Arithmetic Pedagogy for Language Models

Problem
This work addresses the gap in the literature regarding the application of human pedagogical methods to improve arithmetic reasoning in language models. Specifically, it investigates whether structured teaching techniques can enhance the training of models like GPT-2 for arithmetic tasks. The authors note that existing models often struggle with basic arithmetic, and this preprint seeks to fill that gap by leveraging pedagogical insights from human education.

Method
The authors propose a novel training methodology based on the GASING method, an Indonesian pedagogical approach that emphasizes a left-to-right computational procedure for solving arithmetic problems. They operationalize arithmetic operations as computational procedures, generating a serialized execution trace that serves as Chain-of-Thought (CoT) supervision. The model used is a small GPT-2 decoder with 86 million parameters, trained from scratch using a next-token prediction objective. The training dataset consists of arithmetic problems formatted to align with the GASING method. The authors monitor the training process, identifying three distinct learning phases: initial procedural pathway internalization, development of associative “mental-arithmetic” capabilities, and retrieval of intermediate results without explicit computation. Mechanistic analyses, including attention-masking interventions and logit-lens inspections, are employed to understand the model’s learning dynamics.

Results
The trained model achieves over 80% accuracy on held-out arithmetic problems, demonstrating significant performance improvements compared to baseline models. Notably, it competes effectively against larger language models, indicating that pedagogically informed training can yield strong arithmetic capabilities even at a smaller scale. The results suggest that the integration of structured pedagogical methods can lead to enhanced reasoning abilities in language models, with implications for future model training strategies.

Limitations
The authors acknowledge that their approach is limited to basic arithmetic and may not generalize to more complex mathematical reasoning tasks. Additionally, the reliance on a specific pedagogical framework (GASING) may restrict the applicability of their findings to other educational contexts or languages. The study is also a preprint, which means it has not undergone peer review, and the findings should be interpreted with caution until validated by the broader research community.

Why it matters
This research has significant implications for the development of language models, particularly in educational contexts where arithmetic reasoning is essential. By demonstrating that pedagogically grounded training can enhance model performance, the authors provide a framework for future research to explore similar methodologies across various domains. This work suggests that integrating human teaching strategies into machine learning can lead to more efficient and effective training processes, as discussed in related literature on pedagogical approaches in AI, available on arXiv.