The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Chris Rasmussen - One of the best experts on this subject based on the ideXlab platform.
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defining as a Mathematical Activity a framework for characterizing progress from informal to more formal ways of reasoning
The Journal of Mathematical Behavior, 2010Co-Authors: Michelle Zandieh, Chris RasmussenAbstract:Abstract The purpose of this paper is to further the notion of defining as a Mathematical Activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ Mathematical progress.
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defining as a Mathematical Activity a framework for characterizing progress from informal to more formal ways of reasoning
The Journal of Mathematical Behavior, 2010Co-Authors: Michelle Zandieh, Chris RasmussenAbstract:Abstract The purpose of this paper is to further the notion of defining as a Mathematical Activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ Mathematical progress.
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advancing Mathematical Activity a practice oriented view of advanced Mathematical thinking
Communications of Mathematical Education, 2004Co-Authors: Chris Rasmussen, Michelle Zandieh, Karen King, Anne R TeppoAbstract:The purpose of this paper is to contribute to the dialogue about the notion of advanced Mathematical thinking by offering an alternative characterization for this idea, namely advancing Mathematical Activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous Activity. We also use the term Activity, rather than thinking. This shift in language reflects our characterization of progression in Mathematical thinking as acts of participation in a variety of different socially or culturally situated Mathematical practices. We emphasize for these practices the changing nature of student' Mathematical Activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.
Luciano Meira - One of the best experts on this subject based on the ideXlab platform.
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making sense of instructional devices the emergence of transparency in Mathematical Activity
Journal for Research in Mathematics Education, 1998Co-Authors: Luciano MeiraAbstract:This article examines the Mathematical sense-making of children as they use physical devices to learn about linear functions. The study consisted of videotaped problem-solving sessions in which pairs of 8th graders worked on linear function tasks using a winch apparatus, a device with springs, and a computerized input-output machine. The following questions are addressed: How do children make sense of physical devices designed by experts to foster Mathematical learning? How does the use of such devices enable learners to access selected aspects of a Mathematical domain? The concept of transparency is suggested as an index of access to knowledge and activities rather than as an inherent feature of objects. The analysis shows that transparency is a process mediated by unfolding activities and users' participation in ongoing sociocultural practices.
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the microevolution of Mathematical representations in children s Activity
Cognition and Instruction, 1995Co-Authors: Luciano MeiraAbstract:In this article, I discuss children's design of Mathematical representations on paper, asking how material displays are constructed and transformed in Activity. I show that (a) the design of displays during problem solving shapes one's Mathematical Activity and sense making in crucial ways, and (b) knowledge of Mathematical representations is not simply recalled and applied to problem solving but also emerges (whether constructed anew or not) out of one's interactions with the social and material settings of Activity. A detailed characterization of student-designed tables of values to solve problems about linear functions is also presented. The role of notational systems in Mathematical Activity is often assumed to be two-fold: (a) supporting cognitive processing, and (b) mediating communication (Kaput, 1987). Fey (1990) added that, from an auxiliary role, representations can become the object of mathematics itself and yield the study of "unanticipated patterns in concrete situations" (p. 73). Drawing on Skemp's (1979) work, Pimm (1987) detailed the role of notational systems in Mathematical Activity by listing the following uses that symbols can be put to: "communicating," "recording and retrieving knowledge," "helping to show structure [among ideas]," "allowing routine manipulation to be made automatic," and "making reflection possible" (p. 138). In classical mathematics education, the analysis of symbol use tends to oppose cognitive processing (labeled as internal) to the actual manipulation of inscriptions (labeled as external), giving rise to mapping models of the kind proposed
Michelle Zandieh - One of the best experts on this subject based on the ideXlab platform.
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defining as a Mathematical Activity a framework for characterizing progress from informal to more formal ways of reasoning
The Journal of Mathematical Behavior, 2010Co-Authors: Michelle Zandieh, Chris RasmussenAbstract:Abstract The purpose of this paper is to further the notion of defining as a Mathematical Activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ Mathematical progress.
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defining as a Mathematical Activity a framework for characterizing progress from informal to more formal ways of reasoning
The Journal of Mathematical Behavior, 2010Co-Authors: Michelle Zandieh, Chris RasmussenAbstract:Abstract The purpose of this paper is to further the notion of defining as a Mathematical Activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ Mathematical progress.
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advancing Mathematical Activity a practice oriented view of advanced Mathematical thinking
Communications of Mathematical Education, 2004Co-Authors: Chris Rasmussen, Michelle Zandieh, Karen King, Anne R TeppoAbstract:The purpose of this paper is to contribute to the dialogue about the notion of advanced Mathematical thinking by offering an alternative characterization for this idea, namely advancing Mathematical Activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous Activity. We also use the term Activity, rather than thinking. This shift in language reflects our characterization of progression in Mathematical thinking as acts of participation in a variety of different socially or culturally situated Mathematical practices. We emphasize for these practices the changing nature of student' Mathematical Activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.
Ursula Martin - One of the best experts on this subject based on the ideXlab platform.
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Using crowdsourced mathematics to understand Mathematical practice
ZDM, 2020Co-Authors: Alison Pease, Ursula Martin, Fenner Stanley Tanswell, Andrew AberdeinAbstract:Records of online collaborative Mathematical Activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into Mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about Mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of collective intelligence); human–computer interaction (on the factors that led to the success of one such project); network analysis (on the differences between collaborations on open research problems and known-but-hard problems); and argumentation theory (on modelling the argument structures of online collaborations). We also give an overview of qualitative approaches, reviewing work from empirical philosophy (on explanation in crowdsourced mathematics); sociology of scientific knowledge (on conventions and conversations in online mathematics); and ethnography (on contrasting conceptions of collaboration). We suggest how these diverse methods can be applied to crowdsourced mathematics and when each might be appropriate.
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workshop the role of automated deduction in mathematics
Conference on Automated Deduction, 2000Co-Authors: Simon Colton, Volker Sorge, Ursula MartinAbstract:The purpose of this workshop is to discuss the role of automated deduction in all areas of mathematics. This will include looking at the interaction between automated deduction programs and other computational systems which have been developed over recent years to automate different areas of Mathematical Activity. Such systems include computer algebra packages, tutoring programs, Mathematical discovery systems and systems developed to help present and archive Mathematical theories. The workshop will also include discussions of the use of automated theorem proving in the wider Mathematical community. Presentations which detail the employment of automated deduction techniques in any area of Mathematical research have been encouraged.
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workshop the role of automated deduction in mathematics
Lecture Notes in Computer Science, 2000Co-Authors: Simon Colton, Volker Sorge, Ursula MartinAbstract:The purpose of this paper is to discuss the role of automated deduction in all areas of mathematics. This will include looking at the interaction between automated deduction programs and other computational systems which have been developed over recent years to automate different areas of Mathematical Activity.
Jasmine Y - One of the best experts on this subject based on the ideXlab platform.
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reconfiguring Mathematical settings and Activity through multi party whole body collaboration
Educational Studies in Mathematics, 2018Co-Authors: Molly L Kelton, Jasmine YAbstract:This study examines the consequences of whole-body, multi-party Activity for mathematics learning, both in and out of the classroom. We develop a theoretical framework that brings together contemporary theories related to social space, embodied cognition, and Mathematical Activity. Then, drawing on micro-ethnographic and case-comparative techniques, we examine and juxtapose two cases of implementing whole-body, collaborative movement to engage learners in the mathematics of number sense and ratio and proportion. Analytically foregrounding the interdependence among setting, embodied Activity, and Mathematical tools and practices, we illustrate how whole-body collaboration can transform how learners experience learning environments and make sense of important Mathematical ideas. The analysis enriches our understanding of the changing spatial landscapes for learning and doing mathematics as well as how re-instating bodies in mathematics education can open up new forms of collective Mathematical sense-making and Activity.
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multi party whole body interactions in Mathematical Activity
Cognition and Instruction, 2017Co-Authors: Jasmine YAbstract:ABSTRACTThis study interrogates the contributions of multi-party, whole-body interactions to students' collaboration and negotiation of mathematics ideas in a task setting called walking scale geometry, where bodies in interaction became complex resources for students' emerging goals in problem solving. Whole bodies took up overlapping roles representing geometric objects, contributing to the communication and negotiation of problem-solving strategies and engaging as Mathematical instruments for representation.
