Visual Displays, Actions, and Purposes: Patterns of 12th‐Grade Students' Visual Reasoning in a Circle‐Based Geometric Task

ABSTRACT This study examines the visual reasoning reflected in the written solutions of 12th‐grade students in the context of a circle‐based task requiring the creation of visual displays. Students' visual reasoning was analyzed in terms of visual display, visual action, and visual purpose. The dataset consisted of 228 students' written solutions and was analyzed using inductive content analysis. The findings indicate that static geometric structures were more frequently represented than relational visual structures in students' written solutions. Evidence of visual actions varied across action categories, with comparison and equal‐partitioning actions occurring more frequently than quantification and comparisons involving different positions of point P . In terms of the visual purpose component, the written solutions contained evidence of both angle‐determination and generalization purposes, with qualitative generalizations more prevalent than explicit rule construction. The findings generally indicate that the components of visual display, visual action, and visual purpose occurred in different patterns and at different levels of prevalence across students' written solutions. In light of these results, future research should examine students' visual reasoning using complementary forms of evidence, including tasks supported by dynamic geometry software or visually oriented activities targeting different areas of mathematics learning.