2025/11/14 by Ian Benson, Benson, Ian, Semenov, Alexei
Computer Science · Decision Sciences · Social Sciences · #97B50 #97P40 #Chaos, Complexity, and Education #Computers and Society (cs.CY) #FOS: Computer and information sciences #FOS: Mathematics #History and Overview (math.HO) #K.3.2 #Knowledge Management and Technology #Mathematics Education and Teaching Techniques #Programming Languages (cs.PL)
paper · pdf · doi:10.48550/arxiv.2511.11445
openalex publication_date 2025/11/14 · openalex created_date 2025/11/18 · openalex updated_date 2026/07/28
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.