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.
Jodi Fasteen, Neuberger Hall, Room 326, 724 SW Harrison Street, Portland, OR 97207-0751; firstname.lastname@example.org
Kathleen Melhuish, Neuberger Hall, Room M428, 724 SW Harrison Street, Portland, OR 97207-0751; email@example.com
Eva Thanheiser, Neuberger Hall, Room 323, 724 SW Harrison Street, Portland, OR 97207-0751; firstname.lastname@example.org