Developing students' innovative thinking is one of the important goals of the current educational reform. Dynamic Mathematics provides interesting content and interactive technology support for effectively developing innovative thinking. The DIIEE design thinking model is a creative problem-solving process. This paper constructs the DM-DCCSE innovation education model based on Dynamic Mathematics and the DIIEE design model, which has clear objectives, progressive processes, rich activities, interesting knowledge and effective technical support. The results of the study on the teaching practice of Animation Mathematics course under the guidance of this model show that the model is conducive to promoting the development of students' innovative thinking and students are highly satisfied with the teaching effect.

This paper presents KM-SCR, a deductive-database system for automated geometry reasoning that aims to reduce redundant knowledge representation and inference overhead. First, a geometric-object merging mechanism consolidates collinear or coplanar objects and updates their associated relations, reducing redundant representations in the knowledge base. Second, a chain-of-equalities representation facilitates quantitative inference and supports algebraic reasoning through matrix-column compression and equation-system simplification. Third, semi-conditional rules divide rule-matching conditions into base conditions and remaining constraints, enabling staged candidate generation and constraint verification to reduce unnecessary matching operations. We establish the equivalence between semi-conditional rules and their original formulations at the rule-instance level and integrate the three mechanisms into an iterative reasoning workflow. Experiments on all 293 problems in FormalGeo7k-L6 show that KM-SCR solves 288 instances (98.29%), with a mean solving time of 4.06 s among successfully solved instances. On 40 sampled problems from each of levels L1–L5, the success rates range from 97.50% to 100.00%. Further analyses of theoretical inference space, actual rule instantiations, memory consumption, and solving time assess the effects of the proposed mechanisms on knowledge redundancy and inference efficiency.