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Beyond Constructivism
This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendi...
International Perspectives on the Nature of Mathematical Knowledge for Secondary Teaching
This research forum addresses the question: what is the nature of the mathematical knowledge that is needed for secondary teaching? Six international contributors: (1) Australia (Kaye Stacey); (2) Brazil (Marcelo Borba); (3) Israel (Ruhama Even); (4) Norway (Bodil Kleve and Barbara Jaworski); (5) Taiwan (Fou-Lai Lin); and (6) USA (Helen Doerr) respond by making two claims (one related to an area where progress in research has been made and the other related to dilemmas facing researchers): (1) preparing teachers; (2) teaching practice; (3) research designs and methodologies. This structure provides a way of focusing the discussion among forum participants and a means to develop international points of view on the nature of the mathematical knowledge that is needed for secondary teaching. Contained in this document are the following titles: (1) Preparing Teachers--Progress and Dilemmas; (2) Practicing Teachers--Progress and Dilemmas; and (3) Research Design--Progress and Dilemmas. [For complete proceedings, see ED489178.].
Modelling and Applications in Mathematics Education
The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
Perspective-Taking in Middle School Mathematical Modelling
Traditional word problems have not fulfilled the goal of mathematical sense-making for many students. Some studies have shown that authentic contexts, such as model-eliciting tasks, have the potential to engage students in making sense of realistic situations. However, there has been little research on the kinds of knowledge needed by teachers to support this type of student learning activity. In this paper, we report on the results of a case study that investigated the ways in which teachers respond to students' thinking while engaged in a model-eliciting task in data analysis. We describe how one teacher used perspective-taking to initially engage students with the task, to explain and justify their models, to assess the quality of their models, and to make connections to other mathematical ideas. [For complete proceedings, see ED500859.].
Using Students' Ways of Thinking to Re-Cast the Tasks of Teaching about Functions
Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this paper, I present the results of a study in which teachers had extensive opportunities to examine students' ways of thinking as the students developed models for exponential growth and decay. I describe two related aspects of the practice of one teacher: (a) how she listened to students' alternative solution strategies and (b) how she responded to these strategies in her practice. The actions of the teacher supported extensive student engagement with the task and the students' revising and refining their own mathematical thinking. (Contains 1 footnote.) [For complete proceedings, see ED500859.].
Handbook of Research Design in Mathematics and Science Education
The Handbook of Research Design in Mathematics and Science Education is based on results from an NSF-supported project (REC 9450510) aimed at clarifying the nature of principles that govern the effective use of emerging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research designs that: * have been pioneered recently by mathematics and science educators; * have distinctive characteristics when they are used in projects that focus on mathematics and science education; and * have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the develop...
The Future of the Teaching and Learning of Algebra
Kaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist d...
Beyond Constructivism
First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
