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Learning in Collaborative Settings: Students Building on Each Other's Ideas to Promote Their Mathematical Understanding.
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In this article, a group of six high school students 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.Abstract:
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.read more
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教育中的建构主义 = Constructivism in Education
TL;DR: In this article, Gale et al. discuss the relationship between social constructivism and social constructionism in the context of education and the role of the teacher in assisting the learner's construction of cultural knowledge.
Journal ArticleDOI
Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review
Rachel Lambert,Paulo Tan +1 more
TL;DR: In this paper, the authors investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners.
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Growing mathematical understanding through Collective Image Making, Collective Image Having, and Collective Property Noticing
Lyndon C. Martin,Jo Towers +1 more
TL;DR: In this article, the authors developed a theoretical perspective to describe and account for the growth of collective mathematical understanding and discussed collective processes in mathematics, drawing in particular on theoretical work in the domains of improvisational jazz and theatre.
Journal ArticleDOI
Cognitive Activities in Solving Mathematical Tasks: The role of a Cognitive Obstacle
TL;DR: In this article, a cognitive obstacle that students face at the thought plan is created, as well as a cognitive challenge, a phenomenon that occurs in the procedures of solving mathematical tasks.
Journal ArticleDOI
Educative experiences in a games context: Supporting emerging reasoning in elementary school mathematics
P. Janelle McFeetors,Kylie Palfy +1 more
TL;DR: In this article, an action research project with grade 5 and 6 students investigated how growth in reasoning occurred within abstract strategy games and found that students can grow in their capability to reason through multiple experiences of developing convincing arguments in an authentic context.
References
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Situated Learning: Legitimate Peripheral Participation
Jeanne Lave,Etienne Wenger +1 more
TL;DR: This work has shown that legitimate peripheral participation in communities of practice is not confined to midwives, tailors, quartermasters, butchers, non-drinking alcoholics and the like.
Book
The uses of argument
TL;DR: In this paper, the origins of epistemological theory are discussed and the layout of argument and modal arguments are discussed, as well as the history of working logic and idealised logic.
Book ChapterDOI
The Construction of Shared Knowledge in Collaborative Problem Solving
TL;DR: This paper focuses on the processes involved in collaboration using a microanalysis of one dyad’s work with a computer-based environment (the Envisioning Machine) and shows how this shared conceptual space is constructed through the external mediational framework of shared language, situation and activity.