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Multiplication by $10_{\text{five}}$: making sense of place value structure through an alternate base. (English)
Math. Teach. Educ. 3, No. 2, 83-98 (2015).
Summary: Prior research has shown that preservice teachers (PSTs) are able to demonstrate procedural fluency with whole number rules and operations, but struggle to explain why these procedures work. Alternate bases provide a context for building conceptual understanding for overly routine rules. In this study, we analyze how PSTs are able to make sense of multiplication by $10_{\text{five}}$ in base five. PSTs’ mathematical activity shifted from a procedurally based concatenated digits approach to an explanation based on the structure of the place value number system.
Classification: F39 F29
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