Due to the academic and commercial successes in large-language model (LLM) software research and development, there are a lot of activities to utilize this technology. Accordingly, many successful software have been released and developed for various social applications. Among them, mathematics education is one of emerging social applications which is obviously helpful for social welfare. Aligned with the development directions of LLM technologies, the use of direct preference optimization (DPO) is considered. However, one of the biggest hurdles is the lack of training dataset. Therefore, this research introduces fully-automated training dataset generation using the advanced form of LLM, i.e., multi-modal LLM. Based on various generation results based on our multi-modal LLM, various discussions and analysis results are provided. Lastly, it has to be noted that our proposed platform can contribute to providing fair education opportunities for diverse human beings without discrimination, which is definitely beneficial for social welfare.