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Mathematics -- Study and teaching -- Standards, Mathematics -- Study and teaching (Elementary)


This study was designed to investigate preservice elementary school teachers’ (PSTs’) responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs’ conceptions, two correct and two incorrect. Previous findings are replicated for PSTs toward the end of their college careers, and two conceptions are further analyzed to yield three categories of incorrect views of regrouped digits: (a) consistently as 1 value (all as 1 or all as 10), (b) consistently within but not across contexts (i.e., all as 10 in addition but all as 1 in subtraction), and (c) inconsistently (depending on the task).


this is the author’s version of a work that was accepted for publication in Educational Studies in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Educational Studies in Mathematics, December 2010, Volume 75, Issue 3, pp 241-251. The final publication is available at



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