Modeling and Measuring Knowledge and Competencies of Teachers: A Threefold Domain-Specific Structure Model for Mathematics(7 Empirische Studien zur Didaktik der Mathematik)

Because it is seen as one constitutive factor of instructional quality, research in teaching and learning increases attention on teachers' expertise. To explain success in student learning for example, recent studies used content knowledge and pedagogical content knowledge as predicting variables for expertise. This study analyses potential disadvantages of these approaches: Competent situational classroom management requires more than just content knowledge and pedagogical content knowledge. The topic of this publication is the analysis and description of additional domain-specific competencies. It proposes a model compatible with existing approaches which consists of three components of domain-specific competencies: first, a basic component of mathematical and mathematical pedagogical knowledge, second, reflective competencies, and third, action-related competencies. It is also discussed how these three constructs could be operationalized. It is proposed complementing the known paper-and-pencil item formats with video- and computer-based formats to increase the validity of tests. Moreover, design and results of a feasibility study with teachers and prospective teachers from secondary level are reported. The results show that, in principle, it is possible to measure the three areas of competencies separately.

Table of Contents:
I Modeling Knowledge and Competencies of Teachers; 1 Basic Terminology: Knowledge, Competencies, Learning, and Expertise; 1.1 Knowledge; 1.1.1 Procedural, Conceptual, Tacit, Inert, and Abstract Knowledge; 1.1.2 Episodic Knowledge; 1.1.3 Knowledge and Problem Solving; 1.1.4 Meta-Cognition; 1.2 Competencies; 1.3 Learning; 1.4 Expertise; 1.4.1 Experts and Research on Expertise; 1.4.2 Empirical Findings from Non-Teaching Domains; 1.4.3 Empirical Findings in the Teaching Domain; 2 Review: Different Approaches to Teachers' Knowledge and Competencies; 2.1 Focus: Teacher Knowledge; 2.1.1 Shulman's Model and Selected Later Works; 2.1.2 The Michigan Group; 2.1.3 Teacher Education and Development Study (TEDS-M); 2.1.4 The Project COACTIV; 2.1.5 Summary: Research on Teacher Knowledge; 2.2 Focus: Professional Demands of Teachers; 2.2.1 German Teacher Education Standards; 2.2.2 Core Teacher Tasks; 2.2.3 Aspects of High-Quality Teaching; 3 Extended Structure Model: Teachers' Knowledge and Competencies; 3.1 Some Remarks on the Structure Model; 3.2 The Basic Knowledge Component (BK); 3.3 The Reflective Competencies Component (RC); 3.4 The Action-Related Competencies Component (AC); 3.5 Notes on the Assumed Relations between the Three Components; 3.6 Notes on Assumed Differential Characteristics of the Model; II Measuring Knowledge and Competencies of Teachers; 4 Research Questions; 4.1 Feasibility Study: Construction of a Measure; 4.2 Evaluation: Structural and Differential Assumptions; 5 Design of the Feasibility Study; 5.1 Study Design and Computerized Implementation; 5.2 Item Development; 5.2.1 Encountered Limitations; 5.2.2 Operationalization of the Action-Related Component; 5.2.3 Operationalization of the Reflective Component; 5.2.4 Operationalization of the Basic Component; 5.2.5 Assembly of the Items for the Test Session; 5.3 Rating Guidelines and Procedures; 5.3.1 Rating Procedure and Overarching Rating Rationale; 5.3.2 Rating of the Action-Related Component; 5.3.3 Rating of the Reflective Component; 5.3.4 Rating of Items of the Basic Component (BK); 5.3.5 Scoring of the Rated Data; 6 Results; 6.1 Samples; 6.2 Results I: Feasibility Study; 6.2.1 Collection of the Data; 6.2.2 Rating and Scoring of the Data; 6.2.3 Components of the Model; 6.2.4 Discussion: Feasibility Study; 6.3 Results II: Structural and Differential Assumptions; 6.3.1 Relations between the Components; 6.3.2 Further Differential Aspects; 6.3.3 Discussion: Evaluation of the Structure Model; 7 Discussion; 7.1 Measuring Teacher Cognition; 7.2 Possible Implications for Teacher Education

About the Author :
Dr. Anke Lindmeier studied from 1998 to 2005 at the Catholic University Eichstatt-Ingolstadt and finished her studies with a diploma in mathematics and state examinations for secondary teachers (grades 5-12, subject matters mathematics, religious education, computer science). She worked as a research assistant at the mathematics education group of the Ludwig-Maximilians-Universitat Munchen from November 2005 to January 2010. In February 2010, she started as a research assistant at the newly founded School of Education at the Technische Universitat Munchen, Heinz Nixdorf-Chair for Mathematics Education (Prof. Dr. Kristina Reiss). She finished her PhD 2010.

Review :
Lindmeiers Arbeit stellt eine beachtenswerte Erweiterung der bestehenden Forschung dar; die Ergebnisse der Studie stimmen mit den theoretischen Überlegungen überein und das domänenspezifische Strukturmodell zur Beschreibung von professionellem mathematischen Wissen eröffnet eine neue Perspektive auf die kognitiven Ressourcen von Lehrpersonen.