Teachers' Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Teachers' Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Issue/Topic: Curriculum--Mathematics; Teaching Quality--Preparation
Author(s): Baumert, Jurgen; Blum, Werner; Brunner, Martin; Jordan, Alexander; Klusmann, Uta; Krauss, Stefan; Kunter, Mareike; Neubrand, Michael; Tsai, Yi-Miau; Voss, Thamar
Organization(s): Max Planck Institute for Human Development; University of Bielefeld; University of Kassel; University of Luxembourg; University of Michigan; University of Oldenburg
Publication: American Educational Research Journal
Published On: 1/1/2010

There is consensus in teacher education literature that a strong knowledge of the subject taught is a core component of teacher competence. There is disagreement on the necessary breadth and depth of teachers' mathematical training. Few empirical studies have assessed the various components of teachers' knowledge directly and used them to predict instructional quality and student outcomes.

To investigate the extent to which teachers' content knowledge (CK) and pedagogical content knowledge (PCK) influence instructional quality, consequently affecting students' learning gains in mathematics.


Teachers' CK and PCK scores proved to be highly dependent on the type of training program they had attended. In the US, there is wide variety in teacher preservice training, thereby making it difficult for researchers to define treatments and provide evidence for effects. In Germany, however, teacher education is standardized by the state and generally, math teacher candidates are assigned to either academic track schools or non-academic track schools on the basis of certification. As a result, there are marked differences in the CK and PCK of the teachers of the different tracks. Such differences may cause concern that the least qualified teachers will work in low socioeconomic status schools attended by the lowest-achieving students (a concern also experienced in the US). Teacher candidates on the academic track receive an in-depth math training (comparable to a Master’s degree in math), while the education of teachers on the non-academic track emphasizes pedagogy and offers only limited math courses.

Teacher Training Program Attended and Subject Matter Knowledge

The findings show that teachers certified to teach in the academic track had much higher CK scores than did teachers certified for nonacademic tracks or teachers who attended an integrated training program (where courses covered both subject matter and teaching methods). The higher scores may be attributable to the higher requirements placed on teacher candidates in the academic track and/or to the potentially stricter demands of math departments. The findings further did not show the differences in CK and PCK leveling out over the teaching career, indicating that the differences persisted over the entire teaching career.

Mathematical Knowledge of Teachers, Classroom Instruction, and Student Progress

Cognitive level of tasks (i.e., tasks drawing on students' prior knowledge by challenging their beliefs, or rather than simply declaring a solution right or wrong, encouraging students to validate their solutions for themselves or to try out multiple solution paths,), curricular level of tasks and effective classroom management proved to be significant predictors of math achievement at the end of Grade 10. However, teacher knowledge of individual learning support (i.e., providing students with challenging tasks and supporting their learning activities) was not found to have a specific effect on math achievement over and above the joint effect with classroom management. Teachers' domain-specific instructional knowledge seems to be of key significance for student progress in math. PCK seems to influence the cognitive level, curricular level, and learning support dimensions of instructional quality. Classroom management appears to be independent of PCK however.

What Counts: Teacher Content Knowledge (CK) or Pedagogical Content Knowledge (PCK)?

CK was not found to affect the cognitive level of tasks and individual learning support. Only the curricular alignment of the tasks increased with increasing levels of CK. The findings confirm that it is PCK that has greater predictive power for student progress and is decisive for the quality of instruction. This does not imply that CK has no direct influence on instructional features, however. Teachers with higher CK scores were found to be better able to align the material covered with the curriculum, but higher levels of CK have no direct impact either on the potential for cognitive activation or on the individual learning support that teachers are able to provide when learning difficulties occur; as higher levels of PCK do. Both PCK and CK vary independently of effective classroom management.

Policy Implications/Recommendations:
Implication for Teacher Preparation Programs: Pedagogical Content Knowledge (PCK)--the area of knowledge relating specifically to the main activity of teachers, namely, communicating subject matter to students--makes the greatest contribution to explaining student progress. This knowledge cannot be learned incidentally, but rather is acquired in structured learning environments.


Research Design:

10th grade math teachers in 194 classes, comprised of 80 academic track classes and 114 classes distributed fairly equally across nonacademic tracks

Year data is from:


Data Collection and Analysis:
Reports findings from a one-year German study which surveyed a nationally representative sample of Grade 10 classes and their math teachers in order to determine the implications of CK and PCK for processes of learning and instruction in secondary level math

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