An investigation into the definitions and development of pedagogical content knowledge among pre-service and current mathematics teachers

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using for instruction. Additionally, participants indicated their college major, institution attended, years of experience, and participation in various other learning opportunities. This data was analyzed to look for changes in knowledge, first among those still in college, then among those already in the field, and finally as a whole group to look for a pattern of growth from pre-service through working in the classroom. I compared these results to the theories of learning espoused by the creators of these two tests to see which model the data supports. The results indicate that growth in PCK occurs among college students during their teacher preparation program, with much less change once a teacher enters the field. Growth was not linear, but best modeled by an s-curve, showing slow initial changes, substantial development during the 2nd and 3rd year of college, and then a leveling off during the last year of college and the first few years working in a classroom. Among current teachers' the only group that demonstrated any measurable growth were teachers who majored in a non-education field. Other factors like internships and professional development did not show a meaningful correlation with PCK. Even though some of these models were statistically significant, they did not account for a substantial amount of the variation among individuals, indicating that personal factors and not programmatic ones may be the primary determinant of a teachers' knowledge.