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Mathematical Problem Solving
01 Jan 1985-
About: The article was published on 1985-01-01 and is currently open access. It has received 2798 citations till now.
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TL;DR: Collins, Brown, and Newman as mentioned in this paper argue that knowledge is situated, being in part a product of the activity, context, and culture in which it is developed and used, and propose cognitive apprenticeship as an alternative to conventional practices.
Abstract: Many teaching practices implicitly assume that conceptual knowledge can be abstracted from the situations in which it is learned and used. This article argues that this assumption inevitably limits the effectiveness of such practices. Drawing on recent research into cognition as it is manifest in everyday activity, the authors argue that knowledge is situated, being in part a product of the activity, context, and culture in which it is developed and used. They discuss how this view of knowledge affects our understanding of learning, and they note that conventional schooling too often ignores the influence of school culture on what is learned in school. As an alternative to conventional practices, they propose cognitive apprenticeship (Collins, Brown, & Newman, in press), which honors the situated nature of knowledge. They examine two examples of mathematics instruction that exhibit certain key features of this approach to teaching.
14,006Â citations
TL;DR: A review of the literature on classroom formative assessment can be found in this article, where the authors consider the perceptions of students and their role in self-assessment alongside analysis of the strategies used by teachers and the formative strategies incorporated in such systemic approaches as mastery learning.
Abstract: This article is a review of the literature on classroom formative assessment. Several studies show firm evidence that innovations designed to strengthen the frequent feedback that students receive about their learning yield substantial learning gains. The perceptions of students and their role in selfâassessment are considered alongside analysis of the strategies used by teachers and the formative strategies incorporated in such systemic approaches as mastery learning. There follows a more detailed and theoretical analysis of the nature of feedback, which provides a basis for a discussion of the development of theoretical models for formative assessment and of the prospects for the improvement of practice.
6,483Â citations
TL;DR: This paper proposes the development of a new cognitive apprenticeship to teach students the thinking and problem-solving skills involved in school subjects such as reading, writing and mathematics.
Abstract: : Even today, many complex and important skills, such as those required for language use and social interaction, are learned informally through apprenticeshiplike methods -- i.e., methods involving not didactic teaching, but observation, coaching, and successive approximation while carrying out a variety of tasks and activities. The differences between formal schooling and apprenticeship methods are many, but for our purposes, one is most important. Perhaps as a by-product of the specialization of learning in schools, skills and knowledge taught in schools have become abstracted from their uses in the world. In apprenticeship learning, on the other hand, target skills are not only continually in use by skilled practitioners, but are instrumental to the accomplishment of meaningful tasks. Said differently, apprenticeship embeds the learning of skills and knowledge in the social and functional context of their use. This difference is not academic, but has serious implications for the nature of the knowledge that students acquire. This paper attempts to elucidate some of those implications through a proposal for the retooling of apprenticeship methods for the teaching and learning of cognitive skills. Specifically, we propose the development of a new cognitive apprenticeship to teach students the thinking and problem-solving skills involved in school subjects such as reading, writing and mathematics.
4,586Â citations
TL;DR: Problem-based learning (PBL) as mentioned in this paper is an instructional method in which students learn through facilitated problem solving, where the teacher acts to facilitate the learning process rather than to provide knowledge.
Abstract: Problem-based approaches to learning have a long history of advocating experience-based education. Psychological research and theory suggests that by having students learn through the experience of solving problems, they can learn both content and thinking strategies. Problem-based learning (PBL) is an instructional method in which students learn through facilitated problem solving. In PBL, student learning centers on a complex problem that does not have a single correct answer. Students work in collaborative groups to identify what they need to learn in order to solve a problem. They engage in self-directed learning (SDL) and then apply their new knowledge to the problem and reflect on what they learned and the effectiveness of the strategies employed. The teacher acts to facilitate the learning process rather than to provide knowledge. The goals of PBL include helping students develop 1) flexible knowledge, 2) effective problem-solving skills, 3) SDL skills, 4) effective collaboration skills, and 5) intrinsic motivation. This article discusses the nature of learning in PBL and examines the empirical evidence supporting it. There is considerable research on the first 3 goals of PBL but little on the last 2. Moreover, minimal research has been conducted outside medical and gifted education. Understanding how these goals are achieved with less skilled learners is an important part of a research agenda for PBL. The evidence suggests that PBL is an instructional approach that offers the potential to help students develop flexible understanding and lifelong learning skills.
3,823Â citations
TL;DR: The lion's share of my current research program is devoted to the study of learning in the blooming, buzzing confusion of inner-city classrooms, and central to the enterprise is that the classroom must function smoothly as a learning environment before the authors can study anything other than the myriad possible ways that things can go wrong.
Abstract: (1992) Design Experiments: Theoretical and Methodological Challenges in Creating Complex Interventions in Classroom Settings Journal of the Learning Sciences: Vol 2, No 2, pp 141-178
3,738Â citations
Cites background or methods from "Mathematical Problem Solving"
...As Schoenfeld (1992) argued in this issue, these records can be made available to the field, available for continual reanalysis as new and more powerful theories of learning and concomitant...
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...This shift was attended by a need to develop new methods to capture active strategic and monitoring processes (Brown & Campione, 1979; Schoenfeld, 1985)....
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...monitoring processes (Brown & Campione, 1979; Schoenfeld, 1985)....
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