Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the cognitive type refers to the kind of teacher content knowledge and thinking processes required to accomplish a task successfully, in terms of knowledge of facts and procedures (Type 1), knowledge of concepts and connections (Type 2), and/or knowledge of models and generalizations (Type 3).A sample of 102 middle school mathematics teachers (grades 6-8) was assigned to the study from a number of school districts in an urban area in the Southwestern US. Teachers were tested using the Teacher Content Knowledge Survey. Student level data of about 2,400 middle grades students' standardized test passing rates including percentage of students meeting the state standards by objectives were collected. The type of teachers' content knowledge was assessed and tested for association with student achievement on the statemandated standardized test using multivariate methods including tests for variance and independence. The nested research consisted of three phases. Substudy-1 focused on quantitative analysis of the association between cognitive type of teacher content knowledge and student achievement. Substudy-2 aimed at the correlation between cognitive type of teacher content knowledge and teaching practice. Finally, substudy-3 was a case study on examining middle grades mathematics teachers' knowledge and understanding of fraction division.