Mathematics teacher preparation examined in an international context: learning from the Teacher Education and Development Study in Mathematics (TEDS-M) and beyond
This thematic issue contains a collection of papers that resulted from the recent Teacher Education and Development Study in Mathematics (TEDS-M), a study that is the first large-scale international comparative study on mathematics teacher preparation undertaken under the auspices of the International Association for the Evaluation of Educational Achievement (IEA). The significance of TEDS-M itself has been well articulated by different authors in this thematic issue. As the importance of teachers and teaching has been commonly acknowledged for the improvement of studentsrsquo; achievement in school mathematics , it becomes apparent that we need to examine and understand possible influences of system policy and institutional practices on the outcomes of mathematics teacher preparation both within an education system and in an international context. The contributions of this thematic issue build upon TEDS-M, including several reports of selected findings from that study. Moreover, this thematic issue goes above and beyond direct reporting of TEDS-M, and includes unique contributions with different natures. To make these contributions explicit, I will highlight some of them as follows.
1、This thematic issue highlights international collaborative efforts in conceptualizing and examining mathematics teachersrsquo; knowledge needed for teaching.
As direct reporting from TEDS-M, this issue contains papers that highlight different constructs used there to examine pre-service teachersrsquo; knowledge needed for teaching. In particular, teachersrsquo; knowledge needed for teaching is conceptualized as consisting of at least two essential components: mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK). Further specifications for MCK follow the assessment framework for mathematics content from the Trends in Mathematics and Science Studies. It thus consists of four content subdomains (number and operations, algebra and functions, geometry and measurement, and data and chance) together with three cognitive subdomains (knowing, applying, and reasoning). The MPCK framework was developed based on a literature review, findings from a previous study, and critical reviews by international experts in the field. Three subdomains were identified and used in TEDS-M: mathematics curricular knowledge, knowledge of planning for mathematics teaching and learning, and knowledge of enacting teaching.
Such a conceptualization of teachersrsquo; mathematics knowledge needed for teaching had never before been developed and used in a large-scale cross-national study. It represents a big step in coming to a general understanding of different content knowledge components important to mathematics teachersrsquo; competence. Based on this knowledge conceptualization, differences in pre-service teachersrsquo; MCK and MPCK were found both within and across programs and systems. Taking a step further, TEDS-M researchers also identified anchor points for both the MCK scale and the MPCK scale to describe qualitative characteristics of knowledge for teaching mathematics.
Besides MCK and MPCK, general pedagogical knowledge (GPK) is also discussed and accepted in conceptualizing teachersrsquo; knowledge needed for teaching. Although TEDS-M had a focus on the content-related knowledge in the common international tests, a national option was used for assessing pre-service mathematics teachersrsquo; GPK. Three education systems (Germany, Taiwan, and the United States) decided to choose this assessment option. According to Kouml;nig and Blouml;meke, a task-based conceptualization of GPK was used to specify four dimensions of GPK (structure, motivation/classroom management, adaptivity, and assessment) together with three performance requirements (recall, understand/analyze, generate) in answering different GPK test items. It seems that the conceptualization of GPK took a perspective different from conceptualizing MCK and MPCK in TEDS-M. Although possible connections among these three knowledge components are not clear, the inclusion of GPK highlighted an important step in understanding and examining the different knowledge components needed for teaching.
2、This thematic issue examines and compares non-cognitive factors that contribute to pre-service teachersrsquo; performance.
Cognitive components are certainly important in conceptualizing and assessing what pre-service teachers need to have for teaching, but so are non-cognitive components. In fact, beliefs about the nature of mathematics were included as an essential component of teacher professional competence in TEDS-M (Felbrich, Kaiser, and Schmotz). A two-dimensional structure was used to represent the dynamic (mathematics as a process of inquiry) and the static (mathematics as a set of rules and procedures) perspectives about the nature of mathematics. Felbrich, Kaiser, and Schmotz not only reported the results obtained from TEDS-M but also tried to make connections with the cultural orientations (i.e., individualistic or collectivist orientation) embedded in participating education systems. While such cultural connections are not conclusive, based on their analyses the results do suggest likely patterns of pre-service teachersrsquo; belief profiles with their cultural orientation across different education systems.
3、This thematic issue includes papers that connect teacher preparation policies and program practices with pre-service teachersrsquo; performance in knowledge tests.
To make further use of the results concerning pre-service teachersrsquo; knowledge needed for teaching, TEDS-M aimed to examine and understand possible influences of national policy and program practices on the outcomes of mathematics teacher preparation. To make such connecti
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Mathematics teacher preparation examined in an international context: learning from the Teacher Education and Development Study in Mathematics (TEDS-M) and beyond
This thematic issue contains a collection of papers that resulted from the recent Teacher Education and Development Study in Mathematics (TEDS-M), a study that is the first large-scale international comparative study on mathematics teacher preparation undertaken under the auspices of the International Association for the Evaluation of Educational Achievement (IEA). The significance of TEDS-M itself has been well articulated by different authors in this thematic issue. As the importance of teachers and teaching has been commonly acknowledged for the improvement of studentsrsquo; achievement in school mathematics , it becomes apparent that we need to examine and understand possible influences of system policy and institutional practices on the outcomes of mathematics teacher preparation both within an education system and in an international context. The contributions of this thematic issue build upon TEDS-M, including several reports of selected findings from that study. Moreover, this thematic issue goes above and beyond direct reporting of TEDS-M, and includes unique contributions with different natures. To make these contributions explicit, I will highlight some of them as follows.
1、This thematic issue highlights international collaborative efforts in conceptualizing and examining mathematics teachersrsquo; knowledge needed for teaching.
As direct reporting from TEDS-M, this issue contains papers that highlight different constructs used there to examine pre-service teachersrsquo; knowledge needed for teaching. In particular, teachersrsquo; knowledge needed for teaching is conceptualized as consisting of at least two essential components: mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK). Further specifications for MCK follow the assessment framework for mathematics content from the Trends in Mathematics and Science Studies. It thus consists of four content subdomains (number and operations, algebra and functions, geometry and measurement, and data and chance) together with three cognitive subdomains (knowing, applying, and reasoning). The MPCK framework was developed based on a literature review, findings from a previous study, and critical reviews by international experts in the field. Three subdomains were identified and used in TEDS-M: mathematics curricular knowledge, knowledge of planning for mathematics teaching and learning, and knowledge of enacting teaching.
Such a conceptualization of teachersrsquo; mathematics knowledge needed for teaching had never before been developed and used in a large-scale cross-national study. It represents a big step in coming to a general understanding of different content knowledge components important to mathematics teachersrsquo; competence. Based on this knowledge conceptualization, differences in pre-service teachersrsquo; MCK and MPCK were found both within and across programs and systems. Taking a step further, TEDS-M researchers also identified anchor points for both the MCK scale and the MPCK scale to describe qualitative characteristics of knowledge for teaching mathematics.
Besides MCK and MPCK, general pedagogical knowledge (GPK) is also discussed and accepted in conceptualizing teachersrsquo; knowledge needed for teaching. Although TEDS-M had a focus on the content-related knowledge in the common international tests, a national option was used for assessing pre-service mathematics teachersrsquo; GPK. Three education systems (Germany, Taiwan, and the United States) decided to choose this assessment option. According to Kouml;nig and Blouml;meke, a task-based conceptualization of GPK was used to specify four dimensions of GPK (structure, motivation/classroom management, adaptivity, and assessment) together with three performance requirements (recall, understand/analyze, generate) in answering different GPK test items. It seems that the conceptualization of GPK took a perspective different from conceptualizing MCK and MPCK in TEDS-M. Although possible connections among these three knowledge components are not clear, the inclusion of GPK highlighted an important step in understanding and examining the different knowledge components needed for teaching.
2、This thematic issue examines and compares non-cognitive factors that contribute to pre-service teachersrsquo; performance.
Cognitive components are certainly important in conceptualizing and assessing what pre-service teachers need to have for teaching, but so are non-cognitive components. In fact, beliefs about the nature of mathematics were included as an essential component of teacher professional competence in TEDS-M (Felbrich, Kaiser, and Schmotz). A two-dimensional structure was used to represent the dynamic (mathematics as a process of inquiry) and the static (mathematics as a set of rules and procedures) perspectives about the nature of mathematics. Felbrich, Kaiser, and Schmotz not only reported the results obtained from TEDS-M but also tried to make connections with the cultural orientations (i.e., individualistic or collectivist orientation) embedded in participating education systems. While such cultural connections are not conclusive, based on their analyses the results do suggest likely patterns of pre-service teachersrsquo; belief profiles with their cultural orientation across different education systems.
3、This thematic issue includes papers that connect teacher preparation policies and program practices with pre-service teachersrsquo; performance in knowledge tests.
To make further use of the results concerning pre-service teachersrsquo; knowledge needed for teaching, TEDS-M aimed to examine and understand possible influences of national policy and program practices on the outcomes of mathematics teacher preparation. To make such connecti
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