Mathematical reasoning in linear systems learning: a higher education exploratory teaching experiment with prospective teachers

Abstract

Higher education students show difficulties on concepts in linear systems, due to procedural-dominated teaching practices. This emphasizes the need to develop students’ mathematical reasoning using an exploratory teaching approach to promote learning with understanding. This qualitative and interpretative study analyzes the mathematical reasoning that prospective teachers, attending the degree in mathematics, use in solving research tasks involving linear systems, proposed throughout an exploratory teaching experiment and how this context contribute to their learning. Data collection includes participant observation of the teaching experiment classes, and written work of the proposed tasks. The results show that prospective teachers have evolved positively in their understanding and capacity of mathematical reasoning, and in the linear systems learning. The evidenced advantages of this experiment may contribute to a reflection on this integration to improve educational contexts, including preservice teacher education, to overcome their difficulties in learning and develop their knowledge for teaching.