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

Focusing on expanding technical capabilities and new collaborative possibilities, we address 4 challenges for scientists who collect and use video records to conduct research in and on complex learning environments: (a) Selection: How can researchers be systematic in deciding which elements of a complex environment or extensive video corpus to select for study? (b) Analysis: What analytical frameworks and practices are appropriate for given research problems? (c) Technology: What technologies are available and what new tools must be developed to support collecting, archiving, analyzing, reporting, and collaboratively sharing video? and (d) Ethics: How can research protocols encourage broad video sharing and reuse while adequately protecting the rights of research participants who are recorded?

/pdf/conducting-video-research-in-the-learning-sciences-guidance-4dztdyeadv.pdf

Conducting Video Research in the Learning Sciences: Guidance on Selection, Analysis, Technology, and Ethics

This paper compares the way lessons on systems of linear equations unfold in a classroom in the Negev region of Israel with the way they unfold in a Shanghai and Hong Kong classroom. Lessons are viewed as temporal entities describable not only by the nexus of topics they contain but also by how they flow in time. In this light, the lessons in the classroom studied by the authors contrasts strongly with the Shanghai and Hong Kong classroom, the former having a turbulent flow and latter a smooth directed flow. The result is consistent with previous recognized cultural differences in classroom practice and has implications for the bases of international comparisons.

International group for the psychology of mathematics education

Entering the Childʼs Mind: The Clinical Interview in Psychological Research and Practice

This mixed-method case study examined the potential of computer-assisted, math game making activities in facilitating design-based math learning for school children. Sixty-four middle school children participated in Scratch-based, math game making activities. Data were collected via activity and conversation observation, artifact analysis, interviewing, and survey. The study findings indicated that participants developed significantly more positive dispositions toward mathematics after computer game making. The study also found that experience-driven game design processes helped to activate children's reflection on everyday mathematical experiences. Mathematical thinking and content experience were intertwined within the process of computer game authoring. On the other hand, children designers were involved in game-world and story crafting more than mathematical representation. And it was still challenging for them to perform computer game coding with abstract reasoning.

An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing

An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data☆

https://promathmedia.files.wordpress.com/2013/02/condotions-for-promoting-reasoning-in-problem-solving-insight-from-a-longitudinal-study.pdf

Conditions for promoting reasoning in problem solving: Insights from a longitudinal study

The purpose of this study is to contribute insights into how collaborative activity can help promote students’ mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students’ development of mathematical ideas in problem-solving settings. The students solved the problem and produced a valid justification of their solution. This study shows that collaborative activity can help promote students’ mathematical understanding by providing opportunities for students to critically reexamine how they make claims from facts and also enable them to build on one another’s ideas to construct more sophisticated ways of reasoning. Implications for classroom teaching and ideas for future research are also discussed. The study helps address a documented need for a better understanding of how mathematical learning evolves in social settings.

Learning in Collaborative Settings: Students Building on Each Other's Ideas to Promote Their Mathematical Understanding.

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.

Teachers attending to students’ mathematical reasoning: lessons from an after-school research program

Examinamos a literatura sobre metodologia do videoteipe para a pesquisa observacional em Educacao
Matematica. Organizamos este exame apresentando questoes relacionadas a coleta de dados,
preocupacoes eticas, analise de dados, fitas como dados versus transcricoes como dados e apresentacao da
pesquisa. Para lidar com a lacuna percebida na literatura, propomos um modelo para analisar dados no
contexto de investigacoes sobre o trabalho matematico e o desenvolvimento do pensamento de estudantes
engajados em investigacoes matematicas. O modelo que propomos e baseado em quase duas decadas de
experiencias de pesquisa no The Robert B. Davis Institute for Learning, Graduate School of Education,
Rutgers University, New Brunswick, New Jersey, EUA

John M. Francisco

Papers

An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data☆

Conditions for promoting reasoning in problem solving: Insights from a longitudinal study

Learning in Collaborative Settings: Students Building on Each Other's Ideas to Promote Their Mathematical Understanding.

Teachers attending to students’ mathematical reasoning: lessons from an after-school research program

Uma Abordagem à Análise de Dados de Vídeo para Investigar o Desenvolvimento das Idéias Matemáticas e do Raciocínio de Estudantes