Analysis of Teaching and Learning Situations in Algebra in Prospective Teacher Education


  • Neusa Branco Instituto Politécnico de Santarém & Universidade de Lisboa
  • João Pedro da Ponte Universidade de Lisboa



Teacher education, Algebra, Algebraic thinking, Mathematics, Teaching experiment


This paper presents a teacher education experiment that was conducted in an algebra course based on an exploratory approach and articulating content and pedagogy. We investigate the contribution of analysing teaching and learning situations, namely student answers and episodes of classroom work, in developing the mathematical and teaching knowledge of prospective primary school teachers. We use a design research methodology to probe the prospective teachers’ development after having participated in an experiment in their third year of a primary education degree program. The results show that the prospective teachers’ understanding of algebra and grasp of how to use different representations and strategies grew considerably. The results also show that their didactical knowledge regarding tasks, classroom organization, attention to students’ reasoning, and teacher’s questions grew as well. The variety of tasks proposed to the prospective teachers during the course was of vital importance to this outcome, as was the opportunity to reflect, work with elements of real practice, and participate in whole class discussions.


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Author Biographies

Neusa Branco, Instituto Politécnico de Santarém & Universidade de Lisboa

Neusa Branco is an assistant professor in the Higher School of Education at the Polytechnic Institute of Santarém (Portugal). In the last few years, she has worked on a number of research projects in mathematics education and directed master’s students in education. She co-coordinates an educational program of pre-service elementary and kindergarten teachers. Currently, her main research interests are the teaching and learning of algebra and teacher education for elementary school.

João Pedro da Ponte, Universidade de Lisboa

João Pedro da Ponte is a professor and director of the Institute of Education of the University of Lisbon. Currently, his main research interests are mathematics teaching practices and teacher education, with a special focus on the teaching of algebra, rational numbers and statistics, and developing students’ mathematics reasoning. He coordinated a government report on pre-service teacher education (2006) and a new mathematics curriculum for basic education (2007). He is (co)author of several books, book chapters and articles in national and international journals such as Educational Studies in Mathematics and is associate editor of the Journal of Mathematics Teacher Education.