This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of p...

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Content Knowledge for Teaching: What Makes It Special?

This article reports on the literature associated with practising teachers' uptake of information and communications technology (ICT). Studies reveal a number of factors which influence teachers' decisions to use ICT in the classroom: access to resources, quality of software and hardware, ease of use, incentives to change, support and collegiality in their school, school and national polices, commitment to professional learning and background in formal computer training. The review highlights the role of pedagogy and suggests that teachers' beliefs about teaching and learning with ICT are central to integration. It is suggested that successful implementation of ICT needs to address three interlocking frameworks for change: the teacher, the school and policy makers.

Factors affecting teachers' use of information and communications technology: a review of the literature

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.

教育中的建构主义 = Constructivism in Education

The World's a Stage@@@Structure and Insight: A Theory of Mathematics Education

The quality of talk in children’s collaborative activity in the classroom

After surveying high-attaining 14and 15-year-old students about proof in algebra, we found that students simultaneously held 2 different conceptions of proof: those about arguments they considered would receive the best mark and those about arguments they would adopt for themselves. In the former category, algebraic arguments were popular. In the latter, students preferred arguments that they could evaluate and that they found convincing and explanatory, preferences that excluded algebra. Empirical argument predominated in students' own proof constructions, although most students were aware of its limitations. The most successful students presented proofs in everyday language, not using algebra. Students' responses were influenced mainly by their mathematical competence but also by curricular factors, their views of proof, and their genders.

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A study of proof conceptions in algebra

In this paper, we explore the relationship between learners' actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation.

The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In this paper, we explore the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, we show how dynamic software tools can not only scaffold the solution process but also help students move from argumentation to logical deduction. However, by reference to the work of less successful students, we illustrate how software tools that cannot be programmed to fit the goals of the students may prevent them from expressing their (correct) mathematical ideas and thus impede their problem solution.

Software Tools for Geometrical Problem Solving: Potentials and Pitfalls

In this article, we analyze the visual and symbolic strategies developed by students to express generalizations of number patterns and the connections they make between them. By analysis of a series of case studies, we compare the approaches adopted by students working through parallel task sequences, which integrate different computer tools in different ways. Finally, we make suggestions as to how students might be encouraged to exploit visual reasoning alongside the symbolic and draw out implications for curriculum design.

Visual and Symbolic Reasoning in Mathematics: Making Connections with Computers?

The paper presents the main findings of the London-based study, carried out as part of the ESRC project Groupwork with Computers. During this study, we attempted to identify the background and process factors which influence the success of groupwork with computers. The research used a multi-site case study design in six schools and involved eight groups of six mixed-sex, mixed-ability pupils (aged 9–12) undertaking three mathematics tasks, two using LOGO and one a database. Our main findings suggest that group settings are only successful in terms of both group outcome and learning, if the group structures their activity in particular and identifiable ways. These organisational styles and patterns of interaction themselves are conditional on interpersonal and social characteristics of the group and class.

Lulu Healy

Papers

A study of proof conceptions in algebra

The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

Software Tools for Geometrical Problem Solving: Potentials and Pitfalls

Visual and Symbolic Reasoning in Mathematics: Making Connections with Computers?

Groupwork with Computers: An Overview of Findings.