Multiplication by 10 base-5: Making Sense of Place Value Structure Through an Alternate Base

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  • 1 Portland State University, Oregon

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 10five 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.

Contributor Notes

Jodi Fasteen, Neuberger Hall, Room 326, 724 SW Harrison Street, Portland, OR 97207-0751; jfasteen@pdx.edu

Kathleen Melhuish, Neuberger Hall, Room M428, 724 SW Harrison Street, Portland, OR 97207-0751; melhuish@pdx.edu

Eva Thanheiser, Neuberger Hall, Room 323, 724 SW Harrison Street, Portland, OR 97207-0751; evat@pdx.edu

(Corresponding author is Fasteen jfasteen@pdx.edu)(Corresponding author is Melhuish melhuish@pdx.edu)(Corresponding author is Thanheiser evat@pdx.edu)
Mathematics Teacher Educator

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