Recent Research
Rodriguez, J. M. G., & Jones, S. R. (2024). How Students Understand Graphical Patterns: Fine-Grained, Intuitive Knowledge Used in Graphical Thinking. Journal for Research in Mathematics Education, 55(2), 96-118.
ABSTRACT: Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we expand on the current knowledge base on graphical forms to contribute an empirically based catalog. We also situate our cognitively oriented work in relation to research that has emphasized (a) misconceptions and (b) social practices. In addition, we draw connections to the research on covariational reasoning. We end with implications regarding how graphical forms contribute to our understanding of students’ graphical reasoning and how instructors can support students.
Barth-Cohen, L. A., Swanson, H., & Arnell, J. (2023). Methods of research design and analysis for identifying knowledge resources. Physical Review Physics Education Research, 19(2), 020119.
ABSTRACT: Within physics education research (PER), resource theory has proven to be a useful framework for investigating knowledge and learning and informing instructional design. To analyze learning over longer timescales and across cases, PER scholars must first identify and describe the resources activated within and across physics contexts and domains. Despite its importance, a reliable method for identifying resources has not been clearly outlined. This paper presents guidelines for the design of research aimed at identifying knowledge resources. We begin by describing the origin, assumptions, and utility of resource theory. We then introduce methods of data collection and analysis. We end with a discussion of validity and reliability, drawing connections with general principles of qualitative research. With this work, we hope to promote coordination among the many PER scholars who utilize resource theory and to invite new scholars to join in its application and development
Barth-Cohen, L. A., & Braden, S. K. (2022). Unpacking the complexity in learning to observe in field geology. Cognition and Instruction, 40(2), 233-265.
ABSTRACT: Scientific observation is central to classroom inquiry and children’s investigations and explanations in science. Young children can struggle with observation, and research has shown that professional scientists who engage in complex observation tasks, observe detailed patterns when they have well-developed disciplinary knowledge. However, fewer studies address how this observational expertise develops and its specific role as a component of disciplinary knowledge within a larger complex knowledge system. Grounded in an existing theory of conceptual change, Knowledge in Pieces (KiP), we view knowledge as a complex system consisting of both perceptual and inferential parts. We demonstrate how these perceptual and inferential parts can be related to each other in the developing knowledge systems of learners engaged in scientific observation in field geology. In the analysis we examine in-service science teachers’ observations of bedrock while they were aiming to generate an understanding of the relevant historical geological processes. The analysis documents the moment-to-moment complex relationships between the perceptual and inferential parts of a knowledge system and thus offers an empirical account of how observation is situated within a knowledge system. The results challenge the notion that scientific observation is a simple skill by demonstrating how discipline-specific knowledge is mobilized during scientific observation in a field-based setting. This work has implications for science education instruction.
Izsák, A., Beckmann, S., & Stark, J. (2022). Seeking coherence in the multiplicative conceptual field: A knowledge-in-pieces account. Cognition and Instruction, 40(3), 305-350.
ABSTRACT: The present study is motivated by a significant body of research documenting teachers’ perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of multiplication and of fractions and by coordinating symbolic representations with math drawings. The dataset spans 1 semester of Nina’s in-class work during a content course—explicitly designed to foster coherence within the multiplicative conceptual field—as well as her written assignments for the course and her moment-to-moment reasoning during three interviews conducted near the beginning, middle, and end of the semester. A main result is that constructs from coordination class theory, a strand of theory within the knowledge-in-pieces epistemological perspective, were particularly useful for tracking and explaining Nina’s piecemeal progress. The broad contribution of the article is two-fold—(a) a shift in focus from research on reasoning about one or two topics toward reasoning across a wider range of topics related to multiplication and (b) highlighting refinement and coordination of knowledge resources as basic processes by which future teachers can progress toward coherent understandings of critical school mathematics content.
Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: a Knowledge in Pieces perspective on the development of algebraic thinking. ZDM–Mathematics Education, 54(6), 1303-1314.
ABSTRACT: In this paper, we elaborate the seeds of algebraic thinking perspective, drawing upon Knowledge in Pieces as a heuristic epistemological framework. We argue that students’ pre-instructional experiences in early childhood lay the foundation for algebraic thinking and are a largely untapped resource in developing students’ algebraic thinking in the classroom. We theorize that seeds of algebraic thinking are cognitive resources abstracted over many interactions with the world in children’s pre-instructional experience. Further, we provide examples to demonstrate how the same seeds of algebraic thinking present in early childhood can be invoked in reasoning across contexts, grade levels, and different levels of formality of algebraic instruction. The examples demonstrate how the seeds perspective differs from other accounts of the relationship between children’s early activity and their engagement in algebraic reasoning processes. We anticipate this new theoretical direction for characterizing the nature and development of algebraic thinking will lay the foundation for a robust agenda that sheds light on the development of algebraic thinking and informs algebra instruction, particularly how teachers notice and respond to children’s developing algebraic thinking.
Levin, M. (2018). Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective. Cognition and Instruction.
ABSTRACT: This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students’ observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated for decades. Recently, there has been mounting empirical evidence that conceptual and procedural knowledge can develop by mutual bootstrapping in a bidirectional and iterative fashion (e.g., Rittle-Johnson & Schneider, 2014). However, the very constructs of conceptual and procedural knowledge (especially procedural knowledge) have been critiqued for inconsistency in definition and lack of operationalization (Star, 2007). The analysis in this article addresses this critique by modeling the diverse forms of conceptual and procedural knowledge needed to implement a strategy as a complex knowledge system: a strategy system. Furthermore, the strategy system model is used to elaborate processes of mutual bootstrapping between conceptual and procedural knowledge at a moment-by-moment time scale. The strategy system model builds upon the Knowledge in Pieces epistemological perspective (diSessa, 1993), and coordination class theory in particular (diSessa & Wagner, 2005). Both the theoretical notion of a strategy system and the bidirectional model of mutual bootstrapping between conceptual and procedural knowledge are illustrated using data from a case study of a pre-algebra student who iteratively refined a procedure for solving algebra word problems. The strategy system model highlights the complexity of both strategies and concepts and offers a window into what can be learned by students during strategy construction processes.
diSessa, A. A. (2018). A Friendly Introduction to “Knowledge in Pieces”: Modeling Types of Knowledge and Their Roles in Learning. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. X. Cham (Eds.) Invited lectures from the 13th International Congress on Mathematical Education (ICME-13) (pp. 65-84). Cham, CH: Springer Open. doi: 10.1007/978-3-319-72170-5.
ABSTRACT: Knowledge in Pieces (KiP) is an epistemological perspective that has had significant success in explaining learning phenomena in science education, notably the phenomenon of students’ prior conceptions and their roles in emerging competence. KiP is much less used in mathematics. However, I conjecture that the reasons for relative disuse mostly concern historical differences in traditions rather than in-principle distinctions in the ways mathematics and science are learned. This article aims to explain KiP in a relatively non-technical way to mathematics educators. I explain the general principles and distinguishing characteristics of KiP, I use a range of examples, including from mathematics, to show how KiP works in practice and what one might expect to gain from using it. My hope is to encourage and help guide a greater use of KiP in mathematics education.
diSessa, A. A. (2018). Knowledge in Pieces: An evolving framework for understanding knowing and learning. In T. Amin & O. Levrini (Eds.), Converging perspectives on conceptual change: Mapping an emerging paradigm in the learning sciences (pp. 9-16). London, UK: Routledge.
Sherin, B. L. (2018). Elements, Ensembles, and Dynamic Constructions. In T. Amin & O. Levrini (Eds.), Converging perspectives on conceptual change: Mapping an emerging paradigm in the learning sciences (pp. 61-78). London, UK: Routledge.
diSessa, A. A. (2017). Conceptual Change in a Microcosm: A Comparative Analysis of a Learning Event. Human Development 60(1).
ABSTRACT: This article examines a remarkable learning event where a high school class developed, on its own, a stable, normative view of thermal equilibration. The event is also notable because the intuitive ideas that students bootstrapped into their model of equilibration have been thoroughly documented in prior research. Therefore, the process of changing prior conceptions is well delineated. The main point of the article is to review what happened in this microcosm of learning from multiple perspectives to examine how well each perspective can account for the learning that took place. We use three competing views of conceptual change: Knowledge in Pieces, the Theory Theory, and the Ontological View. We argue that Knowledge in Pieces provides a more detailed and more adequate account of the learning that took place, whereas that learning contradicts core commitments of the Theory Theory and of the Ontological View.
Barth-Cohen, L.A. & Wittmann, M. C. (2017). Aligning coordination class theory with a new context: Applying a theory of individual learning to group learning. Science Education, 10(12), 333-363.
ABSTRACT: This article presents an empirical analysis of conceptual difficulties encountered and ways students made progress in learning at both individual and group levels in a classroom environment in which the students used an embodied modeling activity to make sense of a specific scientific scenario. The theoretical framework, coordination class theory, has primarily been used to capture individual learning in interview settings, and here it is applied to analytically capture both individual and group learning in a complex classroom environment. Classrooms of ninth‐grade earth science students used the position of their bodies to model a specific scientific concept, the steady‐state energy of the earth. The students encountered difficulties aligning their understanding of the scientific concept with the models. Subsequently, they changed their models in specific ways that better aligned their understanding of the scientific concept with their newly modified model. The theory is utilized to describe learning by both individuals and the group in this classroom environment and shows how a single student's contribution can dramatically affect the model and subsequent learning. Implications suggest new ways in which the theory may be useful for designing learning environments.
diSessa, A. A., Sherin, B., & Levin, M. (2016). Knowledge Analysis: An Introduction. In A. A. diSessa, M. Levin, & N. J. S. Brown (Eds.) Knowledge and Interaction: A Synthetic Agenda for the Learning Sciences. Routledge, New York: NY.
ABSTRACT: Knowledge Analysis, a methodology for studying human intellectual performance and its development, can be characterized by a number of particular interests and modes of thinking including (1) a strong interest in theoretical innovation as part of the whole research enterprise— prototypically developing views of both the form and content of knowledge simultaneously; (2) a strong concern for “high-resolution” analysis of data, including, often, a fine time grain-size and also especially nuanced descriptions of “ideas”; (3) a “developmental” concern for long-term, complex learning, and the use of development as one important dimension of triangulation on knowledge, even of experts; (4) a persistent focus on contexuality (situatedness) of knowledge; and finally, (5) a respect toward reductionist modeling of human intellectual performance, but also a judiciously slow approach to it. This chapter will broadly serve as an introduction to Knowledge Analysis, exposing both theoretical assumptions and the range of methodological practices characteristic of the method. We will begin by situating Knowledge Analysis broadly both with respect to historical movements and influences within the cognitive/learning sciences and also with respect to contemporary contrasting perspectives on studying processes of knowing and learning. We will then discuss the theoretical assumptions that undergird the work, sketching some of the core methodological issues. Finally, through a review and discussion of recent and representative work, we will provide an illustrative range of analytical practices involved in Knowledge Analysis.
Kapon, S. (2016). Unpacking Sense-making. Science Education. 101(1). 165-198.
ABSTRACT: Learning science involves an ongoing process in which learners construct and reconstruct self‐explanations and evaluate their relative soundness. This work coordinates and aligns complementary methodological and theoretical approaches to learning to both unpack sensemaking and better understand the conditions that facilitate it. I conceptualize people's sense of what constitutes a good explanation as taking place along a multidimensional metric and discuss three dimensions of this metric that are central to the evaluation of explanations of phenomena in the physical world: (1) intuitive knowledge, (2) mechanism, and (3) framing. The study operationalizes each dimension in terms that can be empirically tracked in students’ talk, gestures, and social interactions. The power and function of the multidimensional metric is illustrated through its account of the evolution of self‐generated explanations of two seventh‐grade girls who attempt to understand why a plastic bottle shrinks when air is pumped out of it. The analysis demonstrates that the framework can explain conviction in an explanation, preference for one explanation over another, and the complex conditions that facilitate this change. Methodological and practical implications are discussed.
diSessa, A. A. (2014). The construction of causal schemes: Learning mechanisms at the knowledge level. Cognitive science, 38(5), 795-850.
ABSTRACT: This work uses microgenetic study of classroom learning to illuminate (1) the role of pre‐instructional student knowledge in the construction of normative scientific knowledge, and (2) the learning mechanisms that drive change. Three enactments of an instructional sequence designed to lead to a scientific understanding of thermal equilibration are used as data sources. Only data from a scaffolded student inquiry preceding introduction of a normative model were used. Hence, the study involves nearly autonomous student learning. In two classes, students developed stable and socially shared explanations (“causal schemes”) for understanding thermal equilibration. One case resulted in a near‐normative understanding, while the other resulted in a non‐normative “alternative conception.” The near‐normative case seems to be a particularly clear example wherein the constructed causal scheme is a composition of previously documented naïve conceptions. Detailed prior description of these naive elements allows a much better than usual view of the corresponding details of change during construction of the new scheme. A list of candidate mechanisms that can account for observed change is presented. The non‐normative construction seems also to be a composition, albeit of a different structural form, using a different (although similar) set of naïve elements. This article provides one of very few high‐resolution process analyses showing the productive use of naïve knowledge in learning.
diSessa, A. A. (2013). An Epistemological Perspective on Misinformation. In Rapp, D. N., & Braasch, J. L. G. (Eds.), Processing inaccurate information: Theoretical and applied perspectives from cognitive science and the educational sciences. Cambridge, MA: MIT Press.
ABSTRACT: My aim in this chapter is to bring a slightly exotic perspective, that of epistemology to the study of misinformation. How is it that humans suffer the effects of believing things that are not true? Where does misinformation come from; what are its properties and consequences; and how might we mitigate the acquisition or consequences of misinformation? Science education research has made a great fuss about so-called “misconceptions” that students have, say, coming into physics class. In this paper, I consider the comparison of misconceptions with misinformation, which some literature suggests are quite similar. However, with a refined epistemological view on misconceptions (that provided by p-prims theory), they look really quite different than misinformation. For example, I claim it is a category error to describe misconceptions as true or false—those terms just do not apply. From my point of view, misinformation, though sharing some characteristics of misconceptions, is most likely just a different genre of knowing (or mis-knowing). This larger aim of this chapter is to present an accessible view of contemporary epistemological inquiry to a broader audience, and I propose that such inquiry can be extremely enlightening for the study of misinformation.
Parnafes, O. & diSessa, A. (2013). Microgenetic Learning Analysis: A Methodology for Studying Knowledge in Transition Human Development, 56, 5–37.
ABSTRACT: This paper introduces and exemplifies a qualitative method for studying learning,microgenetic learning analysis (MLA), which is aimed jointly at developing theory and at establishing useful empirical results. Among modern methodologies, the focus on theory is somewhat distinctive. We use two strategies to describe MLA. First, we develop a framework for comparing the focus and means of different methods, particularly qualitative methods, aimed at studying learning. Using the framework, we compare and contrast MLA with two better-known methods, microgenetic analysis and grounded theory. Second, we aim to schematize elements of MLA – from large-scale patterns of work to detailed analytical strategies – and to exemplify some of them in a case study using data collected some years prior to this elaboration of MLA.
DOI: 10.1159/000342945
Kuo, E., Hull, M., Gupta, A., & Elby, A. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problems. Science Education, 97(1), 32-57.
ABSTRACT: Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal mathematical reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended mathematical operations with conceptual reasoning about physical processes, reflecting a view—expressed earlier in his explanation of the equation—that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal mathematical reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements calledsymbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.
Parnafes, O. (2012). Developing Explanations and Developing Understanding: Students Explain the Phases of the Moon Using Visual Representations. Cognition and Instruction 30(4), 359-403.
ABSTRACT: This article presentations a theoretical model of the process by which students construct and elaborate explanations of scientific phenomena using visual representations. The model describes progress in the underlying conceptual processes in students' explanations as a reorganization of fine-grained knowledge elements based on the Knowledge in Pieces perspective. The core case study involved a pair of fifth-grade students who generated visual representations to explain the phases of the moon and collaboratively elaborated and improved their representations and explanations. The model describes the process of developing explanations as iterations of temporarily stable stages of coherence. The progression from one temporary coherent structure to the next is described as the increase of Resolution and/or Range of the explanation. Resolution and Range are newly defined theoretical constructs. The model accounts for the continuity in the students' developing understanding and highlight the productive nature of their intuitive knowledge resources.
Kapon, S. & diSessa, A. (2012). Reasoning Through Instructional Analogies. Cognition and Instruction 30(3), 261-310.
ABSTRACT: This article aims to account for students' assessments of the plausibility and applicability of analogical explanations, and individual differences in these assessments, by analyzing properties of students' underlying knowledge systems. We developed a model of explanation and change in explanation focusing on knowledge elements that provide a sense of satisfaction to those judging the explanation. We call these elements "explanatory primitives." In this model, explanations are accepted or rejected on the basis of (a) the individual's convictions concerning particular explanatory primitives and (b) the fit of these primitives to current circumstances. Data are drawn from clinical interviews with three high school students who worked through a bridging analogies tutoring sequence on the existence of the normal force in mechanics. Methodologically, our work involves fine-grain analysis of process data and explicit principles of empirical accountability; we believe it marks a methodological advance over most previously reported empirical studies of analogical reasoning.
Russ, R., Lee, V., & Sherin, B. (2012). Framing in cognitive clinical interviews about intuitive science knowledge: Dynamic student understandings of the discourse interaction. Science Education, 96(4), 573-599.
ABSTRACT: Researchers in the science education community make extensive use of cognitive clinical interviews as windows into student knowledge and thinking. Despite our familiarity with the interviews, there has been very limited research addressing the ways that students understand these interactions. In this work, we examine students’ behaviors and speech patterns in a set of clinical interviews about chemistry for evidence of their tacit understandings and underlying expectations about the activity in which they are engaged. We draw on the construct of framing from anthropology and sociolinguistics and identify clusters of behaviors that indicate that students may alternatively frame the interview as inquiry, an oral examination, or an expert interview.We present two examples of students shifting between frames during the course of individual interviews. By examining the surrounding interaction, we identify both conceptual and epistemological interviewer cues that facilitate and constrain frame shifts. We discuss the implications of dynamic student framing, that is identifiable in student behaviors and discourse, for researchers who use clinical interviews to map student’s intuitive science knowledge.
http://onlinelibrary.wiley.com/doi/10.1002/sce.21014/abstract
Sherin, B. L., Krakowski, M., & Lee, V. R. (2012). Some assembly required: How scientific explanations are constructed during clinical interviews. Journal of Research in Science Teaching, 49 (2), 166–198.
ABSTRACT: This article is concerned with commonsense science knowledge, the informally gained knowledge of the natural world that students possess prior to formal instruction in a scientific discipline. Although commonsense science has been the focus of substantial study for more than two decades, there are still profound disagreements about its nature and origin, and its role in science learning. What is the reason that it has been so difficult to reach consensus? We believe that the problems run deep; there are difficulties both with how the field has framed questions and the way that it has gone about seeking answers. In order to make progress, we believe it will be helpful to focus on one type of research instrument—the clinical interview—that is employed in the study of commonsense science. More specifically, we argue that we should seek to understand and model, on a moment-by-moment basis, student reasoning as it occurs in the interviews employed to study commonsense science. To illustrate and support this claim, we draw on a corpus of interviews with middle school students in which the students were asked questions pertaining to the seasons and climate phenomena. Our analysis of this corpus is based on what we call the mode-node framework. In this framework, student reasoning is seen as drawing on a set of knowledge elements we call nodes, and this set produces temporary explanatory structures we call dynamic mental constructs. Furthermore, the analysis of our corpus seeks to highlight certain patterns of student reasoning that occur during interviews, patterns in what we call conceptual dynamics. These include patterns in which students can be seen to search through available knowledge (nodes), in which they assemble nodes into an explanation, and in which they converge on and shift among alternative explanations.
Ozdemir, O. (2012). Transfer and conceptual change: the change process from the theoretical perspectives of coordination classes and phenomenological primitives. Instructional Science.
ABSTRACT: The purpose of this study is to understand the nature of pre-instructional knowledge transferred by students into problem situations and the change process on students' knowledge system during classroom discussions. This study was framed by two interrelated theoretical frameworks on knowledge structures, phenomenological primitives and coordination classes. The data were collected through problem solving sessions on turning effect of forces (torques or moment) from ten participants who were seeking a degree to become physics teachers. The analysis of data showed that, in this particular context, students' pre-instructional ideas can be characterized according to phenomenological primitives. The theoretical constructs of the coordination classes generated meaningful results to understand students' particular difficulties in transferring the moment concept across different contexts and the change process on students' knowledge system. The major stimulator of the change process emerged as the students' become aware of the epistemological nature of their knowledge structures and searching the causal mechanisms behind physical phenomena.
http://rd.springer.com/article/10.1007/s11251-012-9219-4
Philip, T. (2011). An “Ideology in Pieces” Approach to Studying Change in Teachers’ Sensemaking About Race, Racism, and Racial Justice. Cognition and Instruction, 29(3), 297-329.
ABSTRACT: This article makes a unique contribution to the literature on teachers’ racialized sensemaking by proposing a framework of “ideology in pieces” that synthesizesHall’s (1982, 1996) theory of ideology and diSessa’s (1993) theory of conceptual change. Hall’s theory of ideology enables an examination of teachers’ sensemaking as situated within a structured society and diSessa’s research on conceptual change provides an analytical lens to understand the elements of ideological sensemaking and the processes of ideological transformation. I use the framework of ideology in pieces to analyze and interpret the ideological sensemaking and transformation of a teacher engaged in a collaborative teacher research group in which participants explored issues of social justice in their high school math and science classrooms. The framework and analysis presented in the article offer a more comprehensive theory of teachers’ ideological sensemaking and transformation that includes their cognitive, social, and structural dimensions.
DOI: 10.1080/07370008.2011.583369
Clark, D. B., D’Angelo, C. & Schleigh S. (2011). Multinational comparison of students’ knowledge structure coherence. Journal of the Learning Sciences, 20(20), 207-261.
ABSTRACT: This study investigates the ongoing debate in the conceptual change literature between unitary and elemental perspectives on students' knowledge structure coherence. More specifically, the current study explores two potential explanations for the conflicting results reported by Ionnides and Vosniadou (2002) and diSessa, Gillespie, and Esterly (2004) in terms of differences in coding schemes and differences in student populations. The current study addresses these questions by applying the coding schemes from both studies to interviews with 201 students drawn from the United States, the Phillipines, Turkey, China, and Mexico. The analyses focus first on the coding schemes, suggesting that differences in coding schemes seem unlikely to account for the differences in the original studies. The analyses then focus on potential differences between student populations, suggesting that some differences exist in terms of consistency and meanings that might result from language, culture, or educational systems, but that these differences are too small to account for the radical differences in findings of the original studies. Two additional explanations are then proposed and explored involving the instruments and the epistemological stances invoked for the students. Overall, the results align more closely with the findings of diSessa, Gillespie, and Esterly (2004).
Gupta, A. & Elby, A. (2011). Beyond Epistemological Deficits: Dynamic Explanations of Engineering Students' Difficulties with Mathematical Sense-making. International Journal of Science Education, 33(18), 2463-2488.
ABSTRACT: Researchers have argued against deficit-based explanations of students’ difficulties with mathematical sense-making, pointing instead to factors such as epistemology. Students’ beliefs about knowledge and learning can hinder the activation and integration of productive knowledge they have. Such explanations, however, risk falling into a ‘deficit trap’—substituting a concepts/skills deficit with an epistemological one. Our interview-based case study of a freshman engineering major, ‘Jim,’ explains his difficulty solving a physics problem (on hydrostatic pressure) in terms of his epistemology, but avoids a deficit trap by modeling the dynamics of his epistemological stabilities and shifts in terms of fine-grained cognitive elements that include the seeds of epistemological expertise. Specifically, during a problem-solving episode in the interview, Jim reaches and sticks with an incorrect answer that violates common sense. We show that Jim has all the mathematical skills and physics knowledge he would need to resolve the contradiction. We argue that his difficulty doing so stems in part from his epistemological views that (i) physics equations are much more trustworthy than everyday reasoning, and (ii) physics equations do not express meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and formalism as either necessary or plausible to accomplish. But Jim’s in-the-moment shift to a more sophisticated epistemological stance highlights the seeds of epistemological expertise that were present all along: he does see common sense as connected to formalism (though not always tractably so), and in some circumstances, this connection is both salient and valued.
Hammer, D., Gupta, A., & Redish, E. F. (2011). On static and dynamic ontologies.The Journal of the Learning Sciences, 20 (1), 163-168.
ABSTRACT: We appreciate Professor Slotta’s responding to our critique (Slotta, this issue) and the editors’ providing him and us space in the Journal of the Learning Sciences for this exchange. It is often difficult to understand subtle new ideas without seeing them defended against misinterpretations. If we have misunderstood Chi’s ideas, then we believe others have as well, and we would be glad to contribute to their further explication. For our part, we believe that Professor Slotta has misinterpreted aspects of our position. There is not space, and it would not be appropriate, for us to reiterate our arguments from the article in question (Gupta, Hammer, & Redish, 2010), but there are two particular points we feel we should clarify. First, we explain here our use of “static ontologies,” which we maintain applies. Second, we respond to the question of how our dynamic view could account for evidence of stabilities. In addition, we take the opportunity to note differences in methodology that, we believe, underlie much of this debate.
Gupta, A., Hammer, D., Redish, E.F. (2010). The case for dynamic models of learners’ ontologies in physics. The Journal of the Learning Sciences, 19(3), 285-321.
ABSTRACT: In a series of well-known papers, Chi and Slotta (M. T. H. Chi, 1992, 2005;M. T. H. Chi & J. D. Slotta, 1993 M. T. H. Chi, J. D. Slotta, & N. de Leeuw, 1994;J. Slotta & M. T. H. Chi, 2006; J. D. Slotta, M. T. H. Chi, & E. Joram, 1995) have contended that a reason for students' difficulties in learning physics is that students think about concepts as things rather than asprocesses and that there is a significant barrier between these 2 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 that these ontologies are better understood as dynamic and context dependent rather than as static constraints. To promote 1 ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources that they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.
Wagner, J. F. (2010). A Transfer-in-Pieces Consideration of the Perception of Structure in the Transfer of Learning, The Journal of the Learning Sciences, 19(4), 443-479.
ABSTRACT: Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract structure in 2 different situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences, not clearly articulated in the literature, have significant implications for accounts of transfer. Using interview data involving undergraduates learning elementary principles of probability and statistics, and Wagner's (2006) transfer-in-pieces perspective, I extend existing constructivist accounts of transfer in at least 2 ways. First, I show how the notion of a concept projection (diSessa & Wagner, 2005;Wagner, 2006) reveals fine-grained mechanisms of transfer that demonstrate how people structure situations and that elaborate on the Piagetian processes of assimilation and accommodation. Second, I examine how what experts consider a single mathematical concept or principle may come to be recognized through a variety of assimilatory cognitive resources whose usefulness is influenced by contextual factors. That is, an individual might structure 2 contextually dissimilar situations differently while perceiving the same mathematical principle at work in both. Similarly, 2 or more individuals may agree on the relevance of a particular mathematical concept in a situation, even though each structures the situation differently.
Lee, V. R. (2010). How different variants of orbit diagrams influence students’ explanations of the seasons. Science Education, 94(6), 985-1007.
ABSTRACT: The cause of the seasons is often associated with a very particular alternative conception: That the earth's orbit around the sun is highly elongated, and the differences in distance result in variations in temperature. It has been suggested that the standard diagrams used to depict the earth's orbit may be in some way responsible for the initial appearance and overall maintenance of this incorrect conceptualization; the elongated shape of the orbit is thought of as a conceptualization cue that invites a fairly predictable way of reasoning. To test whether that is indeed the case, six variants of diagrams depicting differently shaped earth orbits around the sun were presented to 652 ninth-grade students in the United States. From responses to a written assessment, students' ideas about what caused the seasons were identified and analyzed. Elongation of orbit did not appear to have an effect, and there was no reinforcement effect for students who initially believed in an elongated orbit. Additional analyses show instead that other features in the diagrams can instead be more influential as conceptualization cues, such as shading or overlapping shapes, but these cues' influence on student reasoning depend on which other cues accompany them.
http://onlinelibrary.wiley.com/ doi/10.1002/sce.20403/abstract
Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15(2), 81-97.
ABSTRACT: Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as designing for abstraction. In this paper, we draw on detailed design experiments from our research on children’s understanding about chance and distribution to re-present this work as a case study in designing for abstraction. Through the case study, we elaborate a number of design heuristics that we claim are also identifiable in the broader literature on designing for mathematical abstraction. Our previous work on the micro-evolution of mathematical knowledge indicated that new mathematical abstractions are routinely forged in activity with available tools and representations, coordinated with relatively naïve unstructured knowledge. In this paper, we identify the role of design in steering the micro-evolution of knowledge towards the focus of the designer’s aspirations. A significant finding from the current analysis is the identification of a heuristic in designing for abstraction that requires the intentional blurring of the key mathematical concepts with the tools whose use might foster the construction of that abstraction. It is commonly recognized that meaningful design constructs emerge from careful analysis of children’s activity in relation to the designer’s own framework for mathematical abstraction. The case study in this paper emphasizes the insufficiency of such a model for the relationship between epistemology and design. In fact, the case study characterises the dialectic relationship between epistemological analysis and design, in which the theoretical foundations of designing for abstraction and for the micro-evolution of mathematical knowledge can co-emerge.
http://www.springerlink.com/ content/085p7r20627r0867/
Levrini, O. & diSessa, A. A. (2008). How students learn from multiple contexts and definitions: Proper time as a coordination class. Physical Review Special Topics - Physics Education Research, 4(1), 010107.
ABSTRACT: This article provides an empirical analysis of a single classroom episode in which students reveal difficulties with the concept of proper time in special relativity but slowly make progress in improving their understanding. The theoretical framework used is "coordination class theory," which is an evolving model of concepts and conceptual change. The paper will focus on showing to what extent and in what sense most of the conditions and events in the data corpus seem understandable from the point of view of coordination class theory. In addition, however, some extensions of the theory are implicated, although we argue that they are "natural" extensions, improvements that extend, but do not threaten, the core theory. In particular, we observe students articulately aligning different ways of determining proper time, and we conjecture, more generally, that such a process is strongly consistent with coordination class theory and likely to be productive in other cases of conceptual change. The empirical analysis is explicitly connected to the general issue of theories and theory development in studies of conceptual change.
http://dx.doi.org/10.1103/PhysRevSTPER.4.010107
Parnafes, O. (2007). What does "fast" mean? Understanding the physical world through computational representations. Journal of the Learning Sciences, 16(3), 415-450.
ABSTRACT: This article concerns the development of conceptual understanding of a physical phenomenon through the use of computational representations. It examines how students make sense of and interpret computational representations, and how their understanding of the represented physical phenomenon develops in this process. Eight studies were conducted, in which pairs of students were engaged in an exploratory activity of natural harmonic oscillation. They first explored physical oscillators (e.g., springs, pendulums) and then interacted with dynamic and interactive computational representations that represent aspects of natural harmonic oscillation. The analysis focuses on selected episodes demonstrating critical steps in the development of the students' understanding. It offers a detailed description of these steps and closely examines students' interaction with various features of the representations in order to identify the relations between use of representations and students' developing understanding. A theory of conceptual change, coordination class theory (diSessa & Sherin, 1998), is used to track the development process of students' understanding with representations. The detailed analysis aims to construct a model describing mechanisms of developing understanding through the mediation of computational representations. The significance of this study is in its close look at the detailed process of learning and conceptual change in computational environments.
DOI:10.1080/10508400701413443
Please send any current papers you'd like to share with the community to Mari Levin (mariana DOT levin AT wmich DOT edu).
PERticles
It's difficult to keep up with the very large literature in physics education research (PER), but there are online tools that let us gather and share information to make the task simple. PERticles is a CiteULike online reference library which collects citations to new publications in physics education research as it is broadly defined. The library is online at
http://www.citeulike.org/group/10888/library
PERticles is edited by Michael Wittmann (mwittmann AT maine DOT edu).