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Commonsense Conceptions of Emergent Processes: Why Some Misconceptions Are Robust
 Journal of the Learning Sciences
, 2005
"... This article offers a plausible domaingeneral explanation for why some concepts of processes are resistant to instructional remediation although other, apparently similar concepts are more easily understood. The explanation assumes that processes may differ in ontological ways: that some processes ..."
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Cited by 108 (4 self)
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This article offers a plausible domaingeneral explanation for why some concepts of processes are resistant to instructional remediation although other, apparently similar concepts are more easily understood. The explanation assumes that processes may differ in ontological ways: that some processes (such as the apparent flow in diffusion of dye in water) are emergent and other processes (such as the flow of blood in human circulation) are direct. Although precise definition of the two kinds of processes are probably impossible, attributes of direct and emergent processes are described that distinguish them in a domaingeneral way. Circulation and diffusion, which are used as examples of direct and emergent processes, are associated with different kinds of misconceptions. The claim is that stuDo Not Copy dents ’ misconceptions for direct kinds of processes, such as blood circulation, are of the same ontological kind as the correct conception, suggesting that misconceptions of direct processes may be nonrobust. However, students ’ misconceptions of emergent processes are robust because they misinterpret emergent processes as a kind of commonsense direct processes. To correct such a misconception requires a rerepresentation or a conceptual shift across ontological kinds. Therefore, misconceptions of emergent processes are robust because such a shift requires that students know about the emergent kind and can overcome their (perhaps even innate) predisposition to conceive of all processes as a direct kind. Such a domaingeneral explanation suggests that teaching students the causal structure underlying emergent processes may enable them to recognize and understand a variety of emergent processes for which they have robust misconceptions, such as concepts of electricity, heat and temperature, and evolution. Correspondence and requests for reprints should be sent to Michelene T. H. Chi, Learning Research
Thinking in Levels: A Dynamic Systems Approach to Making Sense of the World
 Journal of Science Education and Technology
, 1999
"... The concept of emergent “levels ” (i.e. levels that arise from interactions of objects at lower levels) is fundamental to scientific theory. In this paper, we argue for an expanded role for this concept of “levels ” in the study of science. We show that confusion of levels (and “slippage ” between l ..."
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Cited by 56 (7 self)
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The concept of emergent “levels ” (i.e. levels that arise from interactions of objects at lower levels) is fundamental to scientific theory. In this paper, we argue for an expanded role for this concept of “levels ” in the study of science. We show that confusion of levels (and “slippage ” between levels) is the source of many deep misunderstandings about patterns and phenomena in the world. These misunderstandings are evidenced not only in students ’ difficulties in the formal study of science but also in their misconceptions about experiences in their everyday lives. The StarLogo modeling language is designed as a medium for students to build models of multileveled phenomena and through these constructions explore the concept of levels. We describe several case studies of students working in StarLogo. The cases illustrate students ’ difficulties with the concept of levels, and how they can begin to develop richer understandings.
Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education
 Educational Studies in Mathematics
, 1999
"... ABSTRACT. This paper suggests that from a cognitiveevolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cogniti ..."
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Cited by 15 (4 self)
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ABSTRACT. This paper suggests that from a cognitiveevolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical. This progression was driven by three cognitive advances: the ability to “represent ” events, the development of symbolic reference, and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture: a “virtual ” culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills.
A dialectic analysis of generativity: Issues of network supported design in mathematics and science
 Journal of Mathematical Thinking and Learning
, 2005
"... New theoretical, methodological, and design frameworks for engaging classroom learning are supported by the highly interactive and groupcentered capabilities of a new generation of classroombased networks. In our analyses, networked teaching and learning are organized relative to a dialectic of (a ..."
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Cited by 8 (1 self)
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New theoretical, methodological, and design frameworks for engaging classroom learning are supported by the highly interactive and groupcentered capabilities of a new generation of classroombased networks. In our analyses, networked teaching and learning are organized relative to a dialectic of (a) seeing mathematical and scientific structures as fully situated in sociocultural contexts and (b) seeing mathematics as a way of structuring our understanding of and design for groupsituated teaching and learning. An engagement with this dialectic is intended to open up new possibilities for understanding the relations between content and social activity in classrooms. Features are presented for what we call generative design in terms of the respective “sides ” of the dialectic. Our approach to generative design centers on the notion that classrooms have multiple agents, interacting at various levels of participation, and looks to make the best possible use of the plurality of emergent ideas found in classrooms. We close with an examination of how this dialectic framework also can support constructive critique of both sides of the dialectic in terms of content and pedagogy.
Center for Connected Learning and ComputerBased Modeling
"... There has been a body of emerging research describing students ’ understanding of complex systems. This research has primarily studied students understanding of complex phenomena in science. However, complex phenomena are also pervasive in everyday life. Children observe and participate in them dail ..."
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There has been a body of emerging research describing students ’ understanding of complex systems. This research has primarily studied students understanding of complex phenomena in science. However, complex phenomena are also pervasive in everyday life. Children observe and participate in them daily. How do they reason about such ordinary complex phenomena? In this study, we investigate students’ reasoning about everyday complex phenomena. We report on interviews and a classroom participatory simulation with ten sixthgrade students about ordinary events that could be construed as emergent, such as social situations in which the social pattern emerges from the participating students ’ individual actions. We have observed a widespread studentinitiated strategy for making sense of complex phenomena. We call this strategy “mid level construction, ” the formation of small groups of individuals. Students form these midlevel groups either by aggregating individuals or by subdividing the whole group. We describe and characterize this midlevel strategy and relate it to the students ’ expressed understanding of “complex systems” principles. The results are discussed with respect to (a) students ’ strengths in understanding everyday complex social systems; (b) the utility of midlevel groups in forming an understanding of complex systems; (c) agentbased and aggregate forms of reasoning about complex systems.
Mathematical Power: Exploring Critical Pedagogy
 in Mathematics and Statistics,” in Reinventing Critical Pedagogy: Widening the Circle of AntiOppression
, 2006
"... "It no longer suffices to know how things are constituted: we need to seek how things should be constituted so that this world of ours may present less suffering and destitution. " 19thcentury French statistician Eugene Burét Though traditionally viewed as valuefree, mathematics is act ..."
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"It no longer suffices to know how things are constituted: we need to seek how things should be constituted so that this world of ours may present less suffering and destitution. " 19thcentury French statistician Eugene Burét Though traditionally viewed as valuefree, mathematics is actually one of the most powerful, yet underutilized, venues for working towards the goals of critical pedagogy—social, political and economic justice for all. This emerging awareness is due to how critical mathematics educators such as Frankenstein, Skovsmose and Gutstein have applied the work of Freire. Freire’s argument that critical education involves problem posing that challenges all to reconsider and recreate prior knowledge reads like a progressive definition of mathematical thinking. Frankenstein (1990) supports the idea that critical mathematics should involve the ability to ask basic statistical questions in order to deepen one’s appreciation of particular issues and should not be taught as isolated formulas with little relevance to individual experiences. At first, mathematics seems an unlikely vehicle for liberation. As Anderson (1997, p.
Setting the Tone: A Discursive Case Study of ProblemBased Inquiry Learning to Start a Graduate Statistics Course for InService Teachers
 Journal of Statistics Education
"... www.amstat.org/publications/jse/v19n3/lesser.pdf ..."
11 Representations of Reversal An Exploration of Simpson's Paradox
"... of Mathematics (NCTM) added a preK12 Standard on representation, urging that students be able to develop a repertoire of mathematical representations that can be used purposefully and flexibly to model and interpret physical, social, and mathematical phenomena (NCTM 2000). This article aims to exp ..."
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of Mathematics (NCTM) added a preK12 Standard on representation, urging that students be able to develop a repertoire of mathematical representations that can be used purposefully and flexibly to model and interpret physical, social, and mathematical phenomena (NCTM 2000). This article aims to explore the potential of including multiple representations in one's teaching repertoire through an accessible phenomenon for which full insight is not obvious from using only the single most common representation. The phenomenon chosen, Simpson's paradox, can be concisely defined as the reversal of a comparison when data are grouped. In this particular example, we will see that it is possible for women to be hired at a higher rate than men within each of two departments but at a lower rate than men when the data from both departments are pooled together. THE RELEVANCE OF SIMPSON'S PARADOX Simpson's paradox was first noted in 1951 by the British statistician E. H. Simpson but was discussed as early as 1903 by the Scottish statistician George Yule (Wagner 1983). Simpson's paradox can involve a comparison of overall rates, ratios, percentages, proportions, probabilities, averages, or measurements that are weighted averages of subgroup counterparts. Students are likely vulnerable to this paradox if they have the related "averaging the averages " misconception, in which they compute the ordinary average in problems requiring the weighted average. In a weighted average, an overall average is computed by weighting the individual averages by the sizes of their corresponding individual groups. For example, if the average final exam
Running head: LEVELS OF REASONING ABOUT NATURAL SELECTION 1 Running head: LEVELS OF REASONING ABOUT NATURAL SELECTION
"... Agentbased and aggregate level reasoning elicited by problem scenarios and an agentbased ..."
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Agentbased and aggregate level reasoning elicited by problem scenarios and an agentbased
Studio Mathematics: The Epistemology and Practice of Design Pedagogy as a Model for Mathematics Learning
, 2005
"... Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that the above copyright notice appears on all copies. WCER working papers are available on the Internet at ..."
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Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that the above copyright notice appears on all copies. WCER working papers are available on the Internet at