# To see or not to see: analyzing difficulties in geometry from the perspective of visual perception

## Abstract

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual organization: Gestalt principles, (2) recognition: bottom-up and top-down processing; and (3) representation of perception-based knowledge: verbal vs. pictorial representation, mental images and hierarchical structure of images. Examples given in the paper were mostly taken from Gal's study (2005) which aimed at identifying and analyzing Problematic Learning Situations (after Gal & Linchevski, 2000) in junior high school geometry classes. Gal's study (2005) suggests that while this theoretical perspective became part of teachers' pedagogic content knowledge, the teachers were aware of their students' thinking processes and their ability to analyze and cope with their students’ difficulties in geometry was improved.

## Keywords

Visualization Visual perception Visual perception processing Geometry Problematic learning situation Teacher preparation## Notes

### Acknowledgement

We are grateful to Prof. Shimon Ullman, from Weizmann Institute, Israel, for reading an earlier version of this paper and providing us with his comments and suggestions. We are also grateful to the anonymous reviewers who read the paper and gave us important comments, which were used to improve the paper.

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