Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.
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Connecting Research to Teaching: Why Did You Do That?
Reasoning in Algebra Classrooms
Daniel Chazan and Dara Sandow
Secondary school mathematics teachers are often exhorted to incorporate reasoning into all mathematics courses. However, many feel that a focus on reasoning is easier to develop in geometry than in other courses. This article explores ways in which reasoning might naturally arise when solving equations in algebra courses.
Orly Buchbinder, Daniel I. Chazan, and Michelle Capozzoli
Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching.
Joel Amidon, Daniel Chazan, Dana Grosser-Clarkson, and Elizabeth Fleming
This article explores the ways in which a teacher educator uses digital technology to create a virtual field placement as a way to blur the boundaries between a university methods course and teacher candidates' field placements. After describing his goals for the course, the teacher educator provides a description of three LessonSketch experiences his teacher candidates complete in this virtual field placement site and how these experiences create opportunities for teacher candidates to learn to teach mathematics. The design process and choices of these virtual field placement experiences are explored via interviews with the first author. Reflecting on these LessonSketch experiences, all of the authors then explore affordances of virtual and hybrid placements as resources for supplementing real placements and bridging theory/practice divides in teacher education.
Sandra Crespo, Patricio Herbst, Erin K. Lichtenstein, Percival G. Matthews, and Daniel Chazan
Patricio Herbst, Daniel Chazan, Sandra Crespo, Percival G. Matthews, and Erin K. Lichtenstein
Patricio Herbst, Daniel Chazan, Sandra Crespo, Percival G. Matthews, and Erin K. Lichtenstein
Patricio Herbst, Daniel Chazan, Sandra Crespo, Percival G. Matthews, and Erin K. Lichtenstein
Patricio Herbst, Daniel Chazan, Percival G. Matthews, Erin K. Lichtenstein, and Sandra Crespo
In our editorial last January, echoed a question often raised by reviewers of manuscripts: What is this manuscript's contribution to our research field? In that first elaboration on how manuscripts may contribute to the field of research in mathematics education, we discussed the contributions of basic research. In this editorial, motivated by the illustrations provided by the articles included in this issue, we do a similar exercise with applied research.
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