Sigrid Blömeke

Teacher Education Effectiveness: Quality and Equity of Future Primary Teachers’ Mathematics and Mathematics Pedagogical Content Knowledge

The effectiveness of teacher education was examined by taking two indicators into account (Creemers and Kyriakides, “The dynamics of educational effectiveness: a contribution to policy, practice and theory in contemporary schools”, 2008): future teachers’ mean achievement on a paper-and-pencil test as an indicator of quality and the variability of teacher achievement due to background characteristics as an indicator of equity. In detail, the effects of gender and language on mathematics content knowledge and mathematics pedagogical content knowledge were examined. The analyses were embedded in IEA’s “Teacher Education and Development Study in Mathematics” (TEDS-M) and they referred to primary teachers from 15 countries in their final year of teacher education. The study revealed significant cultural differences in the effectiveness of teacher education. Gender and language effects could be decomposed into direct and indirect effects. The latter represented a combination of differential choices of teacher education programs according to background characteristics and differential achievement of teachers from these programs. Implications for educational policy are discussed.

General Pedagogical Knowledge of Future Middle School Teachers: On the Complex Ecology of Teacher Education in the United States, Germany, and Taiwan

For more than two decades, three components of teacher knowledge have been discussed, namely, content knowledge (CK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK). Although there is a growing body of analytic clarification and empirical testing with regard to CK and PCK, especially with a focus on mathematics teachers, hardly any attempt has been made to learn more about teachers’ GPK. In the context of the Teacher Education and Development Study in Mathematics (TEDS-M), Germany, Taiwan, and the United States worked on closing this research gap by conceptualizing a theoretical framework and developing a standardized test of GPK, which was taken by representative samples of future middle school teachers in these countries. Four task-based subdimensions of GPK and three cognitive subdimensions of GPK were distinguished in this test. TEDS-M data are used (a) to test the hypothesis that GPK is not homogenous but multidimensional and (b) to compare the achievement of U.S. future middle school teachers with future middle school teachers from Germany and Taiwan. The data revealed that U.S. future teachers were outperformed by both the other groups. They showed a relative strength in one of the cognitive subdimensions, generating strategies to perform in the classroom, indicating that in particular they had acquired procedural GPK during teacher education.

Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries

First findings of IEA’s “Teacher Education and Development Study in Mathematics (TEDS-M)” had revealed differences in the demographic background, prior knowledge, opportunities to learn (OTL), and outcomes of primary teacher education between future teachers from different countries. In this chapter, two hypotheses are examined: (1) OTL and teacher background are significant predictors of mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) as teacher education outcomes. (2) OTL effects are partly mediated by differential student teacher intake. Data from multilevel models reveal that effects on MCK are in general larger than on MPCK. Gender, prior knowledge and OTL in mathematics are significantly related to both types of outcomes whereas other background characteristics affect MPCK only. Motivation mediates the effects of prior knowledge and the OTL effects are partly mediated by teacher intake. Consequences for educational policy are discussed based on these results. Policymakers have on the one hand to be aware of the continuing problem of societal inequalities. Providing OTL in mathematics as well as increasing entrance selectivity may, on the other hand, have positive consequences for the outcomes of primary teacher education.

The conceptualisation of mathematics competencies in the international teacher education study TEDS-M

The main aim of the international teacher education study Teacher Education and Development Study in Mathematics (TEDS-M), carried out under the auspices of the International Association for the Evaluation of Educational Achievement (IEA), was to understand how national policies and institutional practices influence the outcomes of mathematics teacher education. This paper reports on the definition of effective mathematics teacher education in TEDS-M, distinguishing between mathematics content knowledge and mathematics pedagogical content knowledge as essential cognitive components of mathematics teachers’ professional competencies. These competence facets were implemented as proficiency tests based on extensive coordination and validation processes by experts from all participating countries. International acceptance of the tests was accomplished whereas, by necessity, national specifications had to be left out, as is common in comparative large-scale assessments. In this paper, the nature of the TEDS-M tests for the primary study is analysed and commented on detail. The aims are to increase our understanding of mathematics content knowledge and mathematics pedagogical content knowledge, which are still fuzzy domains, to provide a substantive background for interpretations of the test results and to examine whether some educational traditions may be more accurately reflected in the test items than others. For this purpose, several items that have been released by the IEA are presented and elaborately analysed in order to substantiate the test design of TEDS-M. Our main conclusion is that the overall validity of the TEDS-M tests can be regarded as a given, but that readers have to be aware of limitations, amongst others from a continental European point of view.

Homogeneity or Heterogeneity? Profiles of Opportunities to Learn in Primary Teacher Education and Their Relationship to Cultural Context and Outcomes

The curriculum of teacher education has been described as heterogeneous across countries and influenced by the context in which it is implemented. The present study investigates this potential heterogeneity by conducting latent class analysis of opportunities to learn mathematics, mathematics pedagogy and general pedagogy in primary teacher education as indicated by future teachers from 15 countries at the end of their training. The aim was to identify curriculaprofiles based on data from the “Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M)”. In each teacher education component, three groups of primary teachers were identified which differed quantitatively and qualitatively. Associations between these profiles and countries revealed broader cultural influences on OTL and thus shared (within a culture) and at the same time distinct (between cultures) visions of what primary teachers should know. Within countries, associations between curricula profiles and teacher education programs pointed to shared (within a program) and at the same time distinct (between programs) visions of what primary teachers should know at the end of their training. The OTL profiles were significantly related to outcomes of primary teacher education in terms of mathematics content knowledge, mathematics pedagogical content knowledge and general pedagogical knowledge.

Content, Professional Preparation, and Teaching Methods: How Diverse Is Teacher Education across Countries?.

A teacher education program offers opportunities to learn (OTL) consistent with its vision of what teachers need to know and be able to do. The “Teacher Education and Development Study: Learning to Teach Mathematics” of the International Association for the Evaluation of Educational Achievement provides, for the first time, the possibility to examine the diversity of OTL across countries. A latent class analysis reveals that it was sufficient to group the 8,000 future teachers from 15 countries into four classes to describe their OTL with respect to the content delivered, their professional preparation and the teaching methods experienced. Such commonality indicates more homogeneity than usually discussed in the comparative literature. This result may be, in turn, an indicator of an inherent logic of mathematics teaching.

Modeling and Measuring Competencies in Higher Education

Measuring competencies acquired in higher education has to be regarded as a widely neglected research field. The progress made in empirical research on the school system since the 1990s – for example, through large-scale assessments such as the Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) and through a massive expansion of instructional research in general – has revealed that nothing comparable exists at the higher education level.

Learning from the Eastern and the Western Debate—The Case of Mathematics Teacher Education

Comparative studies have gained significant influence in the last decades, and school systems of many countries have been revised referring to better results of other countries in international large-scale assessments. Authors of such studies commonly link their interpretations of the results to distinctions between “Eastern” and “Western” cultures, in particular with respect to the consistent and continuing outstanding performance of East Asian learners compared with their Western counterparts. One question is whether the same achievement pattern holds for future teachers and whether similar cultural differences may cause it. International Association for the Evaluation of Educational Achievement’s “Teacher Education and Development Study in Mathematics” (TEDS-M) was the first comparative study that focused on the outcomes of teacher education with standardised testing. In this paper—based on the TEDS-M results—commonalities and differences in the achievement of future teachers from Eastern and Western countries are explored and related to a cultural perspective. Cultural differences between Eastern and Western approaches concerning mathematics, mathematics education and mathematics teachers are analysed with respect to the achievement pattern. The paper closes with reflections on possible consequences concerning the development of teachers’ knowledge and teachers’ expertise in mathematics education.

Theoretical Framework, Study Design and Main Results of TEDS-M

The comparative “Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M)”, carried out under the supervision of the International Association for the Evaluation of Educational Achievement (IEA), provided the opportunity to examine the outcomes of teacher education in terms of teacher knowledge and teacher beliefs both across countries and specifically with respect to mathematics for the first time. This chapter describes the conceptual framework that guided TEDS-M and its study design. The instruments used to measure teacher knowledge and beliefs as well as opportunities to learn (OTL) are described. In addition, core descriptive results, previously only published in German (see Blomeke et al. “Cross-national comparison of the professional competency of and learning opportunities for future primary school teachers”, 2010a; “Cross-national comparison of the professional competency of and learning opportunities for future secondary school teachers of mathematics”, 2010b (in German)), are described. These results serve as the basis for the other chapters in this monograph. It turns out that teacher education institutions structure their provision of OTL in a way that is consistent with their particular philosophy of what teachers need to know and be able to do. The need to strengthen teachers’ content knowledge is one of the dominant ideas that has guided reform efforts in many countries over the past 20 years. The results of TEDS-M which are reported in this chapter are therefore crucial for policymakers. In addition, international comparisons provide benchmarks for national teacher education systems. Countries that do better in TEDS-M may have more effective teacher training programs than countries at the bottom end of the ranking.

Comparing future teachers’ beliefs across countries: approximate measurement invariance with Bayesian elastic constraints for local item dependence and differential item functioning

Using data from the international Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M), the measurement equivalence of teachers’ beliefs across countries is investigated for the case of ‘mathematics-as-a fixed-ability’. Measurement equivalence is a crucial topic in all international large-scale assessments and widely undervalued for non-achievement measures. Although it is well known that cultural differences may affect response styles or meaning of constructs, and although comparability is often not specifically examined, international large-scale assessment results are typically compared across countries in terms of scale means. Full scalar invariance is typically unattainable in such international assessments due to their sheer size and local item dependence issues. To deal with both challenges, a Bayesian approach is introduced that uses informative priors to define elastic equivalence constraints to investigate the comparability of TEDS-M future teachers’ beliefs under a working assumption of approximate measurement invariance. Substantively, a clear pattern of three groups of countries emerged that corroborates preliminary findings in other studies for other teacher beliefs. Future mathematics teachers in Thailand, Malaysia and the Philippines believed more strongly that mathematics is a fixed ability, whereas the USA, Chile, Norway, Germany and Switzerland believed less strongly in this. Taiwan, Singapore, Poland and Russia took the middle ground.