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Arithmetic Pedagogy for Language Models (arxiv.org)
1 point by berlianta 122 days ago | hide | past | pdf | discuss on HN

In plain words: A small language model is taught arithmetic by training on written-out solutions that follow an Indonesian left-to-right method, matching the order words are generated. It then answers over 80% of new problems correctly, rivaling much larger models.

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.

Andhika Bernard Lumbantobing, Hokky Situngkir
arXiv:2606.05106 · cs.CL, cs.AI, cs.CY · submitted Jun 3, 2026
abstract · pdf · html · 18 pages, 6 figures

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