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Students’ images of mathematics

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Abstract

Students’ judgments about “what counts” as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as mathematical, and how they make their judgments. Students completed a photo sorting activity; took, viewed, and captioned their own photos of mathematics; viewed and commented on classmates’ photos; and participated in a small group discussion. Across multiple sources of data, findings showed that students attended to two major features of photos and activities when making judgments: surface cues present in the photos, such as numbers and money, and the possibility for mathematical action. Some students looked for the possibility of mathematics, while others asked if mathematics was necessary. Students also gave higher ratings to activities with which they had personal experience. The article concludes with possible implications for practice.

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Notes

  1. The pattern of results is unchanged if parametric statistics are used instead. For the first photo sort, average rating for personal experience (M = 1.5) was greater than that for family experience (M = 1.4) and for no experience (M = 1.2), repeated measures ANOVA, F(2) = 3.99, p < 0.05. The effect is also present (and is slightly stronger) for the second photo sort.

  2. Spelling has been corrected for readability, but punctuation, capitalization, and other aspects of students’ writing have been retained. Comments are presented in the order in which they were made.

  3. Note that Arcavi (2002) presents locating apartments by number as an area where children may fail to notice the potential for mathematics.

  4. The difficulty in seeing math in unfamiliar activities is not unique to schoolchildren. See González et al. (2001) and Fasheh (1991) for reports of mathematicians marveling at, and struggling to understand, the mathematics of sewing.

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  1. School of Education, University of California, Davis, 1 Shields Avenue, Davis, CA, 95616, USA

    Lee Martin & Pamela Gourley-Delaney

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  1. Lee Martin
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  2. Pamela Gourley-Delaney
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Correspondence to Lee Martin.

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Martin, L., Gourley-Delaney, P. Students’ images of mathematics. Instr Sci 42, 595–614 (2014). https://doi.org/10.1007/s11251-013-9293-2

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