Eye movements in the development of geometric shape recognition: from sensory-motor processes to theoretical perception

Efficient recognition of geometric shapes is an important aspect of proficiency in geometry. Building theoretically on the cultural-historical approach enriched by the physiology of activity, we investigate theoretical perception in geometry—the ability to recognize conceptual geometric aspects of visual figures. Aiming to understand the development of theoretical perception, we investigate how sensory-motor processes of eye movements differ between adults and children when perceiving geometric figures. In an empirical study, we explored the variety of perceptual strategies used by first-grade students and compared them with the adults’ perception. The results reveal the contraction of eye movements: with growing expertise, foveal analysis—namely, an inspection of the figures by directing the gaze to their parts—is substituted by extrafoveal analysis—namely, perceiving without looking directly. The variety of the observed children’s perceptual strategies demonstrates that theoretical perception of different figures is heterogeneous. From the suggested theoretical perspective, the direct foveal inspection of particular figures is critical for the development of general anticipatory images of geometric shapes. Our theoretical analysis and empirical findings lead to distinguishing several functions of sensory-motor processes in theoretical perception in geometry. Those functions include positioning the retina in the best way for the comparison of sensory feedback with the geometric shape’s anticipatory image, advancing an anticipatory image based on visual experience, and regulating covert attention. All of these functions need to be taken into account when interpreting the results of eye-tracking studies in mathematics education research. Notably, our research highlights the limitations of the eye-mind hypothesis: direct fixations on a figure are not always needed for its theoretical perception and, the other way around, a fixation position may indicate the comparison of a broad extrafoveal region with an anticipatory image.