Daniel Chazan

Bio: Daniel Chazan is an academic researcher from University of Maryland, College Park. The author has contributed to research in topics: Teacher education & Teaching method. The author has an hindex of 23, co-authored 66 publications receiving 2132 citations. Previous affiliations of Daniel Chazan include Michigan State University & University of Michigan.

High school geometry students' justification for their views of empirical evidence and mathematical proof

Abstract: Concerns about the use of computer-aided empirical verification in geometry classes lead to an investigation of students' understandings of the similarities and differences between the measurement of examples and deductive proof. The study reports in-depth interviews with seventeen high school students from geometry classes which employed empirical evidence. The analysis focuses on students' reasons for viewing empirical evidence as proof and mathematical proof simply as evidence.

Beyond Being Told Not to Tell

Abstract: For the past several years, we have been developing and studying teaching practices through our own efforts to teach school mathematics. Ball's work has been at the elementary level, in third grade, and Chazan's at the secondary level, grade ten and above, in Algebra I. In our teaching, we have been attempting, among other things, to create opportunities for classroom discussions of the kinds envisioned in the US National Council for Teachers of Mathematics Standards (NCTM, 1989, 1991). At the same time, we have been exploring the complexities of such practice. By using our teaching as a site for research into, and as a source for formulating a critique of, what it takes to teach in the ways reformers promote, we have access to a particular 'insider' sense of the teacher's purposes and reasoning, beyond that which a researcher might have. [1] This article originated with frustration at current math education discourse about the teacher's role in discussion-

Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom

Abstract: Group Investigation - a method for classroom instruction in which students work collaboratively in small groups, and take an active part in establishing their learning goals - continues to gain popularity. With increased interest has come the need for a comprehensive work on the subject - a thesis, a research review, and handbook. In this book, the authors provide an explanation of the philosophy, foundations, and current practice of Group Investigation. The authors give suggestions for ways of developing in a class the necessary discussion and cooperative skills, as well as detailed examples of projects in elementary and upper grades. In addition, they examine the experimental evidence of the method's effectiveness. The Sharans conclude with a presentation of two training programmes, one for teachers applying Group Investigation for the first time, and the other for those with some experience in cooperative learning who wish to expand and refine their techniques. This book should prove an indispensable tool for pre-and in-service teachers, staff developers, and other professionals dissatisfied with traditional "whole class" teaching and wishing to create with their students a learning environment where they are facilitators of cooperative inquiry, guides to acquisition of social skills, and active participants in a rewarding learning process.

Exploring the Practical Rationality of Mathematics Teaching through Conversations about Videotaped Episodes: The Case of Engaging Students in Proving.

Abstract: What might it mean to conceive of mathematics teaching as a practice? Can mathematics teaching be seen as something analogous to criminal law practice or family practice in medicine within the spectrum of human endeavors? As Donald Schon (1983) claims, those practices involve more than the application of technical knowledge expressed in declarative form in some professional canon there ate forms of practical rationality (which Schon calls 'knowledge-in-action' and 'reflection-in-action') that enable practitioners to do what they do. Such rationality cannot be reduced to individual wisdom, gift, sensibility or skill, since these are common to people who perform the same job; yet they ar·e not all part of the explicit regulations that describe this job. As Pierre Bomdieu (1998) puts it, all practices, not just those of professionals, require a "feel for the game" (p. 25), or:

Using comics-based representations of teaching, and technology, to bring practice to teacher education courses

Abstract: This article situates comic-based representations of teaching in the long history of tensions between theory and practice in teacher education. The article argues that comics can be semiotic resources in learning to teach and suggests how information technologies can support experiences with comics in university mathematics methods courses that (a) help learners see the mathematical work of teaching in lessons they observe, (b) allow candidates to explore tactical decision-making in teaching, and (c) support preservice teachers in rehearsing classroom interactions.

The Uses Of Argument

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教育中的建构主义 = Constructivism in Education

Abstract: Contents: J. Gale, Preface. Part I:Radical Constructivism and Social Constructionism. E. von Glasersfeld, A Constructivist Approach to Teaching. K.J. Gergen, Social Construction and the Educational Process. J. Shotter, In Dialogue: Social Constructionism and Radical Constructivism. J. Richards, Construct[ion/iv]ism: Pick One of the Above. Part II:Information-Processing Constructivism and Cybernetic Systems. F. Steier, From Universing to Conversing: An Ecological Constructionist Approach to Learning and Multiple Description. R.J. Spiro, P.J. Feltovich, M.J. Jacobson, R.L. Coulson, Cognitive Flexibility, Constructivism, and Hypertext: Random Access Instruction for Advanced Knowledge Acquisition in Ill-Structured Domains. K. Tomm, Response to Chapters by Spiro et al. and Steier. P.W. Thompson, Constructivism, Cybernetics, and Information Processing: Implications for Technologies of Research on Learning. Part III:Social Constructivism and Sociocultural Approaches. H. Bauersfeld, The Structuring of the Structures: Development and Function of Mathematizing as a Social Practice. J.V. Wertsch, C. Toma, Discourse and Learning in the Classroom: A Sociocultural Approach. C. Konold, Social and Cultural Dimensions of Knowledge and Classroom Teaching. J. Confrey, How Compatible Are Radical Constructivism, Sociocultural Approaches, and Social Constructivism? Analysis and Synthesis I: Alternative Epistemologies. M.H. Bickhard, World Mirroring Versus World Making: There's Gotta Be a Better Way. Part IV:Alternative Epistemologies in Language, Mathematics, and Science Education. R. Duit, The Constructivist View: A Fashionable and Fruitful Paradigm for Science Education Research and Practice. G.B. Saxe, From the Field to the Classroom: Studies in Mathematical Understanding. N.N. Spivey, Written Discourse: A Constructivist Perspective. T. Wood, From Alternative Epistemologies to Practice in Education: Rethinking What It Means to Teach and Learn. E. Ackermann, Construction and Transference of Meaning Through Form. D. Rubin, Constructivism, Sexual Harassment, and Presupposition: A (Very) Loose Response to Duit, Saxe, and Spivey. Part V:Alternative Epistemologies in Clinical, Mathematics, and Science Education. E. von Glasersfeld, Sensory Experience, Abstraction, and Teaching. R. Driver, Constructivist Approaches to Science Teaching. T. Wood, P. Cobb, E. Yackel, Reflections on Learning and Teaching Mathematics in Elementary School. P. Lewin, The Social Already Inhabits the Epistemic: A Discussion of Driver Wood, Cobb, and Yackel and von Glasersfeld. J. Becker, M. Varelas, Assisting Construction: The Role of the Teacher in Assisting the Learner's Construction of Preexisting Cultural Knowledge. E.H. Auerswald, Shifting Paradigms: A Self-Reflective Critique. Analysis and Synthesis II: Epsitemologies in Education. P. Ernest, The One and the Many. Analysis and Synthesis III: Retrospective Comments and Future Prospects. L.P. Steffe, Alternative Epistemologies: An Educator's Perspective. J. Gale, Epilogue.

Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell

Abstract: Teachers who attempt to use inquiry-based, student-centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique and sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task but also begin to align students' disparate ideas and approaches with canonical understandings about the nature of mathematics. Research suggests that this is difficult for most teachers (Ball, 1993, 2001; Leinhardt & Steele, 2005; Schoenfeld, 1998; Sherin, 2002). In this article, we present a pedagogical model that specifies five key practices teachers can learn to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses. We first define each practice, showing how a typical...