Developing an integrated framework for analyzing ways of reasoning in mathematics

Abstract

Mathematics education literature involves studies that sought a way of investigating the mode of reasoning in mathematics textbooks because textbooks are the main resource for teachers in planning their mathematics lessons. In this vein, this study aimed to analyze the ways of reasoning in mathematics textbooks that are currently used in five countries: Slovakia, Czech Republic, Italy, Norway, and Turkiye, as a part of a Horizon 2020 Project. We initially started with a framework that aimed to examine the effect of teachers’ participation in the lesson study on the improvement of students’ mathematical reasoning (Project LESSAM). However, as the textbook analysis of different countries proceeded, we realized that this framework would not solely be sufficient to address the types of reasoning with alternative tasks presented in those textbooks. Thus, our framework development followed four main steps: (1) starting with a proposed framework that focused on different types of reasoning (2) identification of reasoning and proof tasks among worked examples, (3) categorization of ways of reasoning through the proposed framework, and (4) developing new categories based on a review of existing frameworks, to cover and differentiate all types of reasoning in the worked examples. Hence, in this study, we aim to present the integrated framework that we developed to analyze the ways of reasoning in worked examples (the problems with explained solutions) in the above-mentioned countries’ textbooks. We also discuss future research agenda for analyzing mathematics textbooks with this integrated framework.