# Arithmetic Pedagogy for Language Models > Source: > Published: 2026-06-04 05:42:56+00:00 # Computer Science > Computation and Language [Submitted on 3 Jun 2026] # Title:Arithmetic Pedagogy for Language Models [View PDF](/pdf/2606.05106) [HTML (experimental)](https://arxiv.org/html/2606.05106v1) 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. ### Current browse context: cs.CL ### References & Citations Loading... # Bibliographic and Citation Tools Bibliographic Explorer *(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer)) Connected Papers *(*[What is Connected Papers?](https://www.connectedpapers.com/about)) Litmaps *(*[What is Litmaps?](https://www.litmaps.co/)) scite Smart Citations *(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article alphaXiv *(*[What is alphaXiv?](https://alphaxiv.org/)) CatalyzeX Code Finder for Papers *(*[What is CatalyzeX?](https://www.catalyzex.com)) DagsHub *(*[What is DagsHub?](https://dagshub.com/)) Gotit.pub *(*[What is GotitPub?](http://gotit.pub/faq)) Hugging Face *(*[What is Huggingface?](https://huggingface.co/huggingface)) ScienceCast *(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos # Recommenders and Search Tools Influence Flower *(*[What are Influence Flowers?](https://influencemap.cmlab.dev/)) CORE Recommender *(*[What is CORE?](https://core.ac.uk/services/recommender))# arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).