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In Press
Coelho, T., and H. Rocha. "Conhecimento profissional interdisciplinar: divergências e convergências de dois modelos." RISTI - Revista Ibérica de Sistemas e Tecnologias de Informação (In Press).
Capone, R., E. Faggiano, H. Rocha, and M. Bernardi Exploring pre-service Mathematics teachers' perceptions of generative AI in Mathematics Education: A pilot study. ICMET – International Conference on Math Education and Technology., In Press.
Giglione, S., E. Faggiano, and H. Rocha Investigating the impact of technology integration on Italian and Portuguese teachers’ perspectives concerning standardized assessment. MEDA – Mathematics Education at the Digital Age., In Press.
Rocha, H. Knowledge to teach mathematics with technology: the global model. ICMET – International Conference on Math Education and Technology., In Press.
Botelho, M. C., and H. Rocha. "O conhecimento profissional do professor na mobilização de diferentes representações com diferentes tecnologias." RISTI - Revista Ibérica de Sistemas e Tecnologias de Informação (In Press).
Faggiano, E., H. Rocha, and R. Capone Pre-service teachers’ initial use of generative AI as a tool to design and implement teaching activities. ISYDE – Italian Symposium on Digital Education., In Press.
Botelho, M. C., and H. Rocha Representational fluency of the mathematics teacher and the integration of different technologies. ICMET – International Conference on Math Education and Technology., In Press.
Botelho, M. C., and H. Rocha The role of teachers’ knowledge and the use of different technologies in the classroom. MEDA – Mathematics Education at the Digital Age., In Press.
Teixeira, P., H. Rocha, and C. Martins Systematic literature review: limitations and difficulties of the STEAM approach. ICMET – International Conference on Math Education and Technology., In Press.
Rocha, H. The use of the TPACK framework on research about teachers’ knowledge to teach with digital technology. MEDA – Mathematics Education at the Digital Age., In Press.
Sacristán, A., E. Faggiano, M. Santacruz-Rodríguez, and H. Rocha. "Policies and implementations for technology use in mathematics education: perspectives from around the world." Handbook of digital resources in mathematics education. Springer, 2024. 1-35. Abstract

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.

Rocha, H., F. Viseu, and S. Matos. "Problem solving in a real-life context: an approach during the learning of inequalities." European Journal of Science and Mathematics Education. 12.1 (2024). AbstractWebsite

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.

Rocha, H., and A. Babo. "Problem-solving and mathematical competence: a look to the relation during the study of Linear Programming." Thinking Skills and Creativity. 51 (2024): 1-14. AbstractWebsite

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.

Faggiano, E., A. Sacristán, H. Rocha, and M. Santacruz-Rodríguez Addressing the congruence and similarity of figures with technology: A cross-national comparison. ICTMT., 2023.
Rocha, H. "Analyzing teachers’ knowledge based on their approach to the information provided by technology." European Journal of Science and Mathematics Education. 11.1 (2023): 132-145. AbstractWebsite

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.

Ferreira, G., H. Rocha, and A. Rodrigues As conexões matemáticas na resolução de problemas. Atas do EIEM 2023 - Encontro em Investigação em Educação Matemática. Aveiro: SPIEM, 2023.
Botelho, M. C., T. Coelho, and H. Rocha Fluência representacional: a Matemática na resolução de problemas de Física. Atas do EIEM 2023 – Encontro em Investigação em Educação Matemática. Aveiro: SPIEM, 2023.
Martins, R., F. Viseu, and H. Rocha. "Functional Thinking: A Study with 10th-Grade Students." Education Sciences. 13.4 (2023): 1-22. AbstractWebsite

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.