Abstract
This commentary reviews each of the three content chapters in the integers section and offers questions to promote further discussion. In addition to the themes raised in the three chapters, I introduce the role of formal mathematical structure in generalizing systems of number, from natural numbers to integers, and analogously, from real numbers to complex numbers. Integers, in particular, are structured by algebraic relations, which imply, for example, that (−1) ⋅ (−1) = 1. Historical observations and anecdotal evidence of children’s reasoning pertaining to this role raise important cognitive, pedagogical, and metaphysical questions.
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Harel, G. (2019). Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and Instruction. In: Norton, A., Alibali, M.W. (eds) Constructing Number. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-00491-0_15
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