AI as a component in the action research tradition of learning-by-doing
Ian Benson, Alexei Semenov
TL;DR
This paper argues for integrating AI as a collaborative component within an action-research framework for learning mathematics by doing. It weaves together Language/Action theory, mathematics circles, and historical action-research traditions (Cuisenaire-Gattegno) with computational tools (Haskell-type systems, interactive development environments) to reimagine math education beyond instruct-and-perform pedagogy. By foregrounding dialogic practice, equivalence through transformation, and co-design between teachers and researchers, it proposes a learning network that uses AI agents as questions and reasoning partners while maintaining rigorous verification via interactive tools. The proposed model aims to raise mathematical thinking in mass schooling by embedding computation, formal vocabulary, and reflective dialogue, ultimately elevating teacher agency and enabling scalable, co-designed curriculum evolution across circles and pilot schools.
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.