Expanding the instructional triangle: conceptualizing mathematics teacher development

As mathematics educators think about teaching that promotes students’ opportunities to learn, attention must be given to the conceptualization of the professional development of teachers and those who teach teachers. In this article, we generalize and expand the instructional triangle to consider different interactions in a variety of teacher development contexts. We have done so by addressing issues of language for models of teachers’ professional development at different levels and by providing examples of situations in which these models can be applied. Through the expansion of our understanding and use of the instructional triangle we can further develop the concept of mathematics teacher development.     

Changing perspectives: Examining the potential for advanced mathematical studies to influence pre-service teachers' beliefs about mathematics

This study considers the potential for advanced mathematical studies to impact pre-service teachers' beliefs about mathematics. Results show that, after completing a degree which includes advanced mathematical studies, many prospective teachers' beliefs still reflect limited interpretations of key terminology and do not value the theoretical and conceptual network underpinning the rules and procedures of secondary mathematics. Many of their beliefs about the nature of mathematics also fail to recognise its capacity to stimulate analytical thought and creativity. In cases where pre-service teachers showed evidence of well-developed beliefs, the study explores the role of their advanced mathematical studies in this development.     

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.     

Tales out of school: Tracing perspective change through the stories of former teachers

Most public school teachers in the United States now leave the classroom before reaching retirement. This study examined the accounts of certified, experienced teachers who left teaching after making significant investments in the career in order to better understand their exit decisions. Anecdotes told by these invested leavers as they described their career were examined through a narrative lens. The analysis indicated a shift in perspective: as the teachers moved through their career, the primary sources of frustration for these former teachers switched from students to adults.     

Exploring the relationship between teacher enjoyment of mathematics,their attitudes towards student struggle and instructional time amongst early years primary teachers

In this study we explored the relationship between teacher enjoyment of teaching mathematics, their attitudes towards student struggle, and the amount of time teachers spent teaching mathematics. Ninety-eight primary educators were surveyed regarding their attitudes and behaviors towards mathematics instruction. Hierarchical regression analyses revealed that teacher enjoyment of teaching mathematics explained variance in both teacher attitudes towards student struggle and instructional time spent on mathematics, even after relevant educator characteristics were accounted for. Findings suggest that teacher enjoyment of teaching mathematics in the early primary years has important implications for both the quality and quantity of mathematics instruction students receive.     

Living the stories we tell: The sociopolitical context of enacting teaching stories

This article draws from two separate classroom-based studies of early career teachers that yielded overlapping findings about the diminished opportunities teachers and teacher educators have to construct sophisticated stories about the complexities of classroom life and the ongoing process of learning to teach. The teachers' stories represent the intersection of research, policy, and practice, illuminating contradictions between teachers' beliefs about teaching and what they were able to enact in their classrooms. These findings may be leveraged to support teacher educators to support teachers to create coherent narrative identities that help them creatively respond to problems of practice and contextual constraints.     

Opening the black box of field experiences: How cooperating teachers' beliefs and practices shape student teachers' beliefs and practices

This study employed ethnographic methods to describe and explain changes to beginning science teachers' (n = 6) practices and beliefs during a year long internship. Teaching practices were strongly influenced by the cooperating teachers. Initially, all six interns attempted to re-enact lessons they witnessed their cooperating teachers teach, including following lesson structures and borrowing representations, anecdotes, and jokes. Later, they independently implemented instruction that emphasized similar strategies as their mentors, regardless of whether or not they were experiencing success. Interns who were successful also shifted their beliefs to match their mentors.     

Shared beliefs, conflict, and a retreat from reform: the story of a professional community of high school mathematics teachers

This article describes the case of a professional community of high school Pre-algebra teachers who began and later abandoned a collective effort at reform. The community's retreat from reform appears to have been influenced by their beliefs about students and their closely related beliefs about appropriate content and pedagogy for those students. Both sets of beliefs were characterized by conflict and internal inconsistency. Yet, the community avoided addressing the conflicting nature of their beliefs. Both the nature of the community's beliefs and their avoidance of the inherent inconsistencies appear to have shaped the response to reform in this case.     

Conceptualising a pedagogical cultural identity through the narrative construction of early career Aboriginal teachers' professional identities

This paper explores the concept ‘pedagogical cultural identity’ as one that embeds cultural knowledge and lived experience into pedagogical practice. Four narratives were constructed from fifteen in-depth interviews with early career Aboriginal teachers who completed their Aboriginal Studies teaching degree at the University of Sydney. The study found that these teachers enacted their habitus, harnessed their social and cultural capital, and mobilised their relationship building skills in the construction of their professional identity. Significantly, contextual power relations influenced the enactment of a pedagogical cultural identity, challenging assumptions of a presumed identity claim by exploring its potential and limitations.     

Change in beliefs after first-year of teaching: The case of Turkish national curriculum context

The impact of national curriculum context on mathematics related beliefs of 12 beginning middle grades mathematics teachers was investigated after the teacher education program and first-year teaching through interviews and a combination of three belief frameworks. National curriculum requirements, lack of effective mentoring programs, and preservice tutoring experiences were detected as the major factors impacting beliefs. Participants simultaneously had teacher-centered and student-centered beliefs, causing inconsistency in beliefs and practices. While participants’ preservice and first-year experiences contrasted, they developed contextual beliefs to deal with the difficulties. Reflections on teacher education and beginning teacher support policies in national curriculum contexts were discussed.     

Disrespecting teacher: The decline in social standing of teachers in Cape Town,South Africa

This paper examines the declining levels of respect for teachers in two communities in Cape Town, South Africa. Education has been identified as a key area of reform and redress, but a critical skills shortage and under-resourced schools are hindering progress. Data from current and former teachers illustrate how the social and institutional capital of education is being replaced by a focus on economic capital, undermining the prestige of teaching as a career. These problems reflect trends elsewhere in the world and require action to prevent further shortages in education.     

The role of lesson analysis in pre-service teacher education: an empirical investigation of teacher learning from a virtual video-based field experience

A video-based program on lesson analysis for pre-service mathematics teachers was implemented for two consecutive years as part of a teacher education program at the University of Lazio, Italy. Two questions were addressed: What can preservice teachers learn from the analysis of videotaped lessons? How can preservice teachers’ analysis ability, and its improvement, be measured? Two groups of preservice teachers (approximately 140 in total) participated in the program. A three-step lesson analysis framework was applied to three lesson videos: (1) goal(s) and parts of the lesson; (2) student learning; and, (3) teaching alternatives. Preservice teachers’ ability to analyze lessons was measured through an open-ended pre- and post-assessment. In the assessment, preservice teachers were asked to mark and comment on events (in a lesson not included in the program) that they found interesting for: teachers’ actions/decisions; students’ behavior/learning; and, mathematical content. A coding system was developed based on five criteria: elaboration, mathematics content, student learning, critical approach, and alternative strategies. In both studies, the ability to analyze instruction improved significantly on all five criteria. These data suggest promising directions for the development of both an instrument to measure lesson analysis abilities and a model for teacher learning.     

Now and then,in and out of the classroom: Teachers learning to teach through the experiences of their living curricula

How, when, and where do teachers learn to teach? Guided by this question, this article examines the relationships between teachers' living and teaching experiences. Through narrative inquiry, it stories “curricular currents” of three teachers from different teaching contexts, noting the continuity, interaction, and place of the experiences that comprise these currents. It argues that these teachers have learned to teach through their “living curricula,” across all times and places of their lives, not just classroom moments. It concludes by charging teacher education to attend closely to teachers' exploration and analysis of their lives' experiences, in and out of classrooms.     

Motivational beliefs and cognitive processes in mathematics achievement, analyzed in the context of cultural differences: a Korean elementary school example

The relations among students’ motivational beliefs, cognitive processes, and academic achievement were investigated. A 51-item questionnaire together with a mathematics achievement test was administered to 459 fifth graders in Korean elementary school mathematics classrooms. Results indicated that, in general, students’ cognitive processes related closely to competence beliefs, task values, and achievement goals, and more importantly their success or failure in mathematics achievement was closely linked to competence beliefs, performance-avoidance goals, and persistence strategies. Positive evidence of performance-approach goals was observed in math learning relative to task goals. As expected, performance-avoidance goals turned out to be detrimental to students’ math learning. These findings are generally congruent with the motivational theories and support the position that students should be encouraged to adopt task goals and actively involve themselves in math class activities. However, it also behooves us to recognize the potential benefits of performance-approach goals in different cultural contexts, such as the Korean elementary school math classrooms.     

Beginning teachers' experience of the workplace learning environment in alternative teacher certification programs: A mixed methods approach

Workplace learning in early entry (EE) teacher education programs has been proposed as an alternative to traditional programs and as bridging the theory-practice gap in teacher education. However, there is little empirical evidence for the underlying assumption that one can become a highly qualified teacher by merely being a teacher. This article discusses to what extent students of teaching in EE programs experience their work environment as a stimulating learning environment. The results of semi-structured interviews and an online survey suggest that schools tend to hinder rather than serve the purpose of workplace learning. Obstructions and supporting conditions are discussed.     

Intercultural learning in English as foreign language instruction: The importance of teachers’ intercultural experience and the usefulness of precise instructional directives

The development of intercultural competence, especially in foreign language instruction, is considered a key goal of teaching in German schools. The present article sheds light on the teaching of intercultural topics in the context of English as a foreign language (EFL). It presents the results of an analysis of data from a larger study (DESI study – Assessment of Student Achievements in German and English as a Foreign Language) bringing the intercultural experience of teachers and observable aspects of instruction into focus. Videotapes of EFL-classroom instruction of 9th and 10th grade students are analyzed in order to assess characteristic of the implementation of intercultural topics. The study reveals the impact of teachers’ intercultural experience on the quality of their intercultural instruction. Furthermore, the results indicate that precise external directives for particular lessons can help teachers put intercultural topics into practice.     

Decisions to enter and continue in the teaching profession: Evidence from a sample of U.S. secondary STEM teacher candidates

Given its prevalence and cost it is imperative to identify predictors of early career teacher turnover intentions and behavior. During their final year as education majors, 311 US, STEM Secondary Education students rated their student teaching experience, the strength of their teacher identity, and their intent to enter the teaching profession. Within 1–3 years after graduating 191 of them reported whether they remained in the teaching profession. One's identity as a teacher, as well as the perceived quality of student teaching experiences, predicted both intent and actual entry into the teaching profession. Furthermore, teacher identity mediated the relationship between student teaching satisfaction and outcomes.     

Multicultural education: Raj's story using a curricular conceptual lens of the particular

In this study, we employ a curricular conceptual lens of the particular to explore the experience of multicultural education from the perspective of an immigrant student, Raj. Using a school-based narrative inquiry approach, we learn about Raj's experiences at the intersections of immigration and settlement, adaptation and assimilation, English-language acquisition, unemployment, poverty, family violence, and family relocation. We employ Dewey's [(1938). Experience and education. New York: Simon & Schuster] theory of experience, Connelly and Clandinin's [(1988). Teachers as curriculum planners: Narratives of experience. New York: Teachers College Press, Columbia] understanding of curriculum as experience, and Schwab's [(1969). The practical: A language for curriculum. School Review, 78, 1–23] theory of the particular as theoretical frameworks upon which to examine and analyze interactions and events.     

Bodies of knowledge: The concept of embodiment as an alternative to theory/practice debates in the preparation of teachers

The theory/practice divide is a persistent theme in teacher education research. This article reports on a phenomenological study of thirteen newly-qualified teachers across their first two years of teaching and their sense of preparedness to teach. Analysis of interviews with the teachers suggested they equated ‘being prepared’ with ‘being knowledgeable’, with being knowledgeable described in embodied terms, rather than as knowledge held ‘in the head’. We argue that the concept of embodiment, particularly as it has been taken up within the ‘practice turn’ in teacher education, offers a potential alternative to long-standing theory/practice entanglements in debates about learning to teach.