Empirical study on the construction of a cognitive model of factorization in eighth-grade students

The construction of cognitive models is the basis for cognitive diagnosis, and the cognitive models will change based on the purpose of the study. According to the purpose of mathematical education, the cognitive factorization model is constructed based on the competence and knowledge dimensions. The factorization cognitive model was preliminarily constructed using expert-defined and literature surveys, and a small-scale test was subsequently carried out. The rationality of the cognitive model was tested through verbal reports and the regression of the item's difficulty through the cognitive attributes. The study included a sample of 72 students from two eighth-grade classes in a junior high school located in Wuhan. A diagnosis was made based on the mastery of factorization knowledge and the level of mathematical operation ability of the eighth graders in the cognitive model. Research 1 demonstrates that the construction of the cognitive factorization model is reasonable. Research 2 shows that approximately 79% of students' mathematics operation ability can reach the level of knowledge understanding, 71% of students can reach the level of knowledge transfer, and only 28% of students can reach the level of knowledge innovation.