Automatically Inferring Teachers' Geometric Content Knowledge: A Skills Based Approach

2026-04-16 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

A new study introduces an automated method for assessing teachers' geometric content knowledge, specifically their Van Hiele reasoning levels, using large language models (LLMs). This approach addresses the scalability issues of traditional manual expert analysis. Researchers developed a structured skills dictionary, decomposing the five Van Hiele levels into 33 fine-grained reasoning skills. They collected 226 open-ended geometry problem responses from 31 pre-service teachers via a custom web platform, which were then expert-annotated with Van Hiele levels and demonstrated skills. Two classification methods, Retrieval-Augmented Generation (RAG) and Multi-Task Learning (MTL), were implemented with both skills-aware and baseline variants. For both RAG and MTL, the skills-aware variants, which incorporated the skills dictionary, significantly outperformed their respective baselines across multiple evaluation metrics, demonstrating the value of explicit skills information in improving Van Hiele classification.

Key takeaway

For mathematics education researchers and professional development specialists, this automated Van Hiele assessment method offers a scalable solution to evaluate teachers' geometric reasoning. You should consider integrating skills-aware LLM approaches into your assessment frameworks to enable large-scale evaluation and support adaptive, personalized teacher learning systems, moving beyond time-consuming manual analysis.

Key insights

Integrating explicit skills information significantly improves LLM-based classification of teachers' Van Hiele geometric reasoning levels.

Principles

• Van Hiele levels are hierarchical and reflect instructional experience.
• Accurate assessment requires evaluating specific skills, not just correctness.

Method

An automated Van Hiele classification method uses LLMs, a 33-skill dictionary, and either Retrieval-Augmented Generation (RAG) or Multi-Task Learning (MTL) on expert-annotated teacher responses.

In practice

• Use skills dictionaries to guide LLM assessment of hierarchical learning.
• Employ RAG or MTL for robust, scalable educational assessment.

Topics

• Van Hiele Model
• Geometric Reasoning Assessment
• Large Language Models
• Retrieval-Augmented Generation
• Multi-Task Learning

Code references

• zivfenig/Van-Hiele-Level-Classification

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.