Abstract:

Doing mathematics is based on reasoning that may be enacted in different ways, such as deductive and inductive reasoning (Stacey & Vincent, 2009). Therefore, mathematics education researchers put their attention to identifying different modes of reasoning that textbook problems conveyed (e.g., Bieda et al., 2014; Silverman & Even, 2015; Stacey & Vincent, 2009). In those studies, the researchers not only examined the reasoning and proof tasks in textbooks but also aimed to classify ways of argumentation and reasoning involved in the tasks. For instance, Stacey and Vincent (2009) examined the reasoning in nine Australian 8th-grade textbooks in which they identified seven modes of reasoning. These modes formed a classification scheme that both refined and extended previous schemes of Blum and Kirsch (1991), Sierpinska (1994), and Harel and Sowder (2007). In another study, Stylianides (2008) focused on reasoning and proof tasks and developed a framework that could be used as an analysis tool in textbook analysis and as an instructional tool in teacher professional development sessions. In this framework, they particularly looked for ways of making mathematical generalizations and providing support to mathematical claims. Utilizing this framework, Bieda et al. (2014) analyzed seven 5th grade mathematics textbooks published in the U.S. and found that only 3.7% of the tasks in the textbook were reasoning-and-proving tasks, and those mostly involved making and justifying claims empirically. Those studies and many others 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 (Remillard & Heck, 2014).

Following the steps of those researchers in this area, we 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 (for details, see: 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 presentation, 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 counties’ textbooks. We also discuss our future research agenda for further analysis of mathematics textbooks with this integrated framework.

Acknowledgment:
The paper was financially supported by the project 951822 Enhancement of research excellence in Mathematics Teacher Knowledge-MaTeK by H2020. We also thank Jarmila Novotná and Jakub Michal (Czech Republic), Tünde Kiss (Slovakia) and others who have contributed to this study.

Keywords:

Mathematics education, ways of reasoning, mathematics worked examples, mathematics textbook analysis.