# Do prototypical constructions and self-attributes of presented drawings affect the construction and validation of proofs?

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## Abstract

This study investigated the effects of students’ constructions of geometrical concepts related to the circle on their construction and validation of proofs. The participants were 110 high school students. A questionnaire was administered; both qualitative and quantitative methods were used to analyze the results. Afterwards, in-depth interviews were conducted with some of the participants. The findings from the interviews enriched and strengthened the findings from the questionnaire. Together, the findings highlight the impact of two factors on the ability to construct or evaluate proofs: (1) the use of the self-attributes of a single presented drawing instead of the critical attributes of the concept; and (2) the use of prototypical or non-prototypical examples. In this study, the position of the drawing attached to the assignment affected students’ construction of proofs.

## Keywords

Concept image Drawing Geometrical concepts Proofs Prototypical examples## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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