, parecem ser reconhecidos diferentes tipos de&lt;br /&gt;
utilização da tecnologia, geralmente associados à manutenção ou alteração&lt;br /&gt;
das anteriores práticas. O papel do professor e o assumir de uma postura&lt;br /&gt;
mais diretiva ou mais centrada no aluno, associada a uma alteração&lt;br /&gt;
relativamente às tarefas propostas, são igualmente referidos. Quanto à&lt;br /&gt;
terminologia adotada, a diversidade é grande, com casos de diferenciação&lt;br /&gt;
em função de alguns dos elementos referidos e com casos de adoção de&lt;br /&gt;
múltiplos termos aparentemente com significados idênticos.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Aspectos da utilização da tecnologia no ensino da Matemática</style></title><secondary-title><style face="normal" font="default" size="100%">Actas do XII Congresso Internacional Galego-Português de Psicopedagogia</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><publisher><style face="normal" font="default" size="100%">CIEd - IEUM</style></publisher><pub-location><style face="normal" font="default" size="100%">Braga, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">6394-6409</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;O potencial da tecnologia para o ensino e a aprendizagem é há muito reconhecido. Contudo, cada vez mais surgem estudos que indiciam que a sua utilização fica aquém das expectativas. O acesso à tecnologia, o papel que lhe é atribuído na aprendizagem e as características das tarefas em que é utilizada, encontram-se entre as principais influências identificadas sobre a utilização que é feita da tecnologia e potencialmente responsáveis pelas características dessa utilização. O estudo que aqui se apresenta teve como principal objectivo analisar e compreender a utilização que os professores fazem da tecnologia à luz dos aspectos referidos, procurando identificar de que forma estes definem diferentes tipos de utilização. A abordagem metodológica adoptada foi de natureza qualitativa e interpretativa, com a realização de estudos de caso de duas professoras de Matemática que utilizavam a calculadora gráfica. A recolha de dados foi concretizada através de entrevistas semi-estruturadas, observação de aulas e recolha documental, sendo a análise de dados orientada pelo quadro teórico, conciliado com a interpretação destes. As conclusões do estudo sugerem alguma diversidade tanto nas características das tarefas em que as professoras recorrem à tecnologia (exercícios, explorações, problemas, modelação de situações reais), como no papel que lhe é atribuído (obter informação, efectuar cálculos, experimentar), mas apontam também para uma diversidade com características que se traduzem em perfis de utilização da tecnologia distintos: um mais exploratório e outro mais prescritivo.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Knowledge for Teaching Mathematics with Technology - a new framework of teacher knowledge</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.pme2013.de/en/contributions/print-on-demand-proceedings</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">PME</style></publisher><pub-location><style face="normal" font="default" size="100%">Kiel, Germany</style></pub-location><pages><style face="normal" font="default" size="100%">105-112</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Knowledge for Teaching Mathematics with Technology (KTMT) is a theoretical model that seeks to articulate previously existing models on professional knowledge and the conclusions that the investigation around the integration of technology has achieved. KTMT is a dynamic knowledge, informed by the practice, that develops from the knowledge on the base domains (Mathematics, Teaching and Learning, Technology and Curriculum), evolving as knowledge in the base domains interacts and as this promotes the development of inter-domain knowledge, which continue to interact, strengthening relations and leading to the development of an integrated knowledge, where knowledge on the base domains and on the two sets of inter-domains appears deeply integrated into a global knowledge.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teacher knowledge and the implementation of  investigation tasks</style></title><secondary-title><style face="normal" font="default" size="100%"> Proceedings  of the 37th Conference of the International Group for the Psychology  of Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.pme2013.de/en/contributions/print-on-demand-proceedings</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">PME</style></publisher><pub-location><style face="normal" font="default" size="100%">Kiel, Germany</style></pub-location><pages><style face="normal" font="default" size="100%">258</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author><author><style face="normal" font="default" size="100%">Oitavem, I.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A mudança que abala o mundo – Editorial</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><pages><style face="normal" font="default" size="100%">1</style></pages><issue><style face="normal" font="default" size="100%">116</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O recurso a diferentes representações no ensino das funções com o apoio da tecnologia</style></title><secondary-title><style face="normal" font="default" size="100%">Actas do XXIII SIEM – Seminário de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><publisher><style face="normal" font="default" size="100%">APM</style></publisher><pub-location><style face="normal" font="default" size="100%">Coimbra, Portugal</style></pub-location><pages><style face="normal" font="default" size="100%">365-376</style></pages></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A calculadora gráfica e a utilização que delas fazemos</style></title><secondary-title><style face="normal" font="default" size="100%">Educação e Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><pages><style face="normal" font="default" size="100%">41-42</style></pages><issue><style face="normal" font="default" size="100%">112</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A calculadora gráfica no ensino das funções: implicações sobre aspectos da prática de uma professora</style></title><secondary-title><style face="normal" font="default" size="100%">Actas do EIEM – Encontro de Investigação em Educação Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><publisher><style face="normal" font="default" size="100%">SPIEM</style></publisher><pub-location><style face="normal" font="default" size="100%">Póvoa do Varzim, Portugal</style></pub-location></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Rocha, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Teachers’ use of graphing calculators in high school mathematics classroom</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of CERME 7 – Seventh Congress of European Research in Mathematics Education</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><pub-location><style face="normal" font="default" size="100%">Rzezów, Poland</style></pub-location></record></records></xml>