Mathematics teacher quality: its distribution and relationship with student achievement in Turkey

A main purpose of the present study was to investigate the distribution of qualified mathematics teachers in relation to students’ socioeconomic status (SES), as measured by parental education, among Turkish middle schools. Further, relationships between mathematics teacher quality indicators and students’ mathematics achievement were explored. Data from the 2007 Trends in International Mathematics and Science Study were used. Relationships between mathematics teacher quality and students’ mathematics achievement were investigated using hierarchical linear modeling. The current study identified SES-related inequities in access to qualified mathematics teachers in Turkey. Low-SES students were more likely to be taught by mathematics teachers who had less than 3 years of experience or who did not hold a degree in mathematics or mathematics education. On the other hand, years of experience and a degree in mathematics or mathematics education were found to be substantially related to Turkish eighth-grade students’ mathematics achievement. Low-SES students’ mathematics teachers were also more likely to report a lack of confidence in their preparation to teach various mathematics contents.     

Becoming a Teacher of Mathematics

For many years I have engaged future mathematics teachers in activities that focus on emotional dimensions of their learning. Even those teachers who were able to reconstruct themselves as learners of mathematics had difficulties with changing their practice. Through a series of autobiographical stories, I examine my own experiences as a teacher and a learner. These stories—one from a computer class, one from a workshop for elementary teachers, one from college, and one from eighth grade—serve as data from which I draw themes that capture the tensions that I experience as I teach. Sharing these tensions with mathematics teachers has had an impact on the way the teachers talk about their teaching and promises to change how they teach. The paper is written to encourage teacher educators to adopt the practice of sharing teaching and learning stories with their students.     

On Culture and Mathematics Teacher Education

Many countries are multicultural. Mathematics teacher education classes often are composed of students with varied cultural and linguistic backgrounds, and mathematics teachers may be employed in regions from which they do not come. Formal (mathematics) education is a process of cultural interaction, and every child and teacher may experience some degree of social and cultural conflict in that process. This paper describes and reflects on some of these tensions, as they exist in mathematics teacher education in Mozambique. The process of developing among future mathematics teachers an awareness of the social and cultural bases of mathematics is object of reflection.     

高中数学后进生的转化策略探赜

在高中数学教学过程中,数学后进生现象一直困扰着数学教师,如何帮助这部分学生提高数学成绩是每一个高中数学教师都要面对的问题。文章从数学后进生的概念及成因入手,探究提高数学后进生学习成绩的相关对策,希望对高中数学教学有所借鉴。     

Communicating to Learn Multivariable Calculus: Students' Blackboard Presentations as a Means for Enhancing Mathematics Learning

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the benefit of themselves and their peers. The intervention appears to have incentivized students to engage with and learn mathematics contents in an effective way, and it also helped the mathematics teacher to reflect on, adapt, and develop his teaching strategies. To conclude, it would seem that both students and teachers in mathematics have much to gain from giving students opportunities to develop their own voice in learning contexts otherwise relying on books and lectures.     

Undergraduate Mathematics Experience: Its Significance in Secondary Mathematics Teacher Preparation

This paper reports views of studentteachers on a one year secondary teacherpreparation course about their undergraduateexperiences of learning mathematics. Writtenresponse data were collected from 173 studentteachers (trainees) from several differentinstitutions and their views were collated andthematised. The principal issues that arise arethose of discontinuity of experience fromschool to university, the lack of preparednessfor ``struggle' in the face of challengingmathematics at university and an unresponsivestyle of teaching and assessing. Thesignificance of these views to the students asprospective teachers and the ways in which theycould be used by teacher educators on trainingcourses is discussed.     

高师计算机课与中学数学新课程整合的探究

在高师数学系计算机课中整合中学数学新课程,以在职和职前教师能胜任中学数学新课程的教学为研究出发点,选用中学数学新课程充实深化重组计算机课程内容,实施计算机支持的协作学习的六个步骤：教师创设情境和提出问题、教师分析问题和明确方法、学生自主探索和寻求解答、小组协作学习和解决问题、师生总结和评价成果及教学反思,培养学生基于信息技术平台更有效地学数学与教数学的能力,提升他们的信息素养和数学素养．     

Primary School Mathematics Teacher Reflection through a Modelling-Based Professional Development Programme

This article contributes to the discussion on mathematics teacher reflection. Reflection was included in a study of the didactisation practices of primary school mathematics teachers as one of nine didactisation practices. The study involved five volunteer primary school mathematics teachers. A qualitative design-research approach was designed which employed model-eliciting tasks to create new experiences for teachers. This article reports on the nature and development of mathematics teacher reflection. Teacher reflection was gauged at various times during the programme through written responses to open-ended reflective questionnaires. Teachers were involved in three types of sessions for a period of one year: 1) modelling sessions whereby they collaboratively solved a mathematical modelling task; 2) observing primary school students/learners solve the same problems; and 3) sessions discussing traditional and problem-centred teaching and learning. It was found that modelling tasks provided reflective platforms and a window to teacher resources, orientations and goals. It is recommended that further research into mathematics teacher reflection be conducted where teachers specifically implement modelling in their own classrooms.     

试论数学兴趣的培养

兴趣是最好的老师.要想培养学生的数学兴趣,必须从教师和学生两方面着手,一是学生要有数学意识,二是教师要提高教学艺术,激发学生的兴趣,从而培养学生的数学兴趣.     

Science and Mathematics Teachers Working Toward Equity Through Teacher Research: Tracing Changes Across Their Research Process and Equity Views

We investigated secondary science and mathematics teachers engaged in a two-and-a-half-year professional development effort focused on equity. We examined how teachers conducting research on their own instructional practices—a central learning strategy of the professional development project—informed and/or constrained their views related to three strands of equity: teachers and teaching, students and learning, and students’ families and communities. Data collected included recordings of professional development seminars and school-site meetings, three sets of individual interviews with teacher researchers, and drafts and final products of the classroom research teachers conducted. From our qualitative analyses of data, we found that most teachers addressed at least two of the three equity strands in researching their own practice. We also found that most transformed their understandings of teachers and students as a result of their teacher research process. However, teachers’ views of families and communities changed in less substantive ways. We close with recommendations for other researchers and professional developers intent on supporting science and mathematics teachers in using teacher research to work toward equity.     

Between the Academic Mathematics and the Mathematics Education Worlds

Change is always difficult, and there is no great doubt that teachers need time to come to terms with it. This fact is, however, too often forgotten. In the spirit of my earlier work, this paper is shaped by an action research perspective. It provides some insights into the learning experiences of a group of eleven experienced secondary mathematics teacher, who were enrolled in a Perspectives on Mathematics Education two semesters course, within the context of a Masters on Mathematics Teaching programme, held at a Department of Mathematics, in a Portuguese University. The first part of the paper highlights the conflicting pressures and stresses suffered, during the first semester course, by the participating teachers. Confrontation with new ideas about both mathematics and mathematics education, as well as work overload, had a damaging impact on the teachers’ self‐confidence and morale. The second part of the paper covers the second semester course by addressing three fundamental questions for teachers, which aimed at helping the students bridge the academic mathematics and the mathematics education worlds. Finally, brief scenarios of three participating teachers’ professional development throughout the course are discussed in order to illustrate the challenges they had to face and the possibilities the course (and the Masters programme) offered to promote individual change.     

数学创新教育问题探索

从社会教育环境、基础与创新关系问题、数学教学等方面分析了我国数学创新教育存在的问题。要提高学生的数学创新能力,就必须注重将数学教学内容与社会现实相联系。数学教学中要注重学生的探索实践活动,创造性不是教出来的,它主要是在实践活动中形成的。     

Characterizing pivotal teaching moments in beginning mathematics teachers’ practice

Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.     

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.     

Mentor, Mentee and Mathematics: A Story of Professional Development

In this paper, I critically examine my role as a mentor to a group of mid-career mathematics teachers, to better understand how mentoring practices influence teacher learning. The teachers taught mathematics to Grades 5 or 6. They planned and taught lessons to promote conceptual understanding of mathematics through the use of discussions, and reflected on their own and pupils' learning in the process. The study lasted for a year. It draws on qualitative data from sources such as semi-structured interviews, participant observation, and teachers' reflective journals. As a mentor/researcher I found that in the case of mentees' perception of the mentor as a problem solver or evaluator of performance learning was inhibited, whereas mentor and mentee relationships established on mutual trust supported mentees' personal and professional growth. The close work with the teachers also gave me insights into aspects of learning influenced by teachers' beliefs and understanding of mathematics and of how learning takes place. The study has implications for other such teacher education initiatives, particularly in the context of developing countries like Pakistan. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two Teachers' Conceptions of a Reform-Oriented Curriculum: Implications for Mathematics Teacher Development

This paper describes two high school teachers' conceptions of the cooperation and exploration components of a reform-oriented mathematics curriculum. Although the teachers appreciated the themes of cooperation and exploration in theory, their conceptions of these themes with respect to their implementations of the curriculum differed. One teacher viewed the curriculum's problems as open-ended and challenging for students, whereas the other teacher claimed that the problems were overly structured. Each teacher attributed difficulties with students' cooperative work to the amount of structure and direction (too little or too much) offered by the problems. Discussion of such similarities and differences in the teachers' conceptions emphasizes the dynamic, humanistic nature of curriculum implementation and gives rise to important implications for mathematics teacher development in the context of reform. This revised version was published online in July 2006 with corrections to the Cover Date.     

高中数学课程改革的现状及对策

高中数学课程改革是在剖析我国数学教育发展的历史与现状的基础上,综合世界各国课程改革的成果,进行的有益探索。改革的宗旨是力求减轻学生负担、提高学习兴趣、改善教学方式,但在如何处理数学推理证明、学生学业负担、教师业务培训、民族教学传统等方面仍有争议。高中数学教师要主动更新教学理念,转换教学角色;加强课程研究,提升教学能力;关注教学过程,改善教学方式,努力适应并积极参与课程改革。     

Mathematics for teaching and deep subject knowledge: voices of Mathematics Enhancement Course students in England

This article reports an investigation into how students of a mathematics course for prospective secondary mathematics teachers in England talk about the notion of ‘understanding mathematics in depth’, which was an explicit goal of the course. We interviewed eighteen students of the course. Through our social practice frame and in the light of a review of the literature on mathematical knowledge for teaching, we describe three themes that weave through the students’ talk: reasoning, connectedness and being mathematical. We argue that these themes illuminate privileged messages in the course, as well as the boundary and relationship between mathematical and pedagogic content knowledge in secondary mathematics teacher education practice.     

高等数学的教学策略再思考

高等数学教学的知识性概括策略包括:针对课堂教学目标与课程教学目标进行知识概括,针对教材内容安排与知识的历史发展顺序进行知识概括;知识性自我控制策略包括:自我控制的针对性和适度性;知识的多元化交流策略包括:积极应用现代信息交流方式解惑答疑,组织学生开展对所学知识的自教活动,关注知识交流过程中的情感交流.