Using Algebraic Language with Understanding: The Role of Conjectures, Generalizations, and Justifications

Kelly Aguiar; João Pedro Mendes  da Ponte; Marisa Alexandra Ferreira Quaresma

doi:10.35763/aiem29.7118

Authors

Kelly Aguiar Instituto Superior de Educação e Ciências, ISEC Lisboa https://orcid.org/0000-0002-8516-9715
João Pedro Mendes da Ponte Instituto Superior de Educação e Ciências, ISEC Lisboa https://orcid.org/0000-0001-6203-7616
Marisa Alexandra Ferreira Quaresma Instituto Superior de Educação e Ciências, ISEC Lisboa https://orcid.org/0000-0002-0861-6016

DOI:

https://doi.org/10.35763/aiem29.7118

Keywords:

Algebra, Generalizations, Justifications, Learning, Mathematical reasoning

Supporting Agencies

Fundação para a Ciência e Tecnologia (2020.08843.BD)

Abstract

This article aims to address the following research question: what relationships exist between the formulation of conjectures, generalizations, and justifications and students’ use of algebraic language with understanding? Drawing on a teaching experiment and adopting a qualitative and interpretative perspective, data are collected through students’ written and oral answers during classroom work and in interviews. The results show that conjectures, generalizations, and justifications play a fundamental role in reflecting on the meanings of algebraic symbols and on how these can express mathematical relations. Promoting these reasoning processes supports students in assigning meaning to algebraic symbols from multiple perspectives, thereby contributing to the use of algebraic language with understanding.

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