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

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^{1}Centre for Applied Research on Education, Amsterdam University of Applied Sciences, Amsterdam, The Netherlands

^{2}Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands

^{*}Corresponding Author

EUR J SCI MATH ED, Volume 7, Issue 3, pp. 109-136.
https://doi.org/10.30935/scimath/9538

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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.

## CITATION

Palha, S., & Spandaw, J. (2019). The integral as accumulation function approach: A proposal of a learning sequence for collaborative reasoning.

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