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Missing and Mis-in Concept Images of Parallelograms: the Case of Tal

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Abstract

In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students’ concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition–concept image as reported by Tall and Vinner (Educational Studies in Mathematics 12:151–169, 1981), a theory that is widely used in mathematics education. The occurrences during our interviews with one of the first students that we interviewed led us to identify a need to extend this theory. This manuscript suggests to add two new constructs to the theory of concept definition–concept image: missing concept images and mis-in concept images. Missing concept image defines a situation in which an example of a concept is erroneously categorized as a non-example of the concept. Mis-in concept image is the somewhat complementary case, in which a non-example of the concept is mis(takenly) in(cluded) in the set of examples of the concept and consequently this non-example is erroneously identified as an example of the concept. In this manuscript, we introduce these two constructs. We also describe two possible sources of students’ decisions regarding their ways of sorting figures into examples and non-examples of parallelograms that were detected during the interviews. To the best of our knowledge, these sources were not reported in the related literature.

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Authors and Affiliations

  1. Dept. of Mathematics, Science and Technology Education, School of Education, Tel-Aviv University, P.B. 39040, 6997801, Tel Aviv, Israel

    Dina Tirosh & Pessia Tsamir

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  1. Dina Tirosh
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  2. Pessia Tsamir
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Correspondence to Dina Tirosh.

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Tirosh, D., Tsamir, P. Missing and Mis-in Concept Images of Parallelograms: the Case of Tal. Int J of Sci and Math Educ 20, 981–997 (2022). https://doi.org/10.1007/s10763-021-10175-0

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  • DOI: https://doi.org/10.1007/s10763-021-10175-0

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