Mathematics professional development for elementary teachers: Building trust within a school-based mathematics education community

Despite increased attention in professional development to building communities of teachers, few studies have investigated the development of trust in these communities. This paper presents issues related to trust in a professional development project at an elementary school. The project aimed for school-based elementary teachers and university-based mathematics educators to work together to improve mathematics instruction at the school by developing a mathematics education community of learners, where learners were conceived of as both the teachers and the mathematics educators. This paper addresses the following question: What factors in the project supported the development of trust among mathematics educators and teachers as the community was formed? More specifically, the paper is about one aspect of trust, namely, building school-based elementary teachers’ trust in the university-based mathematics educators. We point to three factors that helped the development of trust and we use care theory to further understand and discuss these factors in the context of in-service teacher education initiatives.     

课堂教学视野下的反思性数学学习

数学课程标准对学生的反思性数学学习给予了很高的关注,但当前数学课堂教学中学生反思性学习的现实状况却不容乐观。这主要表现为：教师的课堂权威挤占了学生进行自我反思的空间;学生在数学学习中的自我反思能力水平普遍偏低。通过分析课堂教学视野下反思性数学学习的具体内涵,可以发现数学课堂教学中学生进行反思性学习的重要意义主要在于发展学生的数学思维能力、促成个体化的数学学习方式和促进学生自主性的发展。     

Exploring early childhood preservice teachers’ mathematics anxiety and mathematics efficacy beliefs

Early childhood preservice teachers participated in a qualitative multiple case study to explore and examine the effectiveness of reform-based constructivist methods used in a mathematics methods course to change their mathematics anxiety, mathematics self-efficacy, and mathematics teachers’ efficacy beliefs. Findings indicated that instructor’s use of a variety of reform-based strategies to teach and model concepts were effective in reducing their mathematics anxiety and improving their mathematics self-efficacy and mathematics teaching efficacy beliefs. Based on these findings, it is recommended that mathematics methods course instructors use reform-based constructivist methods in their courses as outlined by the NCTM’s (2014) principles. Teacher educators must also consider carefully their attitudes and disposition toward mathematics along with the type of classroom and learning environment they establish in mathematics methods courses. They must emphasize conceptual understanding during mathematics methods courses, understand the connection between preservice teachers’ mathematics anxiety and mathematics efficacy beliefs, and integrate field experiences as well as peer teaching opportunities into mathematics methods courses.     

第二课堂数学教育教学的实践与认识

第二课堂与第一课堂共同构成高校人才培养系统。第二课堂数学教育教学既是对第一课堂教育教学的有益补充,又是培养新一代实践型大学生的有效途径。本文以新疆工程学院为例,针对高校数学教育教学面临的问题和不足,探讨了第二课堂数学教育教学的途径和方法。通过构建大学第二课堂数学教育教学体系,实现了大学生数学知识、能力、素质协调发展,提升了学生的综合素质,为大学数学教育工作者提供了供参考与借鉴。     

Learning by Exploration in Mathematics Courses: a programme for student teachers

In order to adapt teacher education to new demands in mathematics classrooms, it is necessary to change the courses in mathematics at the university. Teachers’ beliefs about mathematics, learning and teaching has great impact on their teaching. At the University of Göteborg, a co‐operative project has been conducted in order to design a programme based on problem solving in courses taken by prospective Comprehensive School teachers (grade 4‐‐9). The main purpose of the project has been to make student teachers more reflective about mathematics as such, about learning and teaching. Another purpose of the project has been to use a teaching method in a university course‐‐a method which could be applied in a school classroom. The student teachers have worked co‐operatively in small groups of 3‐4 students and the educators role has been that of a facilitator. A preliminary evaluation indicates that student teachers have developed an insight into the complexity of learning and teaching, even though there are variations in this respect. However they still have difficulties in applying the method to teaching mathematics at school.     

数学课堂教学中如何融入思政教育

数学是高中教育阶段的一门重要学科,对学生思维能力形成和综合素养提升具有十分重要的现实意义,实际教学中注重融入思政教育,不仅可以丰富课堂教学内容,还能促进数学教学目标达成。本文联系数学课堂教学中融入思政教育的重要性,从丰富教学素材、打造智慧课堂、渗透数学文化、改进教学方法等方面入手,提出几点有效融入措施,希望可以给其他教育工作者提供有效参考。     

Establishing mathematics for teaching within classroom interactions in teacher education

Teacher educators’ processes of establishing “mathematics for teaching” in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the establishment of mathematics for teaching is dependent on the use of keywords from the mathematics education domain, the introduction of variation, and the use of generic communicative strategies. As such, the study could be seen as a contribution to ongoing research on how mathematics teacher educators interactively deal with mathematics for teaching.     

Learning to Teach Mathematics: Questioning, Listening, and Responding

This paper reports a study designed to explore prospective teachers' learning to teach mathematics in the complex context of a university-based curriculum and instruction course. The course, taught with a focus on inquiry, used prospective teachers' weekly interactions with students as springboards for investigations of mathematics, teaching, and learning. A framework of questioning, listening, and responding is used to analyze prospective teachers' understandings and the tensions they experienced. The difficulties and tensions prospective teachers face in turn pose challenges and tensions for teacher educators. This revised version was published online in July 2006 with corrections to the Cover Date.     

The multiple voices of a mathematics classroom community

Several mathematics educators have expressed their concern about conflicting visions of educational reform among parents and teachers, which could result in the emergence of multiple voices in discussions of achievement and instruction. The aim of this article is to examine the multiple voices of educational reform in the discourse of a third grade classroom community. In order to achieve our aim, we integrated the social and the individual as well as the past, present, and future in our analysis of the discourse in this classroom community using theoretical frameworks and methods from cultural psychology. Although our analyses focused on the classroom teacher, we employed units of analysis capable of bridging the individual and her social context. We began our analysis by focusing on a sample of whole-class discussions of students’ strategies for solving multi-digit word problems. This analysis isolated two distinct voices: one that occurred during discussions of students’ invented strategies and the other that emerged during talk about standard algorithms. We extended our analysis to include information about the historical, social, and institutional context of the classroom community in order to understand the origins and functions of these two voices. This additional information helped us appreciate the interconnections between the teacher’s personal feelings, beliefs, recollections, and expectations; and her interpersonal transactions with her students, their parents, and other educators. We concluded with a discussion of the implications of the study for understanding one of the dilemmas of educational reform and for advancing research in classroom discourse. This revised version was published online in July 2006 with corrections to the Cover Date.     

From Teacher to Teacher Educator: Reframing knowledge in practice

This paper concludes our report of an investigation of two beginning teacher educators making the transition from classroom teacher to university-based teacher educator. The authors combined case study and self-study of teacher education practices to investigate features of the institutional context they encountered, the knowledge they employed in their decision-making, and the merging of their former identities as classroom teachers with their new identities as teacher educators. Our initial paper described the theoretical framework, methodology, and two categories of findings—institutional context and shifting role identification. This paper builds on those insights by addressing the frames of understanding and knowledge employed in this transition, and how these frames informed the decisions made in the arena of teacher education practice. We also explore the implications of these findings by discussing the need for support as educators make the transition from teacher to teacher educator.     

华人数学课堂之透视

同世界其它各地一样,华人地区的新数学课程改革也已经全面铺开,深入到课堂.传统的教学观念和改革取向的教学要求在课堂中产生了激烈的震荡.如何提升数学课堂教学质量,已经成为数学教育和教学工作者的迫切任务.本研究在系统分析有关华人数学课堂研究的基础上,试图刻画华人数学课堂教学的基本特点.最后,讨论如何在张扬传统优点的同时改进华人数学课堂教学.     

Learning Through Reflection in Mathematics Teacher Education

This article is written from our perspective as both researchers and mathematics teacher educators, and describes how our knowledge has grown as we engage concurrently in both teaching and research. Reflection-on-action is a means for us of approaching the relationship between theory and practice that comes out of the development of our work as researchers and mathematics teacher educators. The article presents the different steps we have identified in the relationship between theory and practice during our professional development. In the discussion, we examine the whole sequence of steps showing what we have learnt. Afterwards, we use the sequence of activity of the reflective process as a framework in which we can operate and reflect about our own development.     

The Influences of University-Based Coursework on Field Experience

This study explored the influence of university-based teacher education courses on preservice teachers as they engaged in the field-based portion of their preparation. Forty-two preservice teachers contributed reflective writings about the successes and challenges they faced during field experiences in light of knowledge and skills learned during their university-based coursework. Participants’ self-reflective writings were coded and analyzed for emerging themes that cut across all responses. The results indicated a shift from concerns about performance of teaching tasks in the classroom to concerns about the performance of students in terms of learning. This shift was consistent with a goal of the preservice program, namely, helping preservice teachers focus on student learning.     

Gender Bias in Guatemalan Counselor Education Students: Using an Experiential Activity as a Stimulus

This article features the implementation and outcome of an experiential activity addressing gender bias in students at three university-based Guatemalan counselor education programs. The authors present students’ thematic responses delineating expectations of gender-specific communication styles and roles. A sequence of activities and students’ reflective commentaries are included, with suggestions for counselor educators in addressing gender bias in student populations.     

Reflective states associated with creating inquiry‐based mathematical discourse

A secondary school mathematics teacher and mathematics education researcher engaged in a collaborative professional development experience that focused the teacher’s reflection on videotapes of his instruction. The purpose was to document and explore the teacher’s experiences with respect to his reflections and classroom practice while trying to create inquiry‐based mathematical discourse. Data included videotaped classroom observations, audiotaped interviews, and audiotaped focused reflection sessions. Analysis of the data revealed that over the course of the semester‐long collaboration the teacher exhibited, at various times, four different reflective states (‘explain but not question’, ‘question but not explain’, ‘question and explore’, and ‘exploring’). The identification of these reflective states suggests a more complex relationship between reflection and changing teachers’ practice than previously thought. The results of this article suggest that the interaction of teachers’ reflective activities and reflective states contribute to various kinds of teacher change in the classroom.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

Reflection on the teaching-learning process in the initial training of teachers. Characterization of the issues on which pre-service mathematics teachers reflect

Our aim was to highlight the issues of the reflections of pre-service mathematics teachers in their learning portfolio about the teaching-learning process taking place in a university teacher-training classroom. Category systems were designed which, together with the analysis system used, could provide a method helpful to teacher educators, teachers and to future research. The pre-service teachers showed difficulty in considering themselves as ‘authentic’ mathematics teachers. The study revealed that the preparation of a portfolio can help pre-service teachers learn more about themselves and provide educators insight into how to help pre-service mathematics teachers engage in the teaching-learning process.