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Mirin, Alison; Zazkis, Dov – For the Learning of Mathematics, 2020
Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…
Descriptors: Calculus, Mathematics Education, Mathematical Concepts, Problem Sets
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Rumbelow, Michael – For the Learning of Mathematics, 2021
"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…
Descriptors: Arithmetic, Mathematics Instruction, Mathematical Concepts, Figurative Language
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Leron, Uri; Zazkis, Rina – For the Learning of Mathematics, 1986
The relation between mathematical and computational aspects of recursion are discussed and some examples analyzed. Definition, proof, and construction are considered, as well as their counterparts in computer languages (illustrated with Logo procedures). (MNS)
Descriptors: Computation, Computer Oriented Programs, Induction, Mathematical Concepts