Abstract
Drawing on Harel’s construct of “intellectual need,” I propose an expansion in possible categories of such needs, to include an “intellectual need for relationships.” This is a need to explain how elements work together, as in a system. Freudenthal's term, “mathematizing,” can describe a category of a way of thinking that can emerge from an intellectual need for relationships. This need can engender students’ quantitative and covariational reasoning, important not only for their mathematical development, but also for being informed citizens. I put forward four facets of an intellectual need for relationships, addressing task design considerations for each: attributes in a situation (What are the things?), measurability of attributes (How can things be measured?), variation in attributes (How do things change?), and relationships between attributes (How do things change together?). I conclude with implications for theory and practice.
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Acknowledgements
U.S. National Science Foundation Grants (DUE-1709903, DUE-2013186) have supported the development and implementation of the Ferris wheel Techtivity. Opinions and conclusions are those of the author. I thank Evan McClintock for his feedback on this manuscript.
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Johnson, H.L. (2022). An Intellectual Need for Relationships: Engendering Students’ Quantitative and Covariational Reasoning. In: Karagöz Akar, G., Zembat, İ.Ö., Arslan, S., Thompson, P.W. (eds) Quantitative Reasoning in Mathematics and Science Education. Mathematics Education in the Digital Era, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-031-14553-7_2
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