An A Priori Measure of Visual Difficulty of 2-D Sketches Depicting 3-D Objects

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  • 1 Faculty of Education in Science and Technology, Technion - Israel Institute of Technology, Israel;
  • | 2 Faculty of Mathematics, Technion - Israel Institute of Technology,, Israel;
  • | 3 Department of Science Education, Weizmann Institute of Science, Rehovot, Israel;

Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on two attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). The difficulty of 12 normatively oriented cube-related sketches was theoretically ranked according to their ratios, #PHI/#PMI. The ranking was compared to the actual visual difficulty as measured by the percentage of correct or desired comprehension, individual spatial ability, and study-time allocation. This procedure was repeated for unnormatively oriented sketches, obtained by vertically flipping the original sketches. In both cases, the findings substantiate #PHI/#PMI as an a priori measure of visual difficulty. Practical, theoretical, and methodological implications are inspected and discussed.

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Journal for Research in Mathematics Education


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