Showing papers in "Journal of Mathematics Teacher Education in 1999"
TL;DR: In this paper, the authors describe two high school teachers' conceptions of the cooperation and exploration components of a reform-oriented mathematics curriculum, and discuss the similarities and differences in the teachers" conceptions.
Abstract: 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.
158 citations
TL;DR: In this article, the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63).
Abstract: The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated, what has yet to be fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation.
103 citations
TL;DR: In this paper, the authors focus on the teachers' key roles during the lessons, roles that prospective and beginning teachers are supposed to learn either in a teacher preparation program or through the interaction with their colleagues.
Abstract: One of the characteristics of mathematics lessons in Japanese elementary and lower secondary schools relates to the frequent exposure of students to alternative solution methods for a problem (e.g. Becker, Silver, Kantowski, Travers & Wilson, 1990; Stevenson & Stigler, 1992; Lee, Graham & Stevenson, 1996). Japanese mathematics teachers, particularly in elementary schools, often plan to organize an entire lesson around the multiple solutions to a single problem in a whole class instructional mode (Nagasaki & Becker, 1993; Shimizu, 1996; Stigler, Fernandez & Yoshida, 1996). Alternative solution methods for the problem are usually presented by several of the 30 to 40 students in a class. In this setting, a teacher has to pose the problem and anticipate students’ responses to it. In other words, the teacher has to consider, both in planning and during the lesson, the diversity of experience and knowledge students bring into the classroom. How do Japanese mathematics teachers select the problems for their lessons? Do they have certain techniques for dealing with the diversity of their students? If there are such techniques, how do prospective and beginning teachers learn and develop them? In this article aspects of mathematics teacher education in Japan are discussed. Rather than presenting an outline of the entire education of Japanese teachers, I will focus on the teachers’ key roles during the lessons, roles that prospective and beginning teachers are supposed to learn either in a teacher preparation program or through the interaction with their colleagues. In an effort to provide a context for this aspect of mathematics teacher education, a sample lesson and the typical organization of a mathematics lesson shared by Japanese teachers are described first. Next, I introduce several Japanese pedagogical terms that refer to teachers’ key roles during the lessons. The importance of these roles for educating
88 citations
TL;DR: In this paper, a conceptual framework for studying the relationship between cognition and instructional practices of preservice secondary mathematics teachers is presented, which is used as a basis for structured reflection on their teaching as a means towards their professional growth.
Abstract: This article presents a conceptual framework for studying the relationship between cognition and instructional practices of preservice secondary mathematics teachers. It describes how the framework was used as a basis for activities in which preservice teachers engaged in structured reflection on their teaching as a means towards their professional growth. The approach required student teachers to engage in both prelesson and postlesson reflective activities. These activities are described, and details of two cases are given. This article demonstrates how this approach can facilitate the progression of preservice teachers' pedagogical techniques and conceptions.
73 citations
TL;DR: The Manor Program for the development of teacher leaders and teacher educators is used as a vehicle for addressing this issue as mentioned in this paper, focusing on aspects of curriculum design, discusses the theoretical rationale for the learning opportunities provided by the program, and considers several problematic aspects encountered.
Abstract: This article discusses the development of teacher leaders and inservice teacher educators whose role it is to promote teacher learning about mathematics teaching in the process of changing school mathematics. The Manor Program for the development of teacher leaders and teacher educators is used as a vehicle for addressing this issue. The article focuses on aspects of curriculum design, discusses the theoretical rationale for the learning opportunities provided by the program, and considers several problematic aspects encountered.
62 citations
TL;DR: In this article, a professional development program that introduces middle school teachers to an inquiry approach to mathematics instruction as a vehicle to reform their teaching of mathematics is described, characterized by the use of a few illustrative units that provide an integrated context for experiences as learners and experiences as teachers.
Abstract: This article describes a professional development program that introduces middle school teachers to an inquiry approach to mathematics instruction as a vehicle to reform their teaching of mathematics. The program is characterized by the use of a few illustrative units that provide an integrated context for experiences as learners and experiences as teachers. Project participants consisted of mathematics and special education teachers in school-based support teams led by school facilitators. Results suggest that the illustrative units were of considerable value in promoting reform. The benefits of including an heterogeneous group of teachers in the same professional development program and of involving teachers from the same school are also discussed.
54 citations
TL;DR: In this paper, the authors analyze concept images, difficulties, and errors related to the concept of altitude of a triangle exhibited by 190 preservice primary teachers in a written test.
Abstract: The way teachers understand mathematics strongly influences their teaching and what their pupils learn. Using Vinner's model of acquisition of mathematical concepts with its distinction of concept image and concept definition as a framework, we analyze concept images, difficulties, and errors related to the concept of altitude of a triangle exhibited by 190 preservice primary teachers in a written test. We describe the influence of two variables on the preservice teachers' performances: (a) the presence of a formal definition and (b) previous classroom activities that dealt with the concept of altitude. We categorize and analyze some common errors and identify the concept images that may lead to those errors. Finally, we present some implications of our results for teacher education.
52 citations
TL;DR: A humanistic perspective provided the basis for a problem-solving oriented teacher inservice program as discussed by the authors, which allowed elementary teachers to focus on personal experience as a way of achieving self-understanding and reconstructing their personal meanings about problem solving.
Abstract: A humanistic perspective provided the basis for a problem-solving oriented teacher inservice program. The program was designed to provide opportunities that allowed elementary teachers to focus on personal experience as a way of achieving self-understanding and a way of reconstructing their personal meanings about problem solving and problem-solving instruction. Impact of the program was studied through interviews with the six participants and observations of their teaching. The results indicated that the program had a positive effect on the participants' beliefs about and teaching of problem solving.
40 citations
TL;DR: In this article, the authors describe an action research collaboration between a middle school mathematics teacher and a mathematics teacher educator that focused on the teacher's attempts to change her instructional practice in the direction of the NCTM Standards vision.
Abstract: The vision of mathematics learning and teaching captured in the NCTM Standards documents holds clear implications for needed changes in mathematics teachers' instructional practices. This article describes an action research collaboration between a middle school mathematics teacher and a mathematics teacher educator that focused on the teacher's attempts to change her instructional practice in the direction of the NCTM Standards vision. In particular, the middle school teacher wrote a narrative description of the collaboration and of the changes she made in her instructional practice as a result of the collaboration. An interpretive analysis of the teacher's narrative by the teacher educator reveals that the collaboration itself, the support for change inherent in the collaboration, and the teacher's regular reflections on her own beliefs and practices which derived from the collaboration were important to her process of change.
26 citations
TL;DR: In this article, the authors report on an inquiry into what tends to be taken for granted with regard to the teaching and learning of mathematics, and the importance of interrogating the often-transparent figurative underpinnings of our thinking about thinking.
Abstract: This article reports on an inquiry into what tends to be taken for granted with regard to the teaching and learning of mathematics. The inquiry, undertaken in the context of a course on methods for mathematics teaching, was developed around an examination of the mathematical notions that infuse conventional theories of cognition and that permeate the structures and practices of school mathematics. In particular, concepts drawn from or aligned with Euclidean geometry were examined. Specifically, alternatives drawn from fractal geometry were explored. The importance of interrogating the often-transparent figurative underpinnings of our thinking about thinking is highlighted.
15 citations
Journal Article•
TL;DR: The concept maps and the writing of interpretive essays in mathematics courses for preservice and continuing teachers provide students with rich learning experiences and yield substantial insights into the degree of connectedness of their knowledge with respect to a given topic.
Abstract: The construction of concept maps and the writing of interpretive essays in mathematics courses for preservice and continuing teachers provide students with rich learning experiences and yield substantial insights into the degree of connectedness of their knowledge with respect to a given topic. With this dual approach students are given the opportunity to express their knowledge in different ways, which allows for individual differences in learning styles and verifies the relationships illustrated. As students actively participate in the task of developing connections between related concepts, reflect on their thinking, and become engaged in mathematical discourse, students are provided with an opportunity to mature mathematically and to experience an alternative approach to instruction and assessment.
TL;DR: The Maryland Collaborative for Teacher Preparation (MCTP) is a summer research internship program that places preservice middle grades teachers in extended collaboration with professional mathematicians, scientists, and educators engaged in research and curriculum development activities.
Abstract: Among the initiatives of the Maryland Collaborative for Teacher Preparation (MCTP) is a summer research internship program that places preservice middle grades teachers in extended collaboration with professional mathematicians, scientists, and educators engaged in research and curriculum development activities. We describe the MCTP internship program including the rationale for and structural features of the program. We also highlight the effects of the internship experience on preservice teachers' conceptions of and beliefs about the nature and processes of mathematics and science, and the teaching of mathematics and science. Our findings suggest that the internship experience is a fundamentally significant life experience for preservice teachers. Furthermore, internships have the potential for realizing reform in mathematics and science education; that is, preservice teachers who have participated in MCTP internships intend to bring a holistic, conceptually oriented view of mathematics and science to their classrooms. The paper concludes with a summary of ongoing programmatic and logistical challenges of the MCTP internship program.
Journal Article•
TL;DR: The M 3 Project as discussed by the authors was an effort to improve the teaching and learning of middle school mathematics through collaborative Standards-based mathematics curriculum investigations at the University of Missouri-Columbia.
Abstract: The goal of the project was to improve the teaching and learning of middle school mathematics through collaborative Standards-based mathematics curriculum investigations. The project not only contributed to the improvement of teaching mathematics in the participants’ classrooms, but it also significantly affected the program for prospective middle school mathematics teachers at the University of Missouri-Columbia. This teacher education program is described in this article. An essential ingredient in the successful transition to Standards-based practice at the middle school level is the development of teacher education programs that reflect the fundamental principles of the NCTM Standards (1989). In particular, the mathematical preparation of prospective middle grade teachers, which traditionally had been integrated into the programs for elementary teachers, needs careful consideration. The Mathematical Association of America, in A Call for Change (MAA, 1991), outlined recommendations for the mathematical preparation of middle grade teachers. These recommendations differ significantly from recommendations for the preparation of elementary teachers and provide guidance to those developing new programs for middle grade mathematics teachers. Currently, as in the case of the M 3 Project, much attention is being focused on the improvement of the knowledge and instructional skills of inservice teachers. This is important in order to stimulate immediate and substantive change. However, it is imperative that preservice education be simultaneously improved, so that new teachers entering the field are knowledgeable and can collaborate with their more experienced colleagues in transforming the classrooms in which middle grade students study mathematics. In response to this urgency, college and university faculty throughout the nation are examining and restructuring their teacher preparation courses and programs. These academic activities have created