A Statistically Validated Large Scale Mathematical Chain of Thought Dataset for Symbolic Reasoning and Large Language Model Benchmarking
Hathairat Ketmaneechairat
Journal of Data Processing, Vol. 16, No. 3, 2026.
DOI: https://doi.org/10.6025/jdp/2026/16/3/161-184
Link: https://www.dline.info/jdp/fulltext/v16n3/jdpv16n3_3.pdf
Abstract:
Mathematical reasoning poses a significant challenge for Large Language Models (LLMs) due to the necessity
for structured symbolic manipulation, multi step deduction, and logically consistent inference. While Chainof
Thought (CoT) prompting has substantially advanced reasoning capabilities, existing datasets often lack
transparent, verifiable reasoning trajectories and rigorous statistical validation. This study presents a
statistically validated, large scale mathematical CoT dataset comprising approximately 100,000 samples
spanning six core mathematical domains (Algebra, Geometry, Trigonometry, Matrices, Derivatives, and
Integrals) and three predefined difficulty levels. The dataset preserves complete intermediate reasoning
traces and final solutions in standardized LaTeX notation. We conducted comprehensive structural,
descriptive, and inferential statistical analyses including Chi-square tests, Spearman's rank correlation,
two-way ANOVA, and Tukey's HSD post hoc comparisons to validate the dataset's internal consistency.
Results demonstrate a perfectly balanced distribution across topics and difficulties, with the mathematical
topic emerging as the dominant determinant of reasoning complexity (partial nÃ‚Â² = 0.995). Furthermore, the
corpus exhibits rich symbolic diversity, authentic mathematical syntax, and structured command cooccurrence
networks. This statistically validated corpus provides a reliable and robust benchmark for
supervised fine tuning, curriculum learning, process supervision, explainable AI, and evaluating nextgeneration
mathematical LLMs.