Contrasting Research Perspectives: What the evidence yields

This paper reviews pre-service elementary teachers' beliefs about mathematics and mathematics teaching and, learning from an earlier study of the mathematics methods course of a teacher education program, then overviews the data triangulation, and discusses the inconsistencies and contradictions in the data. Thus, the study offers further insight into the complexities of pre-service teachers' unwavering conceptions and their acquisition of innovative pedagogy. Questions emerged about the inconsistencies between what was said and what was done. For example, why were the pre-service teachers' responses in surveys and interviews inconsistent with their instructional behavior? Explanations to this and other questions are offered to shed some light on two of the most unsettling features of teacher education: changing pre-service teachers' beliefs and their learning of mathematics pedagogy.     

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.     

Cognitive Scientists Prefer Theories and Testable Principles With Teeth

The visions of mathematics classrooms called for by current educational reform efforts pose great challenges for kindergarten through Grade 12 schools and teacher education programs. Although a number of colleges and universities throughout the country are making changes in their teacher education programs to reflect these reform recommendations, we have little systematic information on the nature of these programs or their impact on prospective teachers. These issues are of central concern in the study-Learning to Teach Secondary Mathematics in Two Reform-Based Teacher Education Programs-that we draw on in this article. The article focuses on 1 preservice teacher's (Ms. Savant) knowledge, beliefs, and practices related to proof, tasks, and discourse. A situative perspective on cognition and components of teachers' professional knowledge frame our research. We examined data on Ms. Savant's experiences in her teacher education program to understand the influences of teacher education on her development as a mathematics teacher. This research indicates that Ms. Savant's teacher education experiences did make a difference in her development as a teacher. Her mathematics methods course provided a large collection of tasks, engaged her and her preservice colleagues in discourse, and provided her with both formal and informal experiences with proof-all of these experiences reflecting reform-based visions of mathematics classrooms. The situative perspective on cognition directed our attention to issues of compatibility of goals and visions across the various university and kindergarten through Grade 12 classroom settings, and it helped us to understand why some aspects of reform-based pedagogy are more easily learned than others: Why some ideas and practices learned as a student in the university setting are more easily transported to the novice teacher's kindergarten through Grade 12 field setting. We conclude that compatibility of these settings on several key dimensions is essential for the settings to reinforce each other's messages, and thus work in conjunction, rather than in opposition, to prepare reform-minded teachers.     

Preservice Primary Teachers' Geometric Thinking: Is Pre-Tertiary Mathematics Education Building Sufficiently Strong Foundations?

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that develop preservice teachers' geometric knowledge to support the task of teaching. This study examines the geometric thinking levels of entry-level Irish preservice primary teachers (N = 381). Participants' geometric thinking levels were determined through a multiple-choice geometry test (van Hiele Geometry Test) prior to commencing a Geometry course within their ITE program. The findings reveal limited geometric thinking among half of the cohort and question the extent to which pre-tertiary experiences develop appropriate foundations to facilitate a smooth transition into ITE mathematics programs. The study also examines the nature of misconceptions among those with limited geometric thinking and presents suggestions to enhance the geometric understandings of preservice teachers.     

TELPS: A method for analysing mathematics pre-service teachers' Pedagogical Content Knowledge

A pre-service teacher's Pedagogical Content Knowledge (PCK) and their personal constructs of teaching develop throughout their teacher education program. PCK integrates generic pedagogical knowledge, mathematical teaching methodology and knowledge of the discipline of mathematics and this paper reports on a survey that can be used to assess a pre-service teacher's PCK. TELPS (Teacher Education Lesson Plan Survey) was developed to determine the PCK of pre-service teachers during their teacher education program. TELPS is shown to analyse pre-service teachers' PCK with some indication that the pre-service teacher's development of PCK can be observed.     

Pre-service teachers' beliefs about and attitudes toward mathematics: the case of Dudu

There is a need to move beyond the use of predetermined categories to classify teachers' orientations and an attempt should be made to understand, from the teachers' perspectives, their orientations and the beliefs from which they are generated. Such an understanding may help in the development of mathematics teacher education programmes that will assist teachers to formulate appropriate attitudes toward mathematics. This paper provides an in-depth study of one pre-service elementary teacher's views about mathematics and mathematics teaching. Dudu is a `case' that fits in with the emergent themes identified in the larger sample. Data for the study were collected by means of audio tape, an observational framework, field notes, student's written work and unstructured and formal interviews. The themes that emerged and that were emphasised by the participant were: limited vision for mathematics, construction of meaning in mathematics, knowledge of mathematics content and poor self-perception of pre-service primary mathematics teachers. The findings also suggest that although the participant reported uneasiness in learning mathematics, she was very enthusiastic about her teaching practice.     

Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers

In comparing content knowledge (CK) and pedagogical content knowledge (PCK) of Taiwanese and German inservice mathematics teachers, the present study examines whether the two-dimensional structure of teachers' subject matter knowledge is cross-culturally invariant and whether differences in teacher education and in teacher selection are reflected in teachers' subject matter knowledge. The results confirm that CK and PCK represent two distinct, but correlated dimensions, even in teachers from completely different backgrounds. Taiwanese inservice teachers showed considerably higher CK and also higher PCK scores than German teachers. Teacher education and teacher selection should be considered important levers for reform in mathematics education.     

A proficiency model for pre-service physics teachers' pedagogical content knowledge (PCK)—What constitutes high-level PCK?

This study identifies proficiency levels in pre-service physics teachers' pedagogical content knowledge (PCK) and reveals how teacher education can promote transitions into higher proficiency. Teacher education plays a fundamental role in supporting pre-service teachers' PCK development. Proficiency levels are a powerful source when evaluating this PCK development because they characterize what learners are likely to be able to know on a specific level. Previous research has presented a model of proficiency levels in pre-service physics teachers' PCK; however, evidence for the model's validity is still lacking. According to the Refined Consensus Model of PCK, factors such as teachers' content knowledge (CK), their teaching experience, and their beliefs about teaching and learning science promote PCK development. Thus, understanding how and when pre-service physics teachers' CK, teaching experience, and beliefs contribute to their proficiency can bring insights into how teacher education can promote PCK development. To address this issue, N = 427 observations of pre-service physics teachers were analyzed. Utilizing the scale anchoring procedure, four different proficiency levels in pre-service physics teachers' PCK were identified. Analyzing these proficiency levels showed that lower levels can be characterized as remembering content-unspecific knowledge, whereas higher levels encompass content-specific strategies to structure and elaborate lessons. Additionally, logistic regression models revealed that pre-service physics teachers' CK is crucial for an increase in PCK proficiency. However, transitions into higher levels of PCK additionally require teaching experience and adequate beliefs about teaching and learning. Thus, our proficiency levels can be used to bring insights into how proficiency in PCK can be supported during teacher education. For example, teacher education should provide courses focusing on the science curriculum and the assessment of student learning to promote pre-service physics teachers' progression in PCK.     

Special education pre-service teachers' interest,subject knowledge,and teacher efficacy beliefs in mathematics

Teacher efficacy beliefs is an important characteristic to predict instructional quality and the level of cognitive activation and educational support. Since teacher efficacy beliefs are context and domain specific, this study focuses on how special education pre-service teachers' individual interest and subject knowledge in mathematics predict their efficacy beliefs in teaching mathematics. Data were collected from 57 special education pre-service teachers. The results indicated that the individual interest of pre-service teachers has a strong effect on teacher efficacy beliefs, while subject knowledge has only an indirect effect.     

The Assessment of Mathematics and Science Teacher Quality

The purpose of this study was to examine the types of instruments being used to document mathematics and science teacher quality characteristics in 48 nationally funded mathematics and science education awards. Each of the 48 projects operationalized teacher quality and determined how to assess it. The main research questions examined the instruments awardees used to gather data on mathematics and science teacher quality, and the main characteristics of teachers examined by awardees. Results showed that awardees most frequently used surveys or questionnaires to assess characteristics of mathematics and science teacher quality. The most common teacher characteristics examined by awardees' included teacher behaviors, practices, and beliefs, followed by the assessment of subject and pedagogical knowledge, and the documentation of mathematics and science teachers' certification. A few new instruments were under development and in use to assess characteristics of teacher quality. Detailed information on the development and psychometric properties of the instruments used for these examinations was not available from the reports. Because awardees were at different stages in their funded activities and data collection efforts were ongoing at the time of this analysis, this study offers a preliminary and formative review of the use of assessments to document mathematics and science teacher quality characteristics among these awards.     

Pre-service teachers' dispositions towards diversity: Arguing for a developmental hierarchy of change

This article explores Australian pre-service teachers' beliefs about and attitudes towards diversity. Building on Garmon's [Garmon, M. A. (2004). Changing preservice teachers' attitudes/beliefs about diversity: what are the critical factors? Journal of Teacher Education, 55(3), 201–213] argument that there are three dispositional factors that influence students' likelihood of developing multicultural awareness and sensitivity in teacher education programmes, the authors explore the relationship between such dispositions as exhibited in students' autoethnographic work. In so doing, the authors posit that these dispositions may be hierarchically developed: beginning from ‘self-awareness/self-reflectiveness’; moving towards ‘openness’; and finally a ‘commitment to social justice’. After exploring the nature of this hierarchical development through the in-depth investigation of six representative student accounts, the paper concludes by discussing the implications for teacher education, including the necessity to adjust our expectations of changing the dispositions of pre-service teachers in discrete, short courses.     

Investigating the impact of teacher education strategies on preservice teachers' TPACK

The purpose of this study was to examine preservice teachers' perceptions of the support their teacher education programs provide for developing their technological pedagogical content knowledge (TPACK). The research was conducted with 215 preservice teachers in the last year of teacher education programs and teaching certificate programs in three universities in Turkey. Data sources were the synthesis of qualitative evidence (SQD) scale that was validated in the Turkish context as part of this study and the TPACK-practical scale. The strategies investigated in the SQD-model included: using teacher educators as role models; reflecting on the role of technology in education; learning how to use technology by design; collaboration with peers; scaffolding authentic technology experiences; and providing continuous feedback. The linear regression analysis revealed a positive relation between teacher education strategies and preservice teachers' TPACK. Reflection and teacher educators' as role models were the most frequently used teacher education strategies in teacher education programs included in this study. Results provided recommendations for further research on the connection between the teacher education strategies and the development of preservice teachers' TPACK in teacher education programs.     

Games Teachers Play

An important social concern in mathematics education is that the educational attainment of pupils may be influenced by teachers' competence in the curricular area they are teaching. This paper provides some insight into the relationship between student primary teachers' mathematics subject knowledge and their reported confidence to teach that subject. Eighty Bachelor of Education first year students completed an attitudes survey as well as an online mathematics competence test which consisted of 28 randomly generated questions from a bank of approximately 300 questions based on the attainment targets of the Scottish curriculum 5–14 document at level F with some E. Students were asked to rank teacher attributes. Though 98% of the students ranked basic numeracy skills as the most important, 65% of the cohort did not possess these skills. Moreover 95% suggested confidence was important, but confidence levels were found to be low even among students with higher than minimum entry requirements to the undergraduate primary teaching programme. It is perhaps not the level of mathematics that needs to be changed but the nature of mathematics taught and learned at that level that needs to be addressed. This in turn has implications for the approaches and the programmes deployed by Initial Teacher Education courses.     

Professional identity creation: Examining the development of beginning preservice teachers' understanding of their work as teachers

The importance of reflection in supporting the continued professional learning of preservice practitioners is well recognised. This study examines one aspect of the outcomes of preservice teachers' reflection: the development of their own self-image as a teacher. In making the transition from student to teacher, preservice teachers create their own professional identity. Their ability to articulate this identity is examined through a new construct, a “teachers' voice”. A teachers' voice, develops when preservice teachers interpret and reinterpret their experiences through the processes of reflection. A teachers' voice is articulated as part of the persons' self-image. The construct, a teachers' voice, was investigated by examining changes in preservice teachers' contributions in an online discussion forum. Two complementary approaches of content analysis were applied. Both methods revealed changes in preservice teachers' levels of engagement and showed that in the first semester of preservice teacher education, the majority of preservice teachers moved towards a more professional stance in their contributions.     

Preservice elementary teachers' views of pedagogical and mathematical content knowledge

In broad terms, this study describes preservice elementary teachers' beliefs, conceptions, and practices during the mathematics methods course and teaching practica of a teacher education program. In particular, the study employs qualitative data to investigate preservice teachers' views of mathematical and pedagogical content knowledge. The study reveals symbiotic relationships between their views of content knowledge and their instructional actions which remain problematic. With unwavering beliefs and practices, and without reconceptualizing their roles as future elementary teachers, at the end of the semester the preservice teachers emerge as poor duplicators of mathematics methods instead of initiators of learning.     

Can cooperating teachers help student teachers develop a vision of education?

Abstract

Research in teacher education is increasingly concerned with teachers' visions of education and their sense of calling, mission, and professional identity. Interviews with outstanding cooperating teachers focused on exploring their beliefs on teacher vision, and what makes a good teacher. The teachers were also asked to discuss their beliefs on whether vision—and the independence of spirit that a strong vision is thought to foster—is relevant in their work with student teachers. The teachers revealed a strong sense of why they teach and shared goals around several themes. They also maintained that reflection is key to developing a vision of education. Teacher education programs can support these teachers' views of quality education by developing conceptual frameworks that foster reflection and the development of a vision for education, particularly in the student teaching experience.     

Participants' Roles in the Context of a Video Club

This study examines the nature of teacher participation in the context of a video club. Video clubs are professional development meetings in which teachers watch and discuss excerpts of video from their classrooms. In this study, I adopt a situative perspective to examine how teachers develop in their participation to accomplish the goals of the video club. In particular, I examine the roles participants play and explore teachers' participation in four roles that correspond with key goals of the video club. Analysis revealed that teachers' participation shifted in qualitatively different ways over time, with the teachers coming to prompt the group to discuss student mathematical thinking, to propose a variety of interpretations of student ideas, to build on one another's ideas, and to challenge one another's thinking in order to advance the group's conversations. This analysis suggests that the group learned how to participate in roles central to accomplishing the goals of the video club. Studying teacher learning through a lens of participation provides insight into the ways in which teachers coordinate themselves to engage with the goals of professional development and has implications for designing professional development that helps teachers develop practices for teaching mathematics for understanding.     

An exploratory study of the knowledge base for science teaching

The purpose of this study was to describe the knowledge base of a group of science teachers in terms of their knowledge of the structure, function, and development of their disciplines, and their understanding of the nature of science. The study also aimed to relate the teachers' knowledge base to their level of education, years of teaching experience, and the class level(s) that they teach. Twenty inservice science teachers were selected to respond to a modified version of the Views on Science–Technology–Society (VOSTS) questionnaire to assess their understanding of the nature of science. The teachers then constructed concept maps and were interviewed. The concept maps were scored and the interviews analyzed to assess teachers' knowledge of the structure, function, and development of their disciplines. The teachers' knowledge base was found to be lacking in all respects. Teachers held several naive views about the nature of science and did not demonstrate adequate knowledge and understanding of the structure, function, and development of their disciplines. Moreover, the teachers' knowledge base did not relate to their years of teaching experience, the class level(s) that they teach, and their level of education. It was reasoned that teacher preparation programs are not helping teachers develop the knowledge base needed for teaching science. © 1997 John Wiley & Sons, Inc. J Res Sci Teach 34: 673–699, 1997.     

Teachers' democratic and efficacy beliefs and styles of coping with behavioural problems of pupils with special needs

This study examines how teachers actually cope with behavioural problems of included students. In order to understand the impact of individual differences on teachers' coping strategies, the authors looked at the relationship between these strategies and teachers' democratic beliefs and self‐efficacy. Participants were 33 teachers in Israel, who teach inclusive classes (1st–3rd grade). Data were collected through classroom observations, teacher interviews and questionnaires. In the interviews, teachers reported that they preferred helpful strategies as a solution to behavioural problems; however, classroom observation revealed that teachers actually used more restrictive responses. These results indicated that there is a gap between teachers' hypothetical knowledge and their applications of this knowledge in authentic classroom situations. In addition, positive correlations were found between teachers' democratic beliefs, teacher efficacy and the use of helpful strategies in regard to different behavioural problems. Practical implications for teacher education are discussed.     

Gender inclusion and horizontal gender segregation: stakeholders' strategies and dilemmas in Swedish teachers' education

This paper contributes to our knowledge of teacher educators' strategies for, and dilemmas with, working with gender inclusion in teachers' education. It illustrates how gender is constructed and reconstructed in teachers' education. The study revealed that teachers' education is not only – as earlier described – a highly feminised field, it is also a discipline that is permeated by horizontal and vertical segregation typical of higher education. The study analyses how university teacher educators experience and handle consequences of this horizontal segregation, building on interviews with subject representatives at a Swedish university. The results exemplify how university teachers reflect on gender policies and their own roles when working with teacher students. Heteronormative patterns also become visible in strategies meant to facilitate gender equality and desegregation. The author argues for the need to include university teachers' perspectives in future strategies for developing gender inclusion in university education.