Аннотация
Vision-language models (VLMs) have advanced mathematical reasoning capabilities. However, Kazakh language supporting VLMs capable of mathematical reasoning and being deployed on edge devices are yet to be developed. The aim of this study is to develop and evaluate a compact vision-language model that solves school-level mathematical problems in Kazakh with step-by-step reasoning and runs on consumer hardware. In this work, we present the Qolda-Math model, a 4.3-billion-parameter small VLM developed at the Institute of Smart Systems and Artificial Intelligence (ISSAI) to solve mathematical reasoning tasks in Kazakh. We use a Qolda VLM model and add an additional stage to the training pipeline. We utilize a supervised fine-tuning (SFT) algorithm that uses a dataset composed of 395,309 training examples. Specifically, the dataset spans school curriculum-aligned math problems along with chain-of-thought (CoT) solutions generated by the Qwen3-235B model. We also use general-knowledge data and prompt instructions, including “solve”, “explain”, “teach”, “verify+/verify–”, and handwritten feedback in three languages (i.e., Kazakh, Russian, and English). Under a unified evaluation protocol, Qolda-Math reaches 61.60% on the Kazakh-adapted MathVista benchmark and 50.39% on MathVision-KK, improving over the checkpoint it was fine-tuned from by 3.40 and 4.57%, respectively; both improvements are statistically significant, with 95% bootstrap confidence intervals excluding zero. In addition, the Qolda-Math model maintains competitive performance on general text and vision benchmarks (i.e., the average text benchmark score changed from 72.09 to 72.68). Qolda-Math model is deployable on consumer devices that could further support offline mathematical tutoring in Kazakh. The development of Qolda-Math builds upon advances in mathematical reasoning with language models, AI-powered educational tools, visual mathematical understanding, and Kazakh language processing. The model weights are publicly available at https://huggingface.co/issai/math_qolda.