[2606.05106] Arithmetic Pedagogy for Language Models

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Computer Science > Computation and Language

arXiv:2606.05106 (cs)

[Submitted on 3 Jun 2026]

Title:Arithmetic Pedagogy for Language Models

Authors:Andhika Bernard Lumbantobing, Hokky Situngkir<br>View a PDF of the paper titled Arithmetic Pedagogy for Language Models, by Andhika Bernard Lumbantobing and 1 other authors

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Abstract:We investigate whether methods of human mathematics pedagogy can guide the training of language models toward arithmetic reasoning. Building on the GASING method -- an Indonesian pedagogy that solves basic arithmetic through a left-to-right procedure aligned with the causal order of token generation -- we operationalize each operation as a computational procedure whose execution trace is serialized into natural-language Chain-of-Thought (CoT) supervision. A small GPT-2 decoder (86M parameters) with a syllabic-agglutinative TOBA tokenizer for Indonesian is trained from scratch on this data using only a next-token prediction objective, without reinforcement learning or reward-based optimization. Monitoring training reveals three distinct learning phases, and mechanistic analyses -- attention-masking interventions on the CoT information graph, residual-stream probing, and logit-lens inspection -- show that the model first internalizes a procedural pathway and subsequently develops an associative, ``mental-arithmetic'' capacity that retrieves intermediate results without explicit step-by-step computation. The trained model reaches over 80% accuracy on held-out problems and attains competitive performance against substantially larger language models, indicating that targeted, pedagogically grounded training can yield strong and economical arithmetic capability at small scale.

Comments:<br>18 pages, 6 figures

Subjects:

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Computers and Society (cs.CY)

MSC classes:<br>68T05

ACM classes:<br>I.2.6; I.2.7

Report number:<br>BFI Working Paper Series WP-07-2026

Cite as:<br>arXiv:2606.05106 [cs.CL]

(or<br>arXiv:2606.05106v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2606.05106

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Hokky Situngkir [view email]<br>[v1]<br>Wed, 3 Jun 2026 17:09:25 UTC (1,308 KB)

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