Helena Rocha

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.

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.

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
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.

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
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.

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.

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.

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.

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.

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:
How is the students’ mathematical competence characterized in relation to problemsolving;
What differences can be identified in the resolutions at different moments of the teaching and learning process.
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.

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.

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.

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.