Developing Secondary Mathematics Content Knowledge for Teaching in Secondary Mathematics and Science Teachers

Authors: Marilyn Carlson, Michael Oehrtman

Analysis of pre- post- data revealed significant shifts in teachers' knowledge of concepts of function, proportion and rate of change over one semester of instruction. We have used variations of the PCA as a central tool for measuring change in teachers' knowledge over the functions course. The PCA measured teachers' overall gains in understanding function concepts, proportional reasoning, and covariational reasoning. The following table provided a breakdown of two cohorts of teachers' pre and post course scores by item content.

 

An item analysis of the PCA data indicates that teachers improved significantly on nearly every conceptual subcategory measured by the instrument. Broadly, these include assessments of

1. reasoning in, and across, multiple representations,
2. aspects of transition from an action view to a process view of function,
3. covariational reasoning and reasoning about rates of change,
4. linear and exponential functions, and
5. specific misconceptions related to these categories.

 In addition positive shifts in teachers' beliefs about learning and teaching mathematics were realized over the first course and accompanying PLC sessions. However, observation of these teachers' practices initially revealed minor changes in their teaching practice.  Our coding of the PLC video data also revealed that improving teaching practice towards more inquiry focused and conceptual rich instruction requires teachers to reconceptualize their instructional goals. Concurrently they must acquire knowledge and skills to reconstruct their lessons and assume a different role in their instruction.  We have observed that many secondary mathematics teachers do not possess the knowledge or background to develop and implement conceptually focused, inquiry-based lessons.  Our findings support that ii) teaching practices can be improved by assisting teachers in supporting and assessing student thinking and learning; iii) teachers need faculty support in revising their curriculum to support students in understanding key ideas of their course; iv) developing quality instructional lessons that are inquiry based and conceptually focused requires knowledge of concepts and learning that takes time to construct. iv) pacing instruction in response to student learning is in conflict with the pressure that teachers are under to "cover" content in a pre-described syllabus or textbook; iv) PLCs that are structured to promote inquiry into teaching and learning can be effective in supporting positive shifts in secondary mathematics and science teachers' instructional practices.  These observations were revealed by analyzing secondary mathematics teachers' instructional practices and by analyzing teacher discourse during their PLC sessions.