In this article, we describe a methodology for analyzing the collective learning of the classroom community in terms of the
evolution of classroom mathematical practices. To develop the rationale for this approach, we first ground the discussion
in our work as mathematics educators who conduct classroom-based design research. We then present a sample analysis taken
from a 1st-grade classroom teaching experiment that focused on linear measurement to illustrate how we coordinate a social
perspective on communal practices with a psychological perspective on individual students’ diverse ways of reasoning as they
participate in those practices. In the concluding sections of the article, we frame the sample analysis as a paradigm case
in which to clarify aspects of the methodology and consider its usefulness for design research.
KeywordsClassroom mathematical practices-Design research cycle-Hypothetical learning trajectory-Interpretive framework-Linear measurement
In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts. Comment: The Journal of the Learning Sciences (In Press)
Inquiry experiences can provide valuable opportunities for students to improve their understanding of both science content and scientific practices. However, the implementation of inquiry learning in classrooms presents a number of significant challenges. We have been exploring these challenges through a program of research on the use of scientific visualization technologies to support inquiry-based learning in the geosciences. In this paper, we describe five significant challenges to implementing inquiry-based learning and present strategies for addressing them through the design of technology and curriculum. We present a design history covering four generations of software and curriculum to show how these challenges arise in classrooms and how the design strategies respond to them. Students at all grade levels and in every domain of science should have the opportunity to use scientific inquiry and develop the ability to think and act in ways associated with inquiry...(National Scie...
We present a set of case studies in which students create, customize, and personalize their own scientific instruments -- and thus become engaged in scientific inquiry not only through observing and measuring but also through designing and building. While computational technologies have, in general, contributed to making today's scientific instruments more "opaque" (that is, less understandable) and less aesthetically-pleasing than their predecessors, we argue that these same technologies can be used to bring back a sense of transparency and aesthetics to the design of scientific instruments. We analyze how students, by building their own scientific instruments, can pursue a broader range of scientific investigations of their own choosing, feel a stronger sense of personal investment in their scientific investigations, and develop deeper critical capacities in evaluating scientific measurements and knowledge. 3 Beyond Black Boxes: Bringing Transparency and Aesthetics Back to Scient...
This article focusses on knowledge goals, that is, the goals of a reasoner to acquire or reorganize knowledge. Knowledge goals, often expressed as questions, arise when the reasoner's model of the domain is inadequate in some reasoning situation. This leads the reasoner to focus on the knowledge it needs, to formulate questions to acquire this knowledge, and to learn by pursuing its questions. I develop a theory of questions and of question asking, motivated both by cognitive and computational considerations, and I discuss the theory in the context of the task of story understanding. I present a computer model of an active reader that learns about novel domains by reading newspaper stories. Appears in The Journal of the Learning Sciences, 1(3&4), 273--318, 1991. Also available as Technical Report GIT-CC-92/02, College of Computing, Georgia Institute of Technology, Atlanta, Georgia, 1992. 1 Introduction In this article, I discuss a theory of questions, viewed as a basis for und...
This article provides one example of a method of analyzing qualitative data in an objective and quantifiable way. Although the application of the method is illustrated in the context of verbal data such as explanations, interviews, problem-solving protocols, and retrospective reports, in principle, the mechanics of the method can be adapted for coding other types of qualitative data such as gestures and videotapes. The mechanics of the method we outlined in 8 concrete step. Although verbal analyses can be used for many purposes, the main goal of the analyses discussed here is to formulate an understanding of the representation of the knowledge used in cognitive performances and how that representation changes with learning This can be contrasted with another method or analyzing verbal protocols, the goal of which is to validate the cognitive processes of human performance, often as embodied in a computational model
In this article I bring artistic production into the learning sciences conversation by using the production of representations as a bridging concept between art making and the new literacies. Through case studies with 4 youth media arts organizations across the United States I ask how organizations structure the process of producing autobiographical digital art through a focus on representational tasks and how learning can be traced by examining youth artists' representations over time. Using a distributed cognition framework I analyze data on the process of making digital art in terms of the macro and micro tasks performed in order to identify occasions for external representation construction and use across organizations. I then examine how individual youth engage in these macro and micro tasks by producing representations that demonstrate their understanding. These analyses show that youth media arts organization production processes engage young artists in a representational trajectory that begins with developing a story about the self, moves toward a focus on how the tools of the medium afford representation of that story, and culminates in digital representations that reflect an understanding of the relationship between story and tools.
Electronic Blocks are a new programming environment designed specifically for children aged between 3 and 8 years. These physical, stackable blocks include sensor blocks, action blocks, and logic blocks. By connecting these blocks, children can program a wide variety of structures that interact with one another and the environment. Electronic Blocks provide young children with opportunities to program and observe dynamic behavior without having to acquire complex symbolic notation systems. Young children are able to build and debug program structures by using Electronic Blocks because the syntactic and semantic problems that confront users of conventional programming languages have been reduced.
This article reports on a qualitative study of the construct of shared epistemic agency, investigated in the context of collaborative instructional design activities of university students. The aim of the study is to shed light on the notion of shared epistemic agency and to create empirical grounding for its theoretical description. The current study provides an account of the construct, based on a review of several theoretical conceptualizations and on the analysis of empirical material from 2 case studies from university education. We investigate shared epistemic agency within the specific framework of the knowledge creation perspective on learning, viewing it as the capacity that enables deliberate collaborative efforts of groups to create shared knowledge objects. Our study identifies and describes 2 core dimensions of shared epistemic agency: the epistemic and the regulative dimensions. We identify actions within each dimension that indicate the manifestation of shared epistemic agency in the practice of collaborative creation of shared knowledge objects. This study also distinguishes patterns of action that provide indications of how shared epistemic agency is differently articulated in the 2 groups' collaborative object-oriented activities.
This article investigates the conditions under which diagrammatic representations support collaborative argumentation-based learning in a computer environment. Thirty dyads of 15- to 18-year-old students participated in a writing task consisting of 3 phases. Students prepared by constructing a representation (text or diagram) individually. Then they discussed the topic and wrote a text in dyads. They consolidated their knowledge by revising their individual representation. There were 3 conditions: Students could use either (a) the individual texts they wrote, (b) the individual diagrams they constructed, or (c) a diagram that was constructed for them based on the text they wrote. Results showed that students who constructed a diagram themselves explored the topic more than students in the other conditions. We also found differences in the way collaborating dyads used their representations. Dyads who engaged in deep discussion used their representations as a basis for knowledge construction. In contrast, dyads who engaged in only shallow discussion used their representations solely to copy information to their collaborative text. We conclude that diagrammatic representations can improve collaborative learning, but only when they are used in a co-constructive way.
The current paper represents a methodological proposal. It seeks to address the question of how one might recognize a discovery as a discovery without knowing in advance what is available to be discovered. We propose a solution and demonstrate it using data from a study previously reported by Roschelle (1992). Roschelle investigated two students’ discovery of certain abstract features of Newtonian mechanics while working within a computer-based microworld, the Envisioning Machine. We employ an approach we term discovery-as-occasioned-production to re-examine his data. Such an approach proceeds stepwise from the identification of some matter discovered, working backwards to see just where that matter entered the conversation and, then, finally, tracing from that point forward to illuminate how the proposal for a possible discovery was ultimately transformed into a discovery achieved. The notion of “evident vagueness,” borrowed from Garfinkel, Lynch, and Livingston’s (1981) account of the discovery of an optical pulsar, emerges as an important feature of our analysis. Following Garfinkel (2002), we present our findings as a “tutorial problem” and offer a suggestion for how a program of practice studies in the learning sciences might be pursued.
Full-text of this article is not available in this e-prints service. This article was originally published in the Journal of Learning Sciences, published by and copyright Lawrence Erlbaum Associates. This article may purchased by going to http://www.erlbaum.com/, selecting the journal in question and following the links to purchase the issue required.
We cannot really understand how to create computer support for collaborative learning without first becoming clearer about what we mean by communication, collaboration, and learning. After distinguishing several conceptions of communication, and highlighting transformative communications for learning, I consider how, via broadband telepresence, distributed multimedia learning environments may establish such communications by adequately acknowledging the social and material embeddedness of everyday communication. I then describe high-priority areas for advancing this agenda: in sociocultural theory, in examining conceptual change by means of conversational analysis, and in technically establishing affordances of tools to sustain and potentially enhance joint activity beyond the here-and-now and the face-to-face.
This article explores a new way to help people understand complex, dynamic systems. Participatory simulations plunge learners into life-sized, computer-supported simulations, creating new paths to scientific understanding. By wearing small, communicating computers called Thinking Tags, students are transformed into players in a large-scale microworld. Like classic microworlds, participatory simulations create a scenario, mediated by a set of underlying rules, that enables inquiry and experimentation. In addition, these new activities allow students to "dive into" a learning environment and directly engage with the complex system at hand. This article describes and analyzes a set of participatory simulations that were conducted with a group of high school biology students. The students' experiences are tracked from their initial encounter with an immersive simulation through their exploration of the system and final description of its underlying rules. The article explores the educational potential of participatory simulations. The results of this pilot study suggest an opportunity to further investigate the role that personal experience can play in developing inquiry skills and scientific understanding.
This study investigates how two types of graphical representation tools influence the way in which learners use knowledge resources in two different collaboration conditions. In addition, the study explores the extent to which learners share knowledge with respect to individual outcomes under these different conditions. The study also analyzes the relationship between the use of knowledge resources and different types of knowledge. The type of external representation (content-specific vs. content-independent) and the collaboration condition (videoconferencing vs. face-to-face) were varied. Sixty-four (64) university students participated in the study. Results showed that learning partners converged strongly with respect to their use of resources during the collaboration process. Convergence with respect to outcomes was rather low, but relatively higher for application-oriented knowledge than for factual knowledge. With content-specific external representation, learners used more appropriate knowledge resources without sharing more knowledge after collaboration. Learners in the computer-mediated collaboration used a wider range of resources. Moreover, in exploratory qualitative and quantitative analyses, the study found evidence for a relation between aspects of the collaborative process and knowledge convergence.
Based on a collective case study of the use of an economics Information and Commu- nication Technologies (ICT) tutorial-based package, WinEcon, in 3 British schools, this article examines the activity structures that exist in ICT-mediated lessons situ- ated within their broader sociocultural contexts. Activity theory and its highly devel- oped ideas of the sociocultural conceptions of human nature and cognition are adopted to frame the study. By drawing together Gifford's (1997) mediated learning model and Cole's (1995) culture as garden metaphor, the former captures the activi- ties mediated by students, teachers, ICT, and non-ICT tools in the course, and these are situated in the latter's broader sociocultural settings of the school, education sys- tem, and society at large. Although the article provides an account of the use of WinEcon in economics courses, its emphases are on the issues and problems of ICT integration: course ob- jectives, teaching and learning tools, participants, sociocultural constraints, activi- ties, and design of the learning environment. Consistent with other studies of ICT in- tegration, there are 2 interrelated points for consideration regarding the use of ICT in enculturating students to think "in an economics way": (a) pivotal role of the teacher in the design of the learning environment and (b) object of activities, sociocultural constraints, and the enculturation process.
Discusses the varied perspectives on the interactive processes of teaching and learning in mathematics classrooms. Development of mathematical thinking; Commonality and diversity in conceptualizations, perspectives and concerns.
This article examines the social nature of teachers' conceptions by showing how teachers frame the "mismatch" of students' perceived abilities and the intended school curriculum through conversational category systems. This study compares the conversations of 2 groups of high school mathematics teachers addressing the Mismatch Problem when implementing equity-geared reforms. Although East High teachers challenged conceptions that were not aligned with a reform, South High teachers reworked a reform mandate to align with their existing conceptions. This research found that the teachers' conversational category systems modeled problems of practice; communicated assumptions about students, subject, and teaching; and were ultimately reflected in the curriculum. Because East High teachers supported greater numbers of students' success in advanced mathematics, this study considers the relation between teachers' understandings of student learning and the success of equity-geared math reforms. In addition, this study contributes to the understanding of how teacher conceptions of students are negotiated and reified in context, specifically through interactions with colleagues and experiences with school reform.
Complex systems are commonly found in natural and physical science. Understanding such systems is often difficult because they may be viewed from multiple perspectives and their analysis may conflict with or extend beyond the range of everyday experience. There are many complex structural, behavioral, and functional relations to understand as well. Design activities, which allow explorations of how systems work, can be an excellent way to help children acquire a deeper, more systemic understanding of such complex domains. We report on a design experiment in which 6th grade children learned about the human respiratory system by designing artificial lungs and building partial working models. Structure-behavior-function models are used as a framework for the cognitive analysis of the domain. The design activities helped students learn about the respiratory system. The design students indeed learned more than students receiving direct instruction. They learned to view the respiratory system more systemically. As expected, because of the short time they spent on the exercise, they understood more about structure than function and more about the functions of different parts of the respiratory system than its causal behaviors. This early Learning by Design experiment makes several important suggestions about successful learning from design activities: (a) the need to define design challenges functionally; (b) the importance of dynamic feedback; (c) the need for multiple iterations toward a solution; and most important; (d) thinking about design as a system of activities and allocating time so that the full system can be carried out, allowing its full set of affordances to be realized.
There is a growing national recognition that teachers and teaching are at the heart of successful educational reform. However, few tools exist for measuring classroom instruction. The primary purpose of this article is to describe methods we developed to measure and study teaching, specifically while teachers were using a multimedia intervention for promoting scientific problem solving. Lessons were videotaped, and coding schemes were developed to measure 2 aspects of teaching: (a) the lesson's organization, particularly whole-class instruction used to introduce problems and share students' work; and (b) the nature of tasks and questions given to students. Results showed that the coding schemes were reliable and that they detected differences in instruction across teachers. Qualitative analyses were consistent with the quantitative findings. The codes also captured features of teaching that would have been difficult to detect or verify with qualitative observations alone. Finally, we explored how these measures could be used with student outcome data to examine the relationship between teaching and learning in future studies. We argue that quantitative measures of instruction serve many purposes, not the least of which is allowing researchers to explore the relationship between teaching and student learning at a high degree of granularity. (Contains 4 tables, 8 figures, 4 excerpts, and 3 footnotes.)
For this article, the development of 1 teacher's pedagogical content knowledge (Shulman, 1986) was tracked longitudinally across 2 years as she taught a new instructional unit in middle school mathematics. Growth in pedagogical content knowledge is characterized as the interanimation of 2 Discourses (Gee, 1999). One Discourse refers to characteristic ways that students talk and act about the mathematics of the unit; and the other Discourse, to characteristic ways that the teacher talks and acts as she guides the development of students' mathematical thinking. At the inception of the unit, the variety of small d discourses students and teacher generated were only loosely coupled. Initially, the teacher responded to variations in student talk and activity by employing general revoicing heuristics, such as repeating what a student had said so that others could hear or by asking a question to elicit further elaboration of a particular student's pattern of thought. As the teacher attempted to orchestrate classroom conversations oriented toward developing mathematical understanding, these general heuristics often failed to transform student thinking in ways that she considered mathematically productive. As a consequence, she generated new conversational gambits that were more often tuned to particular elements of students' mathematical talk and activity. Some of these forms of talk created more fruitful classroom discourse about mathematics, which the teacher increasingly recognized as signals of particular ways of thinking about the mathematics (of slope). The teacher was not content with mere recognition. She elaborated and continued to innovate. Conjectures about the growth of pedagogical content knowledge were tested in video-stimulated structured interviews with the teacher and by modeling the syntax of teacher support of student thinking--predicting specific patterns of couplings between student and teacher Discourses. This article concludes with a discussion of the implications of this view for the ontogenesis of adaptive expertise.
This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did not prove to be obstacles to this discussion. Instead, this teacher used student interpretations as resources, built on them, and connected them to canonical mathematical concepts--in particular by highlighting (Goodwin, 1994) a "unitized" (Lamon, 1994, 1996, 2007) view of the scales. Research in mathematics education describes teaching that promotes conceptual development as having two central features: One is that teachers and students attend explicitly to concepts, and the other is that students wrestle with important mathematics (Hiebert & Grouws, 2007). Not only does this classroom discussion provide an example that it is possible to balance these two features, but the analysis provides the details of "how" instruction can simultaneously provide explicit attention to concepts while allowing students to wrestle with these concepts. (Contains 3 tables, 12 figures and 3 footnotes.)
Scientific visualization has the potential to make science education more accessible and to provide a means for authentic scientific inquiry. The role of scientific visualization within science is explicated through examples of its use and by presenting a sociological account of science that portrays scientific visualization as an important new inscriptional system. Three examples of using scientific visualization within education are provided: the ChemViz Project at the National Center for Supercomputing Activities, the Image Processing for Teaching (IPT) project at the University of Arizona, and an undergraduate climatology course at the University of Chicago. Potential problems of integrating scientific visualization within secondary education are described, including students' need to learn basic scientific practices, incompatibilities between the format of the traditional high-school classroom and scientific inquiry, and the need for additional infrastructure within schools. Finally, possible solutions to these problems are described, culminating in a view of scientific visualization as a means to provide education with an important new inscriptional system for exploratory, inquiry-driven learning and to link the aims of education to the practices of science.