The Dialectic Relationship between Research and Practice in Mathematics Teacher Education

This paper addresses issues linking research in student teacher learning with reflection on practice in mathematics teacher education. From a situated perspective on learning and practice, we explore our own practice as teacher educators while researching student teacher learning in our classrooms. We describe a study on student teacher learning, considering student teacher learning as a “process of becoming”, and how the results of this research have affected our development as mathematics teacher educators and members of a community of inquiry. Our work shows how in the mathematics teacher education context the relationship between theory and practice becomes an element of both teacher educator and researcher development.     

Conceptualising Resources as a Theme for Teacher Education

In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.     

Teaching teachers to teach Boris: a framework for mathematics teacher educator pedagogical content knowledge

The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.     

Language of learning and teaching in schools: an issue for research in mathematics teacher education?

Most countries in Africa have introduced the use of local languages as the language of learning and teaching for the first few years of schooling. Meaning that for the first few years of learning, learners learn mathematics in their local languages. In response to this, most research has focused on the challenges of using local languages in multilingual mathematics classrooms in schools. Not much research focuses on how the teacher educators prepare the prospective teachers to teach mathematics in multilingual classrooms. To further knowledge in the area of multilingualism in mathematics education, I, in this paper, present an analysis of the literature on multilingual teacher education in Africa. Specifically, I look at what it is that governments in interested countries are doing in teacher education programs in response to the introduction of local languages in schools. From the literature examined, I found that although there is awareness in a number of countries of the need for multilingual teacher education, not much has been done in order to train mathematics teachers on how to use local languages in the classroom. I therefore recommend that, for those countries that have implemented or planning to introduce the use of local languages in schools, some reforms should also take place in teacher education programs in terms of training the prospective teachers how to teach in local languages.     

PROFESSIONAL NOTICING PRACTICES OF NOVICE MATHEMATICS TEACHER EDUCATORS

The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those educating teachers. This research explores how novice mathematics teacher educators professionally notice as they engage in teaching experiments and create models of student’s mathematical thinking. Findings indicate the novice teacher educators are including some evaluative comments in their professional noticing practices but lack in-depth interpretive analysis about student thinking and rarely make connections between student’s thinking and the broader principles of teaching and learning. These findings provide evidence for the importance of supporting teacher educators with developing their abilities to professionally notice.     

The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators

Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge in teaching “Methods of Teaching Elementary Mathematics” courses. Five mathematics teacher educators, all with experience in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect the individual perspectives by situating them in the context of unifying themes, both theoretical and practical.     

Research on Learners and Teachers of Mathematics and Science: Forerunners to a Focus on Teacher Educator Professional Growth

This introductory paper first reflects the genesis of research in mathematics and science teacher education. The analyses show a movement from foci of research in mathematics and science education from students to teachers, and then to teacher educators. Next, an overview of research in mathematics and science teacher education and its development is provided, including teacher educators’ growth. This is followed by a comparative look at the seven papers in this special issue through three lenses, focusing on who the teacher educators in these papers are, the practices which are the focus for development, and the contexts in which the professional growth is situated. The seven papers not only exemplify how teacher educators might critically and systematically reflect on their own growth, educate new teacher educators, and do corresponding research, but also demonstrate the considerable progress the research community has made with respect to the professional growth of mathematics and science teacher educators in the last decade. Finally, challenges and questions are raised, in particular in relation to raising the quality and quantity of proficient teacher educators in order to strengthen teacher education research, and to have enough human resources to offer more and better professional development opportunities and to support schools.

     

The Dialectic Relationship between Research and Practice in Mathematics Teacher Education

This paper addresses issues linking research in student teacher learning with reflection on practice in mathematics teacher education. From a situated perspective on learning and practice, we explore our own practice as teacher educators while researching student teacher learning in our classrooms. We describe a study on student teacher learning, considering student teacher learning as a “process of becoming”, and how the results of this research have affected our development as mathematics teacher educators and members of a community of inquiry. Our work shows how in the mathematics teacher education context the relationship between theory and practice becomes an element of both teacher educator and researcher development.     

Early career mathematics teachers: Concepts,methods, and strategies for comparative international research

In this article, we report on the challenges entailed in the development of concepts, methods, and strategies for designing and implementing a cross-national research study of the first-years of school-mathematics teaching, including an exploration of how beginning mathematics teachers differ in their preparation, knowledge for teaching, teaching practice, working conditions, and pupil characteristics. The study was designed as a proof-of-concept for a study of teaching and teacher education to be implemented by educationalists, teacher educators, and early career teachers as an ongoing professional endeavor. Primary among the challenges was the development of the sampling design and the construction of measures.     

Mathematics teacher educator knowledge: What do we know and where to from here?

The knowledge that mathematics teacher educators need has attracted limited but increasing attention in recent years. The papers in this special issue build on emerging themes from that work and raise additional questions that contribute towards a future research agenda in the field. Several of the articles develop conceptualisations of teacher knowledge to apply to mathematics teacher educators, introducing new aspects and drawing attention to unique characteristics of mathematics teacher educators in the process. To some extent the questions these papers raise reflect similar questions in mathematics education more generally but for which the implications for mathematics teacher educators warrant attention. In this paper we review the articles in this special issue and use them as a springboard to examine contemporary developments in the field and posit ways forward for research on mathematics teacher educators’ knowledge.     

Peer observations among faculty in a college of education: investigating the summative and formative uses of the Reformed Teaching Observation Protocol (RTOP)

Teacher educators piloted the use of the Reformed Teaching Observation Protocol (RTOP), a peer observation instrument associated with increases in learning in science and mathematics teacher education courses. Faculty participants received a series of trainings in RTOP use and rated each other’s teaching during multiple peer observations. The purpose of this study was to investigate whether the RTOP would prove useful for formative and summative purposes across teacher education courses in general. While participants saw value in the peer observation process and the RTOP instrument, findings suggest that the perceived formative functions of the RTOP outweighed the instrument’s summative value.     

Mathematical biography and key rhetoric

The intention of this article is to consider the use of narrative and rhetorical inquiry as research methods. I construct a mathematical biography of one elementary teacher trainee, Sirpa, who had performed well in her advanced mathematics course in upper secondary school. I describe her development as a mathematics teacher during teacher education from her second-year methods course and teaching practice to fourth-year teaching practice. Narrative inquiry is more than a case study: Sirpa’s mathematical biography is a story that describes how she constructs her mathematical identity. I also analysed the key rhetoric that Sirpa used in her talk, key rhetoric here referring to the strategy by which she constructed continuity and coherence.     

Mathematics, computers, and young children as a research-oriented learning environment for a teacher candidate

The advent of computer technology in the classroom raised the issue of its appropriate use by teachers and their students alike. It has been recommended that teacher education programs provide more opportunities for teacher candidates’ use of technology including teaching their own technology-enhanced lessons. With a goal of integrating scholarship into student teaching, a teacher candidate enrolled in a graduate program in childhood education carried out a technology-enhanced research project within a professional development school. Examining the impact of the project on the teacher candidate, this article describes how one’s pedagogical content knowledge and technological competence can be developed through a research-oriented teaching experience. The article also demonstrates the emergence of a community of practice that shares the goal of providing learning spaces for the teacher candidate and young children in the context of mathematics enrichment with computers.     

An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood

The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics education, so too does the focus on teaching quality. This paper reviews nine instruments designed to measure mathematics teaching quality—their theoretical bases, foci, and psychometrics—and examines their appropriateness for administration in early childhood settings. Three of the nine measures are identified as having highly desirable characteristics, with one of them specifically designed for early childhood administration. The measures, our review process, and our recommendations for practice are presented. As school divisions and teacher educators examine teaching quality, they will be better able to support their teachers’ practice, and better able to reap the benefits in improved child outcomes.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

Discourses about School-based Mathematics Teacher Education in Finland and Sweden

In this cross-case study we focus on school-based teacher education in Sweden and Finland. Through the use of focus-group interviews with mathematics teacher educators in Finland and Sweden, the study shows that there are substantial differences in how school-based teacher education is introduced and portrayed in the discourse about teacher education and prospective teachers' learning. The school-based teacher education among the Finnish groups is made relevant in relation to several aspects of prospective teachers' learning. In the Swedish groups, school-based teacher education is portrayed as an organizational problem and few aspects of prospective teachers' learning are brought into the discourse. The results cannot be generalized to the two countries but show interesting conceptualizations of school-based education potentially useful for teacher educators and scholars.     

Teacher educators mediating curricular reform: anticipating the Australian curriculum

Many education systems are experiencing a re-scaling and consolidation of governance through rolling national agendas of standardisation and centralisation. The present article considers the case of Australia as it moves towards implementing its first national curriculum, to explore how teacher educators plan to retain pedagogical space for debate, diversity and contestation of such systemic curricular reform. The present article reports on an interview study conducted with nine teacher educators across the four curriculum areas included in the first wave of the Australian curriculum: English, science, mathematics and history. The analysis reveals how teacher educators reported professional dilemmas around curricular design, and planned to resolve such dilemmas between the anticipated changes and their preferences for what might have been. While different curricular areas displayed different patterns of professional dilemma, the teacher educators are shown to construe their role as one of active curriculum mediators, who, in recontextualising curricular reforms, will use the opportunity to reinsert both residualised and emergent alternatives in their students’ professional value sets. The study also identifies a new set of dilemmas emerging around the politicisation and standardisation of curriculum, and its impact on the teaching profession and teacher educators.     

Why is Finnish teacher education successful? Some goals Finnish teacher educators have for their teaching

In recent years, Finnish research‐based teaching, according to international surveys, has been shown to lead to excellent results. Previous research has demonstrated that teacher education has often had difficulties in incorporating theory into practice, and that the effects of teacher education on the prior beliefs and views on teaching and learning of student teachers have been weak. The aim of the present qualitative study was to find out how the Finnish teacher education system deals with these problems by investigating the current goals Finnish teacher educators have for their own teaching in theoretical courses. A total of 18 teacher educators were interviewed in five focus groups on different teacher education programmes in Finland. The interview results showed that Finnish teacher educators transmit theoretical and pedagogical aspects by using them in their own teaching, which is research‐based. They also aim to educate reflective and exploring teachers by using a variety of methods in their own pedagogy. The exemplary role the Finnish teacher educators have can be helpful in influencing prospective teachers' behaviour and thinking.     

Multiple representations as sites for teacher reflection about mathematics learning

This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.