Investigating Secondary Mathematics Teacher PCK across the Professional Continuum

Theoretical Framework

Shulman (1986) conceptualized the specific knowledge that applies to content area specialists. In this symposium, we focus on the knowledge that mathematics teachers need and use that distinguishes them from other middle and secondary teachers. This knowledge, pedagogical content knowledge (PCK), represents the transformation of several types of knowledge that is unique to mathematics teachers. PCK includes what teachers know about learners, curriculum, instruction, and assessment that help them transform content knowledge into effective teaching and learning (Grossman, 1990; Magnusson, Krajcik, & Borko, 1999).

Our research team, under the auspices of a five-year research project funded by the National Science Foundation, has developed frameworks to characterize teacher knowledge for mathematics teaching. We adapted the PCK framework by Magnusson, Krajcik, and Borko (1999) for our work. Components of this framework of teacher knowledge include: a) knowledge of curricula; b) knowledge of assessment; c) knowledge of students’ understandings; and d) knowledge of instructional strategies. Further, these researchers argue that each of these knowledge bases is influenced by teachers’ orientations. Specifically, our session will focus on three research questions:

• What are the orientations of beginning mathematics teachers? How do these orientations influence how they design mathematics instruction?
• What PCK develops for beginning mathematics teachers?
• How do expert secondary mathematics teachers draw on four components of PCK as they think through designing instruction?

Methods and Data Sources

To date, the project has collected data from 51 participants during the past five years. These participants were either enrolled in a post-baccalaureate certification/masters program for secondary (grades 5-9, 9-12, or 5-12) mathematics or experienced teachers with more than 5 years teaching experience who were identified as leaders in their schools.

We collected data through several sources, including: a) lesson-planning task and accompanying interview (upon entrance and exit from the research study); b) written responses about a “discrepant event” video segment and questions related to orientations); and c) classroom observation cycle (two-day observation including pre-interview and post-stimulated recall interviews; twice per year). Qualitative methods of data analysis were supported with NVivo software.

Results

Research Paper 1: First, we introduce components of orientations for mathematics teaching by describing participants’ self-reported views and highlighting modifications in views between entry and exit data collection points. Second, we illustrate the impact an orientation for mathematics teaching has on the design of instructional plans. Finally, we explain how we characterize orientations for mathematics teaching based on an analysis of longitudinal data.

Research Paper 2: We present data that contrast two beginning teachers who chose to develop different aspects of PCK, leading to differences in the development of other components of their PCK (e.g., a focus on curriculum lead to few gains in PCK of student understanding or PCK of assessment).

Research Paper 3: In the paper that focuses on how expert secondary mathematics teachers draw on PCK as they think through designing instruction, results focus on three main themes:

• Teachers drew on multiple components of PCK as they planned mathematics instruction.
• · Teachers drew on multiple components of PCK even when they were directed toward a specific PCK component (i.e., assessment).
• · The teachers moved fluidly among the PCK strands as they described their thinking about instruction demonstrating that their knowledge of the four strands of PCK was integrated.

Further, implications for mathematics teacher education will be discussed.

Importance of the Research

The findings of these presentations point to the differences that exist in the orientations and PCK development of mathematics teachers across the professional continuum. These studies extend our knowledge of the development of PCK and emphasize the importance the mentoring of beginning teachers to promote further PCK development. In addition, these studies empirically situate PCK as it is enacted during actual classroom instruction, something lacking in the current literature.

Organization of the Session

The research symposium will focus on the research questions listed above. Participant discussion will occur after each presentation and at the end of the symposium and will be guided by the following questions:

Research Paper 1 (Orientations toward Mathematics Teaching):

• What role do orientations play in the development of PCK for beginning teachers?

Following Research Paper 2 (PCK Development of Beginning Mathematics Teachers):

• How does PCK development differ for beginning mathematics teachers?
• What factors influence the development of PCK for beginning mathematics teachers?

Following Research Paper 3 (Experienced Teachers’ PCK):

• How does PCK differ for beginning and experienced mathematics teachers?
• What implications does the nature of experienced mathematics teacher PCK have for the preparation and professional development of mathematics teachers?

End of Symposium Discussion:

• What implications do the findings from all three studies have for preservice and inservice mathematics teacher education?

Timeline:

1. Introduction and Overview of Research Project and Presenters (10 minutes)
2. Presentation and whole-group discussion of Research Paper 1. (15 minutes)
3. Presentation and whole-group discussion of Research Paper 2. (15 minutes)
4. Presentation and whole-group discussion of Research Paper 3. (15 minutes)
5. Discussant Reaction to Research Papers (10 minutes)
6. Whole-Group Discussion of how these knowledge bases are connected and the implications they have for teacher education. (25 minutes)