The conceptualisation and measurement of pedagogical content knowledge and content knowledge in the COACTIV-study and their impact on student learning

An ongoing question is the extent to which teachers' professional knowledge has an impact on their teaching and, in particular, on their students' achievement. The COACTIV study 1 surveyed and tested the mathematics teachers of the classes sampled for PISA 2003/04 in Germany. The study’s key components were newly developed tests of teachers’ pedagogical content knowledge and content knowledge. This article gives a report of the conceptualisation and operationalisation of both domains of knowledge and describes the construction of the COACTIV tests. Findings from the tests show that there are differences with respect to both knowledge domains regarding teachers’ school types, but that pedagogical content knowledge and content knowledge astoundingly both do not depend on teaching experience. Furthermore we show that the two domains of knowledge correlate positively with constructivist teachers’ subjective beliefs, on the one hand, and with some crucial aspects of their instruction, on the other hand. Finally, we show that pedagogical content knowledge – but not pure content knowledge per se – significantly contributes to students’ learning gains. The COACTIV Study 2003/2004 Although the essential influence of teachers on students’ learning is obvious, empirical studies which assess aspects of the teachers’ professional knowledge systematically, and link them with the students’ achievement, are 46 Journal of Education, No. 56, 2012 The OECD Programme for International Student Assessment, see 2 http://www.oecd.org/pisa/ very rare. The main goal of the German COACTIV study (Cognitive Activation in the Classroom: Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students ́ Mathematical Literacy) was the investigation and testing of mathematics teachers of German PISA classes. The international PISA study 2003, whose 2 main focus lay in the subject of mathematics, has been extended in Germany both to a study based on whole classes (220 altogether) and to a longitudinal study, which means that the students of the grade 9 classes which were tested in PISA 2003 were examined again in grade 10 in the following year. Following this pattern, the COACTIV study investigated the mathematics teachers who taught these PISA classes in grade 9 and grade 10 at both PISA study dates (April 2003 and April 2004; therefore “COACTIV 03/04”). The COACTIV study 03/04, together with PISA, offered a unique opportunity to collect a broad range of data about both the students and their teachers, and to analyse them mutually. Due to the data of the COACTIV study it is not only possible to get an idea of the competencies and experiences of German secondary mathematics teachers, but it is possible to identify characteristics of a teacher empirically as well, which are relevant for the learning progress of students (or for different target criteria of mathematics lessons). In the context of the COACTIV study, numerous instruments for the investigation of mathematics teachers were newly developed or adapted (they include the measurement of professional knowledge, of motivational orientations, beliefs and values, aspects of work-life experiences etc.; a more detailed overview on that study is available in the book: “Teachers' professional competence: Findings of the COACTIV research program” (Kunter, Baumert, Blum, Klusmann, Krauss and Neubrand, forthcoming). Figure 1 illustrates various aspects in which COACTIV collected data together with PISA. Together with the instruments which were used in PISA to examine the students, the teachers were presented with both questionnaires (regarding biography, interests, beliefs and more) and tests (e.g., regarding professional knowledge) in COACTIV. But what should a ‘test’ for teachers look like? With which knowledge should mathematics teachers be equipped? From the point of view of mathematics, the pedagogical content knowledge (PCK) and the content knowledge (CK) are of special interest as central parts Krauss and Blum: The conceptualisation and measurement. . . 47 of the professional knowledge base (see Figure 1, left column). In the context of the COACTIV study, tests for mathematics teachers were developed for both knowledge categories which form the core of this study and which will be presented in the present paper in more detail. In the above-mentioned book (Kunter et al., forthcoming) the interested reader can learn more about results of other aspects which have been examined in the COACTIV study, for example, about the teachers’ experience of stress and ‘burn out’, about enthusiasm or about beliefs (see also left column in Figure 1), about aspects of mathematics lessons in PISA classes from the point of view of teachers and students, and about the mathematics tasks used by teachers (middle column in Figure 1). Interesting results about students (right column in Figure 1) can be taken from the respective PISA book (OECD, 2004). 48 Journal of Education, No. 56, 2012 Figure 1: Conceptual connection of the COACTIV 03/04 study and the PISA 03/04 study and sample aspects of three columns examined: mathematics teachers, mathematics lessons and students