A Case Study of Teacher Responses to a Doubling Error and Difficulty in Learning Equivalent Fractions
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2011, 2011 by The Research Council on Mathematics Learning. All rights reserved. This study qualitatively explored teachers responses to doubling errors (e.g., 3/4 2 = 6/8) that typically reflect students difficulties in understanding the rule for finding equivalent fractions (e.g., 3/4 2/2 = 6/8). Although all teachers claimed to teach for understanding in interviews, their responses varied in terms of effectiveness and types. One teacher grasped the doubling error to explain the reasons underlying the rule using symbolic representations only. The other two used concrete representations to explicate the reasons but tended to either prevent or ignore the doubling error. Although these teaching actions appeared different in form, all teachers essentially held the same perception-based perspectives; that is, they either assumed students could see what they saw or students could directly comprehend mathematical ideas through visualizing pictures only. Such perspectives overlook students available mathematical conceptions and might be at the root of the difficulties with those particular teaching strategies.
