International Portal of Teacher Education

Source: Journal of Mathematics Teacher Education, Vol. 16, No. 6, December 2013, p. 403-426.
(Reviewed by the Portal Team)

The purpose of this study is to examine the development of pedagogical content knowledge (PCK) for two purposefully selected beginning mathematics teachers.

Methods
In this study, the authors focus on two individuals, Keith and Lyle, who completed the alternative certification program and achieved mathematics teacher certification at the middle-school level. The PCK development of these two individuals varied due to their focus on developing particular aspects of their PCK, with one individual focusing on assessment and student understanding, and the other individual focusing on curricular knowledge.

Data were collected through an entry and exit instructional planning task, stimulated recall interviews, observations and field notes.

The findings of this study demonstrate the differences that exist in the development of PCK for beginning mathematics teachers.
These findings also demonstrate that PCK can develop in different ways for beginning teachers. The authors concur that each of these factors impacted the PCK development for Keith and Lyle, and recognize that it is difficult to determine which aspects may have had more or less impact or their PCK development. The findings indicate that these individuals privileged particular aspects of their knowledge, leading to differences in their PCK development. Lyle valued PCK for mathematics curriculum. Keith valued PCK of students’ understanding of mathematics. These values appeared to influence the type of PCK that developed over their first two years.

Despite the similarities in their coursework and internship, Lyle’s focus on developing curricular knowledge led to developing general pedagogical knowledge of instructional strategies and PCK for instructional strategies. Lyle’s development of different PCK components originated in and was filtered through his knowledge of curriculum for mathematics.
In contrast, Keith focused on developing his PCK of assessment and student understanding. As Keith increased his knowledge of assessment strategies, his PCK of student understanding developed in regard to the specific student mathematical difficulties. His PCK of assessment and student understanding led to further development of PCK of instructional strategies and, to a lesser extent, his PCK of curriculum.

Notwithstanding the similarities in their teacher preparation, it was evident that Keith and Lyle developed different knowledge across the four PCK components. Keith’s growth in assessment knowledge for mathematics appeared to deepen his knowledge of student understanding of mathematics, providing an entry point to knowledge of instructional strategies for mathematics and knowledge of mathematics curriculum. However, Lyle’s PCK was limited primarily to knowledge of curriculum for mathematics. His curricular knowledge impacted his PCK development across the other components, but his growth in other components primarily involved general pedagogical knowledge rather than knowledge specific to the teaching of mathematics.
The findings of this research document differences in knowledge growth for these beginning teachers; these findings also illuminate the importance of individualizing the professional development of teachers during their induction years. Mentors of beginning teachers who facilitate knowledge growth in various aspects of an individual’s PCK may better assist beginning teachers in their knowledge development.

The differences in the PCK that Keith and Lyle developed over the 2 years have implications for the ways in which we support beginning teachers’ knowledge growth. The authors suggest that providing opportunities for beginning teachers to unpack students understandings from specific student work or of student interviews may allow beginning teachers to gain insight into student understanding that can impact other aspects of their PCK.