TY - JOUR

T1 - Reflections on "Multiplication as Original Sin"

T2 - The implications of using a case to help preservice teachers understand invented algorithms

AU - Harkness, Shelly Sheats

AU - Thomas, Jonathan

PY - 2008

Y1 - 2008

N2 - This article describes the use of a case report, Multiplication as original sin (Corwin, R. B. (1989). Multiplication as original sin. Journal of Mathematical Behavior, 8, 223-225), as an assignment in a mathematics course for preservice elementary teachers. In this case study, Corwin described her experience as a 6th grader when she revealed an invented algorithm. Preservice teachers were asked to write reflections and describe why Corwin's invented algorithm worked. The research purpose was: to learn about the preservice teachers' understanding of Corwin's invented multiplication algorithm (its validity); and, to identify thought-provoking issues raised by the preservice teachers. Rather than using mathematical properties to describe the validity of Corwin's invented algorithm, a majority of them relied on procedural and memorized explanations. About 31% of the preservice teachers demonstrated some degree of conceptual understanding of mathematical properties. Preservice teachers also made personal connections to the case report, described Corwin using superlative adjectives, and were critical of her teacher.

AB - This article describes the use of a case report, Multiplication as original sin (Corwin, R. B. (1989). Multiplication as original sin. Journal of Mathematical Behavior, 8, 223-225), as an assignment in a mathematics course for preservice elementary teachers. In this case study, Corwin described her experience as a 6th grader when she revealed an invented algorithm. Preservice teachers were asked to write reflections and describe why Corwin's invented algorithm worked. The research purpose was: to learn about the preservice teachers' understanding of Corwin's invented multiplication algorithm (its validity); and, to identify thought-provoking issues raised by the preservice teachers. Rather than using mathematical properties to describe the validity of Corwin's invented algorithm, a majority of them relied on procedural and memorized explanations. About 31% of the preservice teachers demonstrated some degree of conceptual understanding of mathematical properties. Preservice teachers also made personal connections to the case report, described Corwin using superlative adjectives, and were critical of her teacher.

KW - Case reports

KW - Invented algorithms

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U2 - 10.1016/j.jmathb.2008.07.004

DO - 10.1016/j.jmathb.2008.07.004

M3 - Article

AN - SCOPUS:53349165540

SN - 0732-3123

VL - 27

SP - 128

EP - 137

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

IS - 2

ER -