https://salonisnaik.github.io/tags/preprint/PreprintHugo Blox Builder (https://hugoblox.com)en-usSun, 09 Aug 2026 00:00:00 +0000https://salonisnaik.github.io/media/icon_hu_d5771401cc4f5bdb.pnghttps://salonisnaik.github.io/tags/preprint/https://salonisnaik.github.io/preprints/algebra-eyes/Sun, 09 Aug 2026 00:00:00 +0000https://salonisnaik.github.io/preprints/algebra-eyes/<p>Algebra exemplifies the human capacity for abstract, structural reasoning. How do people reason algebraically? One possibility is that algebraic expertise is partly visual: Experts learn to move their eyes strategically in ways that reflect the hierarchical structure of written equations. Alternatively, the structure of written equations might scaffold novice reasoning but matter less for experts. We tested these accounts by tracking eye movements of U.S. undergraduates (N = 60) as they viewed algebraic equations. Greater expertise predicted better performance. When reasoning algebraically, participants’ eye movements mirrored the expressions’ hierarchical structure; critically, this pattern increased with algebraic expertise. Moreover, the link between expertise and performance was explained by whether participants’ eye movements tracked expressions’ hierarchical structure. Thus, despite its highly conceptual and abstract content, algebraic reasoning involves perceptual skill. These results highlight the perceptual and situated aspects of mathematical reasoning, with implications for mathematics education and theories of abstract reasoning.</p>