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Preservice teachers’ use of contrasting cases in mathematics instruction


Drawing comparisons between students’ alternative solution strategies to a single mathematics problem is a powerful yet challenging instructional practice. We examined 80 preservice teachers’ when asked to design a short lesson when given a problem and two student solutions—one correct and one incorrect. These micro-teaching events were videotaped and coded, revealing that fewer than half of participants (43%) made any explicit comparison or contrasts between the two solution strategies. Those who did were still not likely to use additional support strategies to draw students’ attention to key elements of the comparison. Further, correlations suggest that participants’ mathematical content knowledge may be related to whether participants’ showed contrasting cases but not to whether they used specific pedagogical cues to support those comparisons. While these micro-teaching events differ from the interactive constraints of a classroom, they reveal that participants did not immediately orient toward differing student solutions as a discussion opportunity, and that future instruction on contrasting cases must highlight the utility of this practice.

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    Please note that because the prompt was originally an item on the CKT-M assessment form b, the student solutions cannot be provided publicly. For more information see Hill et al. (2005, 2008).


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This work was supported by a National Science Foundation CAREER Award to the second author, NSF#0954222, and an NSF Science of Learning Center, SPE 0541957. We would like to thank the three anonymous reviewers for their feedback on previous versions on this paper.

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Correspondence to Katerina Schenke.

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Schenke, K., Richland, L.E. Preservice teachers’ use of contrasting cases in mathematics instruction. Instr Sci 45, 311–329 (2017).

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  • Teacher cognition and practices
  • Professional development
  • Mathematics education