The effectiveness of a proposed strategy based on the cognitive apprenticeship and Wheatley models to develop a depth of mathematical knowledge and a deep understanding in mathematics of primary school students" Abstract: The research aimed to measure the effectiveness of a proposed strategy based on the cognitive apprenticeship and Wheatley models in developing levels of depth of mathematical knowledge and deep understanding in mathematics among primary school students. The experimental method was used; The research sample was selected from sixth grade primary school students at (AL-Shahid Ahmed Abdullah Al-Zaqqaqi) School, Mit Ghamr Educational Administration/Dakahlia Governorate. It was divided in to: an experimental group (n = 33) and a control group (n = 35). The research prepared a test on levels of depth of mathematical knowledge, and a test on deep understanding skills in mathematics, and they were applied pre- and post-test to the two research groups. After the experimental treatment and testing the validity of the hypotheses, the results showed: There is a statistically significant difference between the average scores of the students in the experimental group and the scores of the students in the control group in the post-application test for the levels of depth of mathematical knowledge in favor of the students in the experimental group, and the presence of a statistically significant difference between the average scores of the students in the experimental group and the scores of the students in the control group. In the post-application of the deep understanding test in mathematics for the benefit of the experimental group students; That is, the proposed strategy led to the development of levels of depth of knowledge and deep understanding skills in mathematics among the students of the research sample. The results also revealed the presence of a strong, statistically significant positive correlation at the level (0.01) between the levels of depth of knowledge and deep understanding among the students of the experimental group. The results did not reveal There was a statistically significant difference between the average scores of the experimental group’s students in the two applications (post and follow-up) of the tests for levels of depth of knowledge and deep understanding in mathematics. Which indicates the continued effectiveness of the proposed strategy in developing levels of depth of mathematical knowledge and deep understanding in mathematics. Keywords: cognitive apprenticeship model - Wheatley model - levels of depth of mathematical knowledge - deep understanding in mathematics