Analysis of Mathematical Reasoning Tasks in Grade 8 Mathematics Textbooks: A Perspective on Opportunities for Reasoning and Proving

Source abstract

This study aimed to investigate how opportunities for reasoning and proving (ORP) are provided in Grade 8 mathematics textbooks. Focusing on opportunities for learning logic as a meta-discourse of proof, this study applied Weingarden & Buchbinder’s (2026) task characteristics framework to analyze the ORP embedded in intended reasoning tasks. As a result, the tasks were classified through cluster analysis into four types: ‘Limited ORP’, ‘Mathematical-reasoning ORP’, ‘Mathematical process-reasoning integrated ORP’, and ‘Fully-integrated ORP’. Although ‘Fully-integrated ORP’ tasks were the least frequent, they appeared across all content domains and mainly addressed topics prone to misconceptions or conceptual transitions. These tasks mainly involved quantified statements, requiring students to evaluate the universal validity of statements or the sufficiency of conditions and to provide counterexamples for refutation, thereby offering opportunities to learn the logical aspects of proof. This study contributes by refining the original ‘Mathematical-reasoning ORP’ proposed by Weingarden & Buchbinder (2026) into two types: ‘Mathematical-reasoning ORP’ and ‘Mathematical process-reasoning integrated ORP’. The findings also show that opportunities for learning logic are provided across all content domains at an informal level. These results provide a basis for strengthening the connection between Grade 8 mathematics and High School Common Mathematics 2 and for supporting teachers in analyzing and adapting textbook tasks to provide richer opportunities for reasoning and proving.