  The automatic generation of high-quality mathematical problems is practically
valuable in many educational scenarios. Large multimodal model provides a novel
technical approach for the mathematical problem generation because of its wide
success in cross-modal data scenarios. However, the traditional method of
separating problem solving from problem generation and the mainstream
fine-tuning framework of monotonous data structure with homogeneous training
objectives limit the application of large multimodal model in mathematical
problem generation. Addressing these challenges, this paper proposes COMET, a
"Cone of Experience" enhanced large multimodal model for mathematical problem
generation. Firstly, from the perspective of mutual ability promotion and
application logic, we unify stem generation and problem solving into
mathematical problem generation. Secondly, a three-stage fine-turning framework
guided by the "Cone of Experience" is proposed. The framework divides the
fine-tuning data into symbolic experience, iconic experience, and direct
experience to draw parallels with experiences in the career growth of teachers.
Several fine-grained data construction and injection methods are designed in
this framework. Finally, we construct a Chinese multimodal mathematical problem
dataset to fill the vacancy of Chinese multimodal data in this field. Combined
with objective and subjective indicators, experiments on multiple datasets
fully verify the effectiveness of the proposed framework and model.
