The integral as accumulation function approach: A proposal of a learning sequence for collaborative reasoning

Sonia Palha, Jeroen Spandaw

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11th grade students’ mathematical thinking and reasoning. The results show that the integral-as-accumulation-function has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.
Original languageEnglish
Pages (from-to)109-136
JournalEuropean Journal of Science and Mathematics Education
Volume7
Issue number3
DOIs
Publication statusPublished - Jul 2019

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