Dependence-based image-role taxonomy for visual math items¶

Theory · All theories
Evidence · no claims cited

Description¶

The article operationalizes a four-code taxonomy of image roles in math problems: REQUIRED, USEFUL, NOTREQUIRED, and INSUFFICIENT. An item is REQUIRED when "At least one task-critical quantity, relation, label, or structural constraint is present only in the image and cannot be recovered from the text alone without inventing information"; USEFUL items are solvable from text with a redundant-but-helpful figure. A conservative flag-then-review refinement downgraded six items, yielding 376 Required items of 541 image-containing items (69.5%). An independent second-rater audit (n=153) yielded 88.2% agreement with Cohen's κ=0.764 on the Required-vs-non-Required boundary.

Design Implications¶

Context¶

Requirements¶

• A frozen operational codebook applied before reliability auditing, with decision rules documented and disagreements reported via confusion matrices

Constraints¶

• Image-role labeling necessarily involves judgment; labels are treated as operational categories rather than objective ground truth, and disagreements concentrated near the Required–Useful boundary

Target Learners¶

• middle-school mathematics students (Grades 6–8)

Target Learning Objectives¶

• determining which math problems require visual information for a unique solution

Claims¶

Related Theories¶

Examples¶

• Gold and ultra-gold benchmark subsets of consistently solved image-Required items
• Use refusal-first behavior and description-substitution experiments to support accessible visual math

Key Sources¶

• Croteau, E., & Heffernan, N. (2026). Seeing Is Solving: MLLMs, Reasoning, and Refusal in Visual Math. https://osf.io/ct7bg/