### Abstract

The present study tries to identify the ‘picture in mind’ that students’ have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have identified different ways of considering defining, proving and modelling: superficial, utilitarian and intrinsic, which were maintained by some students for the three elements in the different written representations. This coherence can be perceived as a characteristic of students’ mathematical understanding. Our results provide an analytical scheme whose domain goes beyond the way of students’ approaching to the mathematical elements considered in the study.

### License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 8, Issue 2, 2012, 95-102

https://doi.org/10.12973/eurasia.2012.823a

Publication date: 12 Jan 2012

Article Views: 1600

Article Downloads: 1002

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