Teacher Education And Development Study In Mathematics Research Articles

Identifying and dealing with student errors in the mathematics classroom: Cognitive and motivational requirements.

Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students' knowledge and skills. Mathematics teachers need to be highly attentive to students' thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students' errors. To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers' ability to identify students' errors was assessed based on (a) a digitalized speed test showing different students' solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson's mathematical content. Teachers were asked to analyze students' thinking and to determine how best to react. In addition, teachers' mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers' abilities to identify, analyze, and deal with students' errors. The results indicate that all components are interrelated. However, path analysis reveals that teachers' ability to deal with students' errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students' errors is largely dependent on their mathematics content knowledge. The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.

Costa Rican Preservice Mathematics Teachers’ Readiness to Teach

Mathematics teachers’ knowledge for teaching mathematics has been broadly studied in recent years, and many theoretical frameworks and instruments have been created to measure and improve knowledge and competencies to teach mathematics. The knowledge gained from these studies has been crucial in understanding and determining what mathematics teachers should learn. In Costa Rica, there is a lack of regulations regarding the training that mathematics teachers receive and the knowledge and competencies they acquire in the different teacher education programs. This study investigates the knowledge for teaching mathematics of Costa Rican preservice teachers using the Teacher Education and Development Study in Mathematics (TEDS-M) instrument to identify strengths and weaknesses in their training. A mixed-method analysis of the responses of 79 participants revealed that they were well prepared for cognitive application skills but showed weaknesses in the development of reasoning skills. Additionally, the solutions highlighted significant deficiencies in participants’ monitoring of their own work and in the ability to provide feedback on students’ work. We hope that our findings could inform universities and policy makers to improve the quality of teacher education programs.

Teacher noticing and its growth toward expertise: an expert\u2013novice comparison with pre-service\xa0and in-service secondary mathematics teachers

Although strong references to expertise in different theoretical approaches to teacher noticing have been made in the last decades, empirical knowledge about the development of teacher noticing from novice to expert level is scarce. The present study aims to close this research gap by comparing three different groups of mathematics teachers with different degrees of professional teaching experience—pre-service teachers at the master’s level, early career teachers, and experienced teachers—using data sampled in the frame of the research program from the Teacher Education and Development Study in Mathematics (TEDS-M). Furthermore, the construct of teacher noticing is assessed in a differentiated way by analyzing different noticing facets. Findings confirm that three facets of teacher noticing can be empirically distinguished—perception of important classroom events, their interpretation, and decisions regarding further developments. The results reveal a considerable increase in professional noticing between master’s students and practicing teachers. However, in contrast to other studies, among examples from East Asia, a stagnation or decrease in professional noticing between early career teachers and experienced teachers could be observed. Overall, the study highlights the cultural dependency of expertise development regarding teachers’ noticing.

Mathematics Teacher Education in Turkey through the Lens of International TEDS-M Study

This paper is a part of a broader study which aims to investigate mathematics teacher candidates' mathematical knowledge for teaching (MKT) by using the Turkish translated versions of TEDS-M (Teacher Education and Development Study in Mathematics) Primary and Secondary Released Items. The sample of the study comprised freshman (first year) and senior (fourth and fifth year) students from primary and secondary mathematics teacher education programs. Firstly, this study aimed to examine differences in MKT of teacher candidates at the beginning and at the end of their undergraduate education. For both departments, senior students had statistically significant higher scores than freshman students. Secondly, this study also aimed to examine participating Turkish preservice mathematics teachers’ mathematical knowledge for teaching by using international results of TEDS-M Study. Participating senior preservice teachers’ correct response percentages were higher than international average in all domains except “data” in primary level, and “data”, “mathematical modelling” and “symmetry” in secondary level. The common content domains where primary and secondary preservice teachers’ percentages were lower than international average is “data”. In this paper, these areas will be examined within the context of Turkish education.

Mathematical Beliefs Held by Costa Rican Pre-Service Teachers and Teacher Educators

Beliefs have been conceived as a hidden variable in mathematics education. It is important to know teachers’ beliefs as they can inform the way that teachers teach mathematics, make decisions in the classroom, and form opinions about the abilities of students. In Costa Rica, studies about beliefs have been conducted with in-service teachers, but there is no research on pre-service teachers and the beliefs they bring to the classroom from their teacher education programs (TEPs). This research aims to describe the beliefs held by 76 pre-service teachers and 19 teacher educators from four Costa Rican public universities, using the Teacher Education and Development Study in Mathematics (TEDS-M) questionnaire. The results suggest that both pre-service teachers and teacher educators believe in a constructivist orientation focused on the learner. Both groups support the view of mathematics as a process of inquiry and active learning and agree that mathematical skills are not fixed or associated with gender or culture. In the literature, the beliefs manifested by the participants are associated with positive results regarding student outcomes and teaching practices. Therefore, policymakers should be concerned with providing environments that allow and encourage teachers to continue with these belief orientations when they start teaching.

Differences in teacher education programmes and their outcomes across Didaktik and curriculum traditions

ABSTRACT Teacher education is of vital importance for what teachers are capable to do for their pupils, but little is known about student teachers’ pedagogical knowledge. The Didaktik and the curriculum traditions are two main education approaches underpinning formal schooling and teacher education programmes (TEPs) in the Western world. The main difference between the two traditions lies in the content and objectives of teacher education, which are either theoretical or action-oriented. Two questions are addressed quantitatively: How do teacher education programmes and their outcomes vary across Didaktik and curriculum traditions? How do opportunities to learn and beliefs about teaching methods affect mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) scores? Empirical data from the Teacher Education and Development Study in Mathematics (TEDS-M) are used, with samples from Norway, Germany, Switzerland, and the US. The study offers alternative explanations for variations of TEPs’ outcomes within the Western world.

What skills and knowledge do university mathematics teacher education programs give future teachers in Costa Rica?

High-quality teaching is crucial for improving mathematics education. Teaching mathematics requires specific knowledge, including knowledge of both content and pedagogy. In this study, we analyzed the knowledge for teaching mathematics among 80 future teachers from four mathematics teacher education programs in Costa Rica. Using the Teacher Education and Development Study in Mathematics (TEDS-M) questionnaire, we studied the opportunities to learn the programs provide and the participants’ performance in tests of their mathematical content and pedagogical knowledge. The results showed that all the teaching programs involved gave more emphasis to the topics covered in tertiary level mathematics than to aspects of general and mathematics pedagogy. Moreover, the results highlighted the variation among universities in the participants’ performance in the tests and demonstrated that the number and content of the courses taken was not correlated with the participants’ performance. These findings offer insights to the Costa Rican government and policymakers into the actual structure, variability, and characteristics of teacher education programs, which could serve as a tool for making decisions on measures to improve the quality of teaching.

Perception of student errors under time limitation: are teachers faster than mathematicians or students?

The ability to offer constructive feedback to students concerning their errors is an indispensable requirement for mathematics teachers, for the purpose of providing cognitively challenging learning opportunities. However, if they are to react adequately, teachers need to identify student errors immediately. The fast perception of student errors can therefore be described as an indispensable part of mathematics teachers’ professional competence. Data on this facet of teacher competence were gathered as part of a national follow-up-study of the IEA’s international TEDS-M (Teacher Education and Development Study in Mathematics) that used a time-limited test to measure teachers’ perception of student errors. This paper aims to provide evidence for the validity of the test interpretation of fast student-error perception as an indicator of professional competence by drawing on contrast groups already used in other studies. Overall, the study could support the validity of the test interpretation because the chosen contrast groups were found to perform either better than the tested teachers—as is the case for the contrast group of mathematicians—or more poorly, as is the case for the group of students. Furthermore, the present study shows that the competence facet of fast student error perception is closer to the domain of teachers’ mathematical content knowledge than it is to the domain of teachers’ mathematics pedagogical content knowledge.

Field Experience and Prospective Teachers' Mathematical Knowledge and Beliefs

This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics learning. Early instruction-focused field experience (i.e., leading directly to classroom instruction) was positively related to the study outcomes in programs with such field experience of median or shorter duration. Moreover, the duration of instruction-focused field experience was positively related to study outcomes in programs without early instruction-focused field experience. By contrast, the duration of exploration-focused field experience (e.g., observation) was not related to the study outcomes. These findings suggest that field experience has important but largely overlooked relationships with prospective teachers' mathematical knowledge and beliefs. Implications for future research are discussed.

Measurement of job motivation in TEDS-M: testing for invariance across countries and cultures

The paper presents the challenges of cross-country and cross-cultural research on the motivation to become a mathematics teacher based on data from the “Teacher Education and Development Study in Mathematics (TEDS-M)”. Referring to studies from cross-cultural psychology, measurement invariance (MI) of constructs representing different motivations to become a teacher was examined in confirmatory factor analysis (CFA) across the countries that participated in TEDS-M. The data supported metric invariance which means that comparing relationships between motivation and other constructs across countries is permitted, with the exception of extrinsic motivation in Taiwan. Scalar invariance was not supported by the data across countries but across cultures: Scale means can be compared between Germany, Switzerland and (with regard to intrinsic motivation) Norway and Poland as well as between Singapore and Taiwan (with regard to the intrinsic motivation) and Malaysia, Philippines and Thailand (again regarding intrinsic motivation).

Professional competencies of (prospective) mathematics teachers—cognitive versus situated approaches

Recent research on the professional competencies of mathematics teachers, which has been carried out during the last decade, is characterized by different theoretical approaches on the conceptualization and evaluation of teachers’ professional competencies, namely cognitive versus situated approaches. Building on the international IEA Teacher Education and Development Study in Mathematics (TEDS-M) and its follow-up study, TEDS-FU, the paper compares cognitive and situated approaches on professional competencies of teachers. In TEDS-FU, the cognitive oriented framework of TEDS-M has been enriched by a situated orientation including the novice-expert framework and the noticing concept as theoretical approaches on the analyses of classroom situations. Correspondingly, the evaluation instruments were extended by using video vignettes for assessing teachers’ perception, interpretation, and decision-making competencies in addition to cognitive oriented knowledge tests. The paper discusses the different kinds of theoretical frameworks and the consequences for the evaluation methods, the strengths, and weaknesses of both approaches. Furthermore, connecting the results of TEDS-FU with TEDS-M allows comprehensive insight into the structure and development of the professional competencies of mathematics teachers, the complex interplay between the different facets of teachers’ competencies, and the high relevance of teaching practice for the development of these competencies. The analyses show on the one hand that both approaches—cognitive and situated—are needed for a comprehensive description of teachers’ professional competencies. On the other hand, it is shown that both approaches can be integrated in a productive way. The paper closes with prospects on further studies coming even closer to the real classroom situation.

About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers’ Competence

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 “Teacher 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 decision-making skills. Reliability and validity concerns remain an issue of such assessments for which solutions are proposed. Overall, the paper shows that a more comprehensive evaluation of teachers’ competence comprising cognitive-affective and situated facets is possible and has been achieved.

The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers’ knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this study is to explore whether elementary teaching candidates’ MCK and MPCK are associated with their opportunities to learn in mathematics courses and mathematics methods courses in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components.

A Comparative Study of Mathematics Teachers’ Beliefs and Practices in Russia, Estonia, and Latvia

Teachers’ beliefs should be changed in order to introduce modern teaching methods in education. The notion of “belief” combines the ideas, attitudes, and personal philosophies teachers apply in their work. We differentiate between traditional beliefs about teaching as a direct transfer of knowledge and constructivist beliefs assuming that students construct their knowledge themselves through specifically organized activities. We have analyzed the key teacher belief research projects: the OECD’s Teaching and Learning International Survey (TALIS), the cross-cultural Teacher Education and Development Study in Mathematics (TEDS-M), and the Nordic-Baltic Comparative Research in Mathematics Education (NorBA) that we borrowed a questionnaire from. Our survey involved teachers of mathematics in three countries: 390 teachers in Latvia (of which 95 with Russian as their native tongue), 332 teachers in Estonia (of which 92 with Russian as their native tongue), and 1,096 teachers in the Russian Federation. We have found that differences between teachers in different countries were statistically important in all the variables used in the study, regardless of whether Estonian and Latvian teachers were Russian-speaking or not. All teachers implemented their beliefs in their everyday classroom practices. 36% of teachers in Russia had a high level of constructivism (as compared to 26% in Latvia and 18% in Estonia). Proportion of teachers with low levels of traditionalism in Latvia and Estonia (appr. 25% in both) was higher than the same proportion among Russian teachers (17.5%). We have come to a conclusion that different approaches to education system reforms in Russia and in the Baltic states have resulted in a significant diversity of beliefs among teachers of mathematics. Thus, proportion of teachers with low levels of traditionalist beliefs has grown in the Baltic countries more than in Russia, which explains to some extent higher PISA points of Estonian and Latvian students.

Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M) by M. T. Tatto, , John Schwille, , S. L. Senk, , Lawrence Ingvarson, , Glenn Rowley, , Ray Peck, , Kiril Bankov, , Michael Rodriguez, and Mark Reckase. Amsterdam: IEA, 2012. 295 pp. €40

Previous articleNext article No AccessPolicy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M) by M. T. Tatto, , John Schwille, , S. L. Senk, , Lawrence Ingvarson, , Glenn Rowley, , Ray Peck, , Kiril Bankov, , Michael Rodriguez, and Mark Reckase. Amsterdam: IEA, 2012. 295 pp. €40 (paper) or free download (from IEA website). ISBN 978-9-079-54912-2.Esther LevensonEsther Levenson Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Comparative Education Review Volume 57, Number 4November 2013 Sponsored by the Comparative and International Education Society Article DOIhttps://doi.org/10.1086/674063 Views: 73Total views on this site Citations: 1Citations are reported from Crossref For permission to reuse, please contact [email protected]PDF download Crossref reports the following articles citing this article:Aļesja Šapkova THE RELATIONSHIPS BETWEEN THE TRADITIONAL BELIEFS AND PRACTICE OF MATHEMATICS TEACHERS AND THEIR STUDENTS’ ACHIEVEMENTS IN DOING MATHEMATICS TASKS, Problems of Education in the 21st Century 58, no.11 (Mar 2014): 127–143.https://doi.org/10.33225/pec/14.58.127

Considerations for correlation analysis using clustered data: working with the teacher education and development study in mathematics (TEDS-M) and other international studies

The Teacher Education and Development Study in Mathematics (TEDS-M) of 2008 focused on how teachers are prepared to teach mathematics in primary and lower-secondary schools in 17 countries. The main results were published in 2012, and the associated public-use database provides a valuable source for secondary analysis of the collected data. The data originate from complex samples and present a hierarchical structure. With future teachers embedded in programs embedded in institutions, various types of cluster effects can be observed. Complex methods, including the use of sampling weights and replication methods for variance estimation, are therefore required for data analysis. This paper focuses on the aspects that need to be considered during any exploration of relationships between variables. Correlation analysis may produce misleading results if attention is not paid to the structure under which the data were collected. We illustrate our points with exemplary analysis of TEDS-M data and propose some guidelines to address the issue.

ARE TAIWANESE AND SINGAPOREAN FUTURE TEACHERS SIMILAR IN THEIR MATHEMATICS-RELATED TEACHING COMPETENCIES?

This study investigates the similarities and differences of mathematics-related teaching competencies between the future secondary school teachers of Taiwan and Singapore by using data from the international Teacher Education and Development Study in Mathematics (TEDS-M), organized by the International Association for the Evaluation of Educational Achievement. Taiwan and Singapore are identified as the only two Asian countries integrating the Chinese/Confucian tradition in their education regarding TEDS-M. The relative strengths and weaknesses of these two countries, as compared to other TEDS-M higher-achieving Western countries, such as Germany, Poland, Russia, Switzerland, and the USA, are examined after reselecting and reclassifying the achievement items based on Niss’ (2003) mathematics competence and Hsieh’s (Secondary Education, 63(3), 2012) mathematics teaching competence structures. This study shows that Singaporean future teachers are weaker in the competence of devising formal mathematical arguments and transforming heuristic ideas into valid proofs than Taiwanese future teachers. Taiwan and Singapore demonstrate relative strengths at primary, lower-, and upper-secondary levels in mathematics competencies but show relative weaknesses at the tertiary level than do other higher-achieving Western countries. Comparing these two countries, Taiwan shows relative strengths at upper-secondary and tertiary levels, and Singaporean strengths are at primary and lower-secondary levels. This distinction is primarily because of the thought-oriented category of mathematics competencies. This study also finds that Taiwan and Singapore belong to different clusters compared with the higher-achieving Western countries regarding their future teachers’ relative strengths and weaknesses in either mathematics or mathematics teaching competence.

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 students’ achievement in school mathematics (e.g., Sowder 2007), 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 (e.g., Wilson, Floden, and Ferrini-Mundy 2001) and in an international context (e.g., Leung and Li 2010). 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.

Knowledge of future primary teachers for teaching mathematics: an international comparative study

This article reports the results of the Teacher Education and Development Study in Mathematics (TEDS-M) that are related to prospective primary teachers’ knowledge for teaching mathematics. TEDS-M was conducted under the auspices of the International Association for the Evaluation of Educational Achievement with additional support from the US National Science Foundation and the participating countries. In 2008 more than 15,000 future primary teachers, enrolled in about 450 institutions that prepare future primary teachers, were surveyed. Two domains of knowledge for teaching mathematics were assessed using items that had been developed and validated in a cross-national field trial. Large differences in the structure of teacher preparation programs are reported. Differences in mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) were also observed both within and between programs and countries. Anchor points on the MCK and MPCK scales are used to describe qualitative characteristics of knowledge for teaching mathematics.

Preparing primary teachers in the United States: balancing selection and preparation

The recent movement in the United States toward common (national) mathematics standards brings to the fore issues of implementation which includes how teachers are prepared to teach. The Teacher Education and Development Study in Mathematics (TEDS-M) provide an international context for an in depth analysis of the US primary future teachers’ TEDS-M results. The US education system is decentralized with many aspects controlled by the states and many other aspects controlled by over 16,000 local school districts. Consequently, there is great variation in what secondary mathematics individuals have had before entering teacher preparation. In addition, as certification is a state regulation, teacher preparation programs also differ in what is provided to prospective teachers. Analyses reveal significant relationship between both of these to the mathematics content knowledge and mathematics pedagogical content knowledge of US future primary teachers. A two-stage hierarchical model is used to explore the relative contribution of these two factors.