Research on the evaluation of the professional knowledge of mathematics teachers (comprising for example mathematical content knowledge, mathematics pedagogical content knowledge and general pedagogical knowledge) has become prominent in the last decade; however, the development of video-based assessment approaches is a more recent topic. This paper follows the call for more situated and performance-related ways to assess teacher competence. We discuss the theoretical and methodological challenges connected to the development of such instruments and exemplify these by an instrument developed within the follow-up study of the international BTeacher Education and Development Study in Mathematics (TEDS-M)^, called TEDS-FU. Drawing on the novice-expert framework from cognitive psychology allows analysing the structure and development of mathematics teachers' professional competence. More recent concepts on teacher noticing of classroom situations and students' activities are incorporated into this video-based evaluation instrument, which is described in detail in this paper, by assessing perceptual, interpretative and decisionmaking skills. Reliability and validity concerns remain an issue of such assessments for which solutions are proposed. Overall, the paper shows that a more comprehensive Int J of Sci and Math Educ evaluation of teachers' competence comprising cognitive-affective and situated facets is possible and has been achieved.
Beginning primary teachers' knowledge and beliefs were assessed at the end of teacher education and 4 years later. In addition, they reported about their school context and job satisfaction and took a videobased assessment on their perception, interpretation, and decision-making skills. Research questions were (1) whether we have to deal with a "reality shock" in that beginning teachers' beliefs about the nature of mathematics or the teaching and learning of mathematics change to more traditional ones or whether their mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), or general pedagogical knowledge (GPK) decreases, (2) whether the school context in terms of appraisal and a climate of trust influences the knowledge and belief development, and (3) to what extent the beginning teachers' knowledge and beliefs predict their perception, interpretation, and decisionmaking skills. Data from 231 German primary teachers in their third year in the profession neither revealed changes of beliefs towards traditional ones nor a substantial loss in knowledge. In contrast, GPK grew significantly and beliefs on the nature of mathematics were more dynamic 3 years after teacher education. Thus, drawbacks are a rare phenomenon in our sample. Those teachers who had perceived a stronger climate of trust revealed higher MCK, MPCK, and GPK as well as more dynamic beliefs. These teachers also revealed significantly stronger skills.
This paper addresses an important task teachers face in class: the identification and support of creative and high-achieving students. In particular, we examine whether primary teachers (1) have acquired professional knowledge during teacher education that is necessary to foster creativity and to teach high-achieving students, and whether they (2) possess the situationspecific skills necessary to do so. For this purpose, (1) the knowledge of German primary school teachers who participated in the TEDS-M study at the end of teacher education is analyzed. (2), a subset of these teachers interpreted classroom video scenes that require identifying and supporting creative and high-achieving students in the longitudinal Follow-Up study to TEDS-M (TEDS-FU) after three years of work experience. Contingency analyses between teachers' professional knowledge and their skills to identify and support mathematically creative and high-achieving students were carried out. They revealed that those teachers who have difficulties in logical reasoning and understanding structural aspects of mathematics also have difficulties with identifying and supporting creative and highachieving students. It was difficult for them to identify students' thinking processes based on structural reflections and pattern recognition as well as to further develop mathematically rich answers by students. In line with these results, teachers with strong professional knowledge were able to meet identify and support mathematically creative and high-achieving students. Thus, the study reveals that a connection between teachers' professional knowledge and their skills to identify and support mathematically creative and high-achieving students exists but that many future and early career teachers seem to have deficits in these respects.
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