The integral as accumulation function approach
A proposal of a learning sequence for collaborative reasoning
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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‐accumulationfunction
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.