Thamar Voss

Mathematics teachers' beliefs

Teacher beliefs are thought to play a decisive role in the provision of classroom instruction (Richardson. Handbook of research on teacher education. Macmillan, New York, pp 102–106, 1996). This chapter investigates mathematics teachers’ beliefs about the nature of knowledge (epistemological beliefs) and about mathematics teaching and learning. To this end, 328 mathematics teachers from the COACTIV study were administered 44 Likert items tapping their professional beliefs. Confirmatory factor analyses revealed that epistemological beliefs and beliefs about mathematics teaching and learning tend to co-occur into two characteristic, and negatively correlated, patterns of beliefs: a transmissive orientation and a constructivist orientation. The results of multilevel structural equation modeling confirmed the relevance of teacher beliefs for instructional practice and student learning outcomes: Constructivist beliefs were positively related to instructional quality and student achievement, whereas the potential for cognitive activation mediated the relationship between teacher beliefs and students’ achievement. Tentative implications for practice are drawn in the Discussion, followed by an outlook on two other aspects of teacher beliefs investigated in COACTIV: beliefs about the role of the teacher and beliefs about the cultural diversity of the student population.

The Model of Instructional Quality in COACTIV: A Multicriteria Analysis

This chapter describes the concept of instruction on which the COACTIV approach is based and presents empirical findings obtained using the measurement instruments developed in the COACTIV framework. The chapter starts by describing the understanding of instruction that guided research in COACTIV, namely, as an opportunity for insightful learning. It then outlines empirical results from the COACTIV study, distinguishing between sight structures and deep structures of instructional quality. Descriptive findings on sight structures show that teacher-led discussion, seatwork, and work with a partner continued to predominate, while individualized approaches were rare. A multicriteria approach was taken to deep structures, with analyses considering three core dimensions of high-quality instruction: classroom management, cognitive activation, and teacher support for a variety of student outcomes. Latent two-level structural equation models showed that students’ mathematics achievement was substantially fostered by efficient classroom management and a high level of cognitive activation, that their enjoyment of mathematics was promoted by efficient classroom management and individual learning support, and that their anxiety was reduced by individual learning support. Teachers varied substantially in their instructional quality, in terms of both sight and deep structures.

Teachers’ General Pedagogical/Psychological Knowledge

This chapter focuses on general pedagogical/psychological knowledge (PPK) as a constitutive element of teachers’ professional knowledge. It introduces the conceptualization of PPK used in the COACTIV research program, describes the development of a test directly assessing PPK, and summarizes first findings from a validation study. PPK, as the knowledge needed to create and optimize teaching–learning situations across subjects, is conceptualized as a multifaceted construct including knowledge of classroom management, teaching methods, classroom assessment, and student heterogeneity. A 39-item measure using multiple-choice items, short-answer items, and video-based items was developed to assess this domain of teacher knowledge. Experts rated the items to be relevant for teaching, domain general, and authentic. The measure was then administered to 746 teacher candidates in the context of COACTIV-R. Results provided empirical support for the theoretically derived structure of PPK and showed that the facets of PPK could be assessed with satisfactory reliability, that the measure was sensitive to differences between groups, and that the knowledge assessed did not overlap to any great extent with discriminant constructs. Furthermore, PPK was positively related to the quality of instruction as perceived by students.

Using Digital Media to Assess and Promote School and Adult Education Teacher Competence

Classrooms are informational environments that are highly complex in nature. Teachers need to make use of many different information sources in the classroom in order to adapt to these environments, perform successfully, and develop competence. Hence, effective design research in teacher education has to take this high complexity into account too, for instance by using video technologies. In the chapter presented here, we describe a research program that uses the advantages of digital media to assess and promote teacher competence. A web-based learning and testing environment was designed and implemented in several studies with school and adult education teachers. We successfully developed a test instrument to measure the pedagogical/psychological knowledge of teachers in the two chosen educational contexts via the web-based environment. Results of several intervention studies indicated that the web-based learning and testing environment with integrated video case studies is a powerful tool to promote taking on new perspectives and applying knowledge among school and adult education teachers. Implications for research, practice, and the required web-based infrastructure are discussed.

Linking teacher and parent ratings of teacher-nominated gifted elementary school students to each other and to school grades

This study investigated teacher and parent ratings of teacher-nominated gifted elementary school students’ verbal abilities, mathematical abilities, deductive reasoning, creative thinking, and engagement, and connected these ratings to school grades. Teacher and parent ratings were compared with regard to accuracy levels and halo effects. Furthermore, this study explored the correlations between teacher and parent ratings and how they are related to school grades. The study was based on data from 572 elementary school students participating in an enrichment program. The results indicated the same accuracy levels for teachers and parents. However, teacher ratings were more strongly affected by halo effects than parent ratings. The correlations between teacher and parent ratings were small to medium. Both raters’ ratings were independently and positively associated with German grades when controlling for each other. Positive teacher or parent ratings of mathematical abilities and engagement buffered the relation between the other rater’s ratings and math grades.