Abstract
This chapter introduces the tests of secondary mathematics teachers’ pedagogical content knowledge and content knowledge that were developed and administered in the COACTIV framework. It reports on the conceptualization of the two knowledge constructs based on Shulman’s (Harv Educ Rev 57(1):1–22, 1987) theoretical taxonomy of teacher knowledge, describes the construction of tests to assess the two constructs, and presents results from N=198 secondary mathematics teachers in different school tracks. Specifically, the chapter presents findings on the dimensionality of teachers’ domain-specific professional knowledge, the scaling of the tests, evidence for their reliability, and first results on construct validity. This chapter serves as the basis for Chap. 9, which examines the validity of pedagogical content knowledge and content knowledge to predict quality of instruction and student progress.
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Notes
- 1.
In some COACTIV publications, slightly different numbers of PCK items are reported. The reason for the discrepancy is that the number of items in the explanations and representations subtest was later modified in response to the findings of in-depth content and psychometric analysis. However, these differences did not lead to any substantial changes in the results presented.
- 2.
The Michigan research group subsumes CK and PCK to the category of mathematical knowledge for teaching (MKT) and distinguishes this knowledge from pedagogical knowledge. For example, Bass and Ball (2004) have compiled a catalog of “core tasks and problems of teaching” that includes, for example, “analyzing and evaluating student responses” but also “evaluating a textbook’s approach to a topic” and then state: “And it is knowledge of mathematics, not knowledge of pedagogy or of cognitive psychology.”
- 3.
For example, it would have been possible to distinguish between content categories (e.g., algebra, geometry) or between procedural and declarative knowledge. An exploratory factor analysis of the COACTIV items did not identify any specific and interpretable subdimensions of CK (Krauss et al. 2008b). Given the relatively low number of items implemented, however, definitive conclusions cannot yet be drawn (see, e.g., Blömeke et al. 2008, 2010).
- 4.
Given the small numbers of teachers in multi-track schools (N = 22) and comprehensive schools (N = 21; including three who were licensed to teach in the academic track) in the sample, no general conclusions can be drawn for these subpopulations. However, it can be noted that whereas teachers in all nonacademic tracks showed similar performance levels on the CK test, teachers in intermediate-track schools (N = 70) tended to outperform the other two groups on the PCK test.
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Krauss, S. et al. (2013). Mathematics Teachers’ Domain-Specific Professional Knowledge: Conceptualization and Test Construction in COACTIV. In: Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., Neubrand, M. (eds) Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers. Mathematics Teacher Education, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5149-5_8
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