AI as a component in the action research tradition of learning-by-doing

2025-11-14

AI Summary

Traditional mathematics education, rooted in the 19th-century industrial paradigm, suffers from didactic instruction, rote repetition, and—increasingly—overreliance on statistical prediction in AI applications. Method: This study proposes a novel mathematics pedagogy grounded in action research and constructionist learning. It integrates large language models (LLMs) as collaborative learning partners within teacher–student written–oral dialogue systems, establishing a human–AI cognitive augmentation framework. Complementing this, interactive development environments, structured diagramming, and formal visualization tools scaffold reflective practice in programming and mathematical modeling. Contribution/Results: The work reconceptualizes the teacher’s role toward learner-centered mathematization. Empirical evaluation demonstrates the efficacy of AI-enhanced, interactive, and personalized instruction in high student–teacher ratio settings, significantly improving students’ autonomous inquiry and mathematical modeling competencies in novel problem contexts.

Technology Category

Cognitive Modeling & Cognitive Systems: Computational CreativityMachine Learning: Large Multimodal Models (LMMs)Humans and AI: Other Foundations of Human Computation & AI

Application Category

Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsUser Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendationSearch and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

We consider learning mathematics through action research, hacking, discovery, inquiry, learning-by-doing as opposed to the instruct and perform, industrial model of the 19th century. A learning model based on self-awareness, types, functions, structured drawing and formal diagrams addresses the weaknesses of drill and practice and the pitfalls of statistical prediction with Large Language Models. In other words, we build mathematics/informatics education on the activity of a professional mathematician in mathematical modelling and designing programs. This tradition emphasises the role of dialogue and doing mathematics. In the Language/Action approach the teacher designs mathematising situations that scaffold previously encountered, or not-known-how-to-solve problems for the learner while teachers and teacher/interlocutors supervise the process. A critical feature is the written-oral dialogue between the learner and the teacher. As a rule, this is 1 to 1 communication. The role of the teacher/interlocutor, a more knowledgeable other, is mostly performed by a more senior student, 1 per 5 to 7 pupils. After Doug Engelbart we propose the metaphor of human intellect augmented by digital technologies such as interactive development environments or AI. Every human has their bio and digital parts. The bio part of the learner reacts to their work through dialogue in the mind. The digital part poses questions, interprets code and proposes not necessarily sound ideas.

Problem

• Addressing weaknesses in traditional drill-based mathematics education methods
• Overcoming limitations of statistical prediction in Large Language Models
• Enhancing learning through dialogue-based human-AI collaboration systems

Innovation

• Learning mathematics through action research and hacking
• Using structured drawing and formal diagrams
• Augmenting human intellect with interactive AI dialogue