Exploring reversible thinking through comparison task in mathematical praxeology textbooks

DOI: https://doi.org/10.34007/jdm.v6i3.2903
Aneu Pebrianti(1), Latifah Darojat(2), Fahmi Nugraha Heryanto(3),


(1) Universitas Singaperbangsa Karawang, Karawang, West Java, Indonesia, 41313
(2) Universitas Singaperbangsa Karawang, Karawang, West Java, Indonesia, 41313
(3) Monash University, Wellington Road, Clayton VIC 3800, Australia

Abstract


The capacity for reversible thinking is a fundamental aspect of proficient mathematical problem-solving. However, existing research indicates that students continue to encounter challenges in cultivating this cognitive process. One contributing factor to this difficulty is the inclination of textbook tasks to prioritize procedural learning over conceptual exploration. The objective of this study was to examine the task sequence structure in seventh-grade mathematics textbooks on the subject of comparison, specifically in two primary tasks: comparing two similar quantities and comparing two quantities with differing units. The textbook analysis technique employs a mathematical praxeology approach. The analysis encompasses four components of praxeology: tasks, techniques, technology, and theory. The textbook utilized is Mathematics, Grade 7, junior high school, Semester 2. The findings reveal that the majority of problem-solving techniques are presented directly within the textbook, thereby restricting students’ opportunities to develop their own strategies, particularly reversible thinking strategies. Furthermore, the majority of tasks are designed to promote forward thinking, thereby limiting students’ opportunities to develop two-way thinking skills. To address this issue, the study recommends formulating an alternative sequence of tasks that explicitly encourages the development of reversible thinking strategies.

Keywords


Reversible thinking; mathematics textbooks; mathematical praxeology; series of task; learning obstacle

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DOI: https://doi.org/10.34007/jdm.v6i3.2903

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DOI: https://doi.org/10.34007/jdm.v6i3.2903

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