← 研踪 PaperTrailarXiv:2611.13368 · v1
Ender: Visual Scaffolding for Geometric Proof Comprehension
首次提交 2026-11-10 07:44
版本更新 2026-11-10 07:44
雷达观测 2026-11-11 11:04
摘要
Geometric proof is a foundational but notoriously difficult topic in secondary mathematics, primarily due to the high cognitive load required to integrate visual diagrams with logical text. As proofs evolve, tracking the initial givens and an expanding set of derived truths can easily overwhelm working memory. While established scaffolding techniques are often visual and diagram-based, current digital learning environments mostly rely on static, text-heavy interfaces that force students to manage these complex mental models on their own. This paper introduces Ender, an interactive rendering system designed to visualize the logical status of two-column proofs. Ender's design is grounded in four literature-derived requirements: (1) diagram annotation, (2) structural tracing, (3) support for partial or incorrect work, and (4) synchronization between the diagram and text. To evaluate the system, we conducted a between-subjects, think-aloud experiment with 12 secondary school students in the United States, comparing Ender against a traditional digital proof interface. Our results indicate that students using Ender performed significantly better on proof comprehension tasks--specifically in identifying and correcting logical errors. These findings suggest that dynamic visual scaffolding may ease the working memory burden of digital interfaces, offering a promising building block for future AI-based proof tutoring systems.
作者备注：10 pages, 7 figures
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v1 · 2026-11-10 07:44 · 最新观测版本
Ender: Visual Scaffolding for Geometric Proof Comprehension
Geometric proof is a foundational but notoriously difficult topic in secondary mathematics, primarily due to the high cognitive load required to integrate visual diagrams with logical text. As proofs evolve, tracking the initial givens and an expanding set of derived truths can easily overwhelm working memory. While established scaffolding techniques are often visual and diagram-based, current digital learning environments mostly rely on static, text-heavy interfaces that force students to manage these complex mental models on their own. This paper introduces Ender, an interactive rendering system designed to visualize the logical status of two-column proofs. Ender's design is grounded in four literature-derived requirements: (1) diagram annotation, (2) structural tracing, (3) support for partial or incorrect work, and (4) synchronization between the diagram and text. To evaluate the system, we conducted a between-subjects, think-aloud experiment with 12 secondary school students in the United States, comparing Ender against a traditional digital proof interface. Our results indicate that students using Ender performed significantly better on proof comprehension tasks--specifically in identifying and correcting logical errors. These findings suggest that dynamic visual scaffolding may ease the working memory burden of digital interfaces, offering a promising building block for future AI-based proof tutoring systems.
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