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Mis-in and mis-out concept images: the case of even numbers

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Abstract

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times “something” (i.e., 2i is an even number), or to reject the evenness of zero. The notion of concept image serves in the analysis of the findings, and the findings serve in offering two refinement notions: mis-in concept images that mistakenly grant non-examples the status of examples (e.g., 2i is an even number), and mis-out concept images that mistakenly regard examples as non-examples (e.g., zero is not an even number). We discuss possible benefits in distinguishing between these two refinement notions in mathematics education.

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The datasets generated during the current study are available from the corresponding author on reasonable request.

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  1. Department of Mathematics, Science and Technology Education, Tel-Aviv University, Tel-Aviv, Israel

    Pessia Tsamir & Dina Tirosh

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  1. Pessia Tsamir
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Correspondence to Dina Tirosh.

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Tsamir, P., Tirosh, D. Mis-in and mis-out concept images: the case of even numbers. Educ Stud Math 112, 207–224 (2023). https://doi.org/10.1007/s10649-022-10183-z

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