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From practice to research – How to measure teachers' pedagogical content knowledge in math?

Enrollment is Closed

About This Course

Imagine you are a mathematics teacher. A student puts his hand up and says: “I don’t understand why -1 times -1 equals 1. I know it’s the correct result, but it makes no sense to me. Why does multiplying two negative numbers give a positive number?” How would you explain this result to your student? Scenarios like these are typical for the task of teaching. In order to respond appropriately, teachers not only need to understand the mathematical concepts underlying the question, they also need to know how these concepts can best be explained to students. The relevance of teachers’ domain-specific knowledge to high-quality instruction has been discussed, particularly in the context of mathematics teaching …. Quantitative evidence shows that students’ learning gains in mathematics may be predicted by their teachers’ mathematics-related knowledge (see Krauss et al., 2008, p. 716).

Learning Outcomes

After the course, the participant is able to:

  • Reflect on the characteristics of a “good teacher” and on possible intercultural differences within Europe
  • Bridge the gap between subjective perceptions and objective ways to measure teacher competences
  • Gain insight into empirical research in math education
  • Reflect on the relevance of the findings for other subjects and transfer task structures and designs
  • Adopting the role of (student) teachers as researchers – continuously exploring the links between theory, reflection and practice (during university studies and in the later work as teachers)


In the SoNetTE OCW course “From practice to research – How to measure teachers' pedagocical content knowledge in mathematics and other subjects”, the participants – student teachers, teachers, teacher educators and researchers – are welcomed to contrast and compare their own images of a “good teacher” (as often rooted in their early experience as pupils) with a research based approach to measurable and intersubjectively verifiable teacher competences. In the beginning, students are invited to reflect upon their own experience as a pupil as well as on teachers’ behavior in TIMSS videos from different corners of Europe. Guided by scientific articles they are then supposed to think about how to link their own impressions and convictions with possibilities of how to measure good teaching, more precisely pedagocical content knowledge (PCK) of mathematics teachers, objectively. In the next stage, students design tasks for teachers which could be used as items within a broader research instrument with the aim of measuring different aspects of teachers’ pedagogical content knowledge. Finally, the developed tasks are evaluated and assessed in virtual peer mentoring arrangements (on Moodle) as well as by a team of experienced teachers and university lecturers. The tasks and their evaluation results are then uploaded and discussed in a final forum to find answers to the joint research question in this study group: How can we measure teachers’ pedagogical content knowledge (PCK) with verifiable items which fulfill the basic standards of empirical educational research? The course is designed as a blended-learning course and will be taught in English. According to activities, assignments and target groups, students’ mother tongues may also be used. The study group meets in the course environment on Moodle, where assignments are given and where the participants deliver their products. The instructor and peers as well as other participants give continuous feedback on assignments and teaching implementations.


Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM – The International Journal on Mathematics Education, 44(3), 223–247. PDF(external link) Kersting, N., Givvin, K., Thompson, B., Santagata, R., & Stigler, J. (2012). Measuring Usable Knowledge Teachers’ Analyses of Mathematics Classroom Videos Predict Teaching Quality and Student Learning. American Educational Research Journal, 49(3), 568–589. PDF(external link) Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Pedagogical content knowledge and content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 64, 90-106. doi: 10.1177/0022487112460398. PDF(external link) Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., et al. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716–725. doi: 10.1037/0022-0663.100.3.716. PDF(external link)

Course Staff

Georg Bruckmaier

Georg Bruckmaier

  1. Course Number

  2. Classes Start

    Oct 01, 2014
  3. Classes End

    Dec 31, 2014