Towards functional thinking in elementary mathematics: An analysis of pattern generalization tasks in Korea and U.S. elementary mathematics textbooks
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In mathematics, generalization is undoubtedly important and critical to learning and doing mathematical reasoning and is considered as not only a means contributing to the construction of new knowledge but also the essence of mathematical reasoning. Recent reforms in mathematics education emphasize the importance of fostering functional thinking early from the elementary level, with pattern generalization (PG) recognized as a key pathway toward this goal. However, prior research has highlighted the limited variety and depth of PG opportunities presented in elementary mathematics textbooks, particularly in their support for developing foundational algebraic concepts such as variable and function. In this study, we analyzed PG tasks (PGTs) as represented in Korean elementary textbooks and U.S. elementary textbooks to examine the nature of PG tasks using the Relating Forming-Extending framework (Ellis et al., 2022) for PG activities and another analytic framework for an analysis of the nature of PGT. Results indicate that the nature of PGT is limited in the sense that student’s recursive thinking may not sufficiently be challenged and thus be progressed to functional thinking. These findings highlight the need to reconsider how PGTs are structured in elementary mathematics textbooks in order to better support students’ progression from recursive reasoning to functional thinking.
Abstract
In mathematics, generalization is undoubtedly important and critical to learning and doing mathematical reasoning and is considered as not only a means contributing to the construction of new knowledge but also the essence of mathematical reasoning. Recent reforms in mathematics education emphasize the importance of fostering functional thinking early from the elementary level, with pattern generalization (PG) recognized as a key pathway toward this goal. However, prior research has highlighted the limited variety and depth of PG opportunities presented in elementary mathematics textbooks, particularly in their support for developing foundational algebraic concepts such as variable and function. In this study, we analyzed PG tasks (PGTs) as represented in Korean elementary textbooks and U.S. elementary textbooks to examine the nature of PG tasks using the Relating Forming-Extending framework (Ellis et al., 2022) for PG activities and another analytic framework for an analysis of the nature of PGT. Results indicate that the nature of PGT is limited in the sense that student’s recursive thinking may not sufficiently be challenged and thus be progressed to functional thinking. These findings highlight the need to reconsider how PGTs are structured in elementary mathematics textbooks in order to better support students’ progression from recursive reasoning to functional thinking.