Wittmann, International J of Science Ed (2002)

The Object Coordination Class Applied to Wavepulses: Analysing Student Reasoning in Wave Physics

M. C. Wittmann, International Journal of Science Education, 24(1), p 97-118 (2002). (link to journal article)

Abstract: Detailed investigations of student reasoning show that students approach the topic of wave physics using both event-like and object-like descriptions of wavepulses, but primarily focus on object properties in their reasoning. Student responses to interview and written questions are analysed using diSessa and Sherin's coordination class model which suggests that student use of specific reasoning resources is guided by possibly unconscious cues. Here, the term reasoning resources is used in a general fashion to describe any of the smaller grain size models of reasoning (p-prims, facets of knowledge, intuitive rules, etc) rather than theoretically ambiguous (mis)conceptions. Student applications of reasoning resources, including one previously undocumented, are described. Though the coordination class model is extremely helpful in organising the research data, problematic aspects of the model are also discussed.

Lising & Elby, Am J Phys (2005)

The impact of epistemology on learning: A case study from introductory physics

L. Lising & A. Elby, American Journal of Physics, 73(4), p 372-382 (2005). (html version)

Abstract: We discuss a case study of the influence of epistemology on learning for a student in an introductory college physics course. An analysis of videotaped class work, written work, and interviews indicates that many of the student's difficulties were epistemological in nature. Our primary goal is to show instructors and curriculum developers that a student's epistemological stance - her ideas about knowledge and learning - can have a direct, causal influence on her learning of physics. This influence exists even when research-based curriculum materials provide implicit epistemological support. For this reason, curriculum materials and teaching techniques could become more effective by explicitly attending to students' epistemologies.

Elby, J of Mathematical Behavior (2000)

What students' learning of representations tells us about constructivism

A. Elby, Journal of Mathematical Behavior, 19, p 481-502 (1999). (html version)

Abstract: This paper pulls into the empirical realm a longstanding theoretical debate about the prior knowledge students bring to bear when learning scientific concepts and representations. Misconceptions constructivists view the prior knowledge as stable alternate conceptions that apply robustly across multiple contexts. By contrast, fine-grained constructivists believe that much of students' intuitive knowledge consists of unarticulated, loosely-connected knowledge elements, the activation of which depends sensitively on context. By focusing on students' intuitive knowledge about representations, and by fleshing out the two constructivist frameworks, I show that they lead to empirically different sets of predictions. Pilot studies demonstrate the feasibility of a full-fledged experimental program to decide which flavor of constructivist describes students more adequately.

Hammer, Enrico Fermi Summer School Proceedings (2004)

The variability of student reasoning, lectures 1-3

D. Hammer, in Proceedings of the Enrico Fermi Summer School, Course CLVI, E. Redish & M. Vicentini (Eds.), Bologna: Italian Physical Society (2004).

Lecture 1: Case studies of children's inquiries, p 279-299.

Abstract: Classroom observations show variability in student reasoning, from young children through adults, even moment-to-moment for the same students in the same class. This varied phenomenology conflicts with views of naïve theories, entrenched conceptions and stages of development as stable attributes. Student knowledge and reasoning is better understood in terms of a manifold ontology of more fine-grained, context sensitive resources. Expectations of variability in student knowledge and reasoning suggest different approaches and objectives in instruction, especially in early science education.
This is the first lecture in a series of three. It introduces the overall agenda and then begins with a series of examples of children’s inquiries to reflect on the beginnings of scientific expertise.

Lecture 2: Transitions, p 301-319.

Abstract:This lecture continues the phenomenology of student reasoning from the first, beginning with brief examples of introductory physics students failing to apply basic logic and common sense. These contrast with the examples from the first lecture of children’s reasoning, but it would be a mistake to interpret the university students’ behavior as evidence that they are not capable of what we saw in elementary students. Rather, students at all ages are capable of reasoning in a variety of ways, and the bulk of this lecture focuses on examples of students shifting in their approaches and ideas over short time scales. Often these shifts follow epistemological prompts from an instructor, suggestions for how students should think about knowledge and learning.

Lecture 3: Manifold cognitive resources, p 321-340.

Abstract: The previous lectures focused on phenomenology: What sorts of occurrences do we see in students’ reasoning? This third and final lecture focuses on ontology: What sorts of things do we attribute to students’ minds? It has become conventional to speak and think in terms of conceptions, naïve theories, and stages of development. These are all attributions of stable properties, and they account well for patterns that can occur in student reasoning. They do not account well, however, for the variability and multiple patterns illustrated in the previous lectures. Research in cognitive science provides an alternative ontology of multiple, fine-grained cognitive resources that are contextsensitive in their activation. This lecture reviews some of that work and draws implications for elementary science education.

Hammer & Elby, J of the Learning Sciences (2003)

Tapping students' epistemological resources

D. Hammer & A. Elby, Journal of the Learning Sciences, 12(1), p 53-91 (2003). 

Abstract: Research on personal epistemologies has begun to consider ontology: Do naive epistemologies take the form of stable, unitary beliefs or of fine-grained, context-sensitive resources? Debates such as this regarding subtleties of cognitive theory, however, may be difficult to connect to everyday instructional practice. Our purpose in this article is to make that connection. We first review reasons for supporting the latter account, of naive epistemologies as made up of fine-grained, context-sensitive resources; as part of this argument we note that familiar strategies and curricula tacitly ascribe epistemological resources to students. We then present several strategies designed more explicitly to help students tap those resources for learning introductory physics. Finally, we reflect on this work as an example of interplay between two modes of inquiry into student thinking, that of instruction and that of formal research on learning.

Hammer & Elby, Personal Epistemology (2002)

On the form of a personal epistemology

D. Hammer & A. Elby, in Personal Epistemology: The Psychology of Beliefs about Knowledge and Knowing, B. K. Hofer & P. R. Pintrich (Eds.), p 169-190, Mahwah, NJ: Lawrence Erlbaum. 

Elby & Hammer, Science Education (2001)

On the substance of a sophisticated epistemology

A. Elby & D. Hammer, Science Education, 85(5), p 554-567 (2001).

Abstract: Among researchers who study students’ epistemologies, a consensus has emerged about what constitutes a sophisticated stance toward scientific knowledge. According to this community consensus, students should understand scientific knowledge as tentative and evolving, rather than certain and unchanging; subjectively tied to scientists' perspectives, rather than objectively inherent in nature; and individually or socially constructed rather than discovered. Surveys, interview protocols, and other methods used to probe students’ beliefs about scientific knowledge broadly reflect this outlook.

Our paper questions the community consensus about epistemological sophistication. We do not suggest that scientific knowledge is objective and fixed; if forced to choose whether knowledge is certain or tentative, with no opportunity to elaborate, we would choose “tentative.” Instead, our critique consists of two lines of argument. First, the literature fails to distinguish between the correctness and productivity of an epistemological belief. For instance, elementary school students who believe that science is about discovering objective truths to questions such as whether the earth is round or flat, or whether an asteroid led to the extinction of the dinosaurs, may be more likely to succeed in science than students who believe science is about telling stories that vary with one's perspective. Naive realism, although incorrect (according to a broad consensus of philosophers and social scientists), may nonetheless be productive for helping those students learn.

Second, according to the consensus view as reflected in commonly-used surveys, epistemological sophistication consists of believing certain blanket generalizations about the nature of knowledge and learning, generalizations that do not attend to context. These generalizations are neither correct nor productive. For example, it would be unsophisticated for students to view as tentative the idea that the Earth is round rather than flat. By contrast, they should take a more tentative stance towards theories of mass extinction. Nonetheless, many surveys and interview protocols tally students as sophisticated not for attending to these contextual nuances, but for subscribing broadly to the view that knowledge is tentative.

Tuminaro & Redish, Phys Rev STPER (2007)

Elements of a Cognitive Model of Physics Problem Solving: Epistemic Games

J. Tuminaro & E. F. Redish, Phys Rev ST PER, 3, 020101 (2007). 

Abstract: Although much is known about the differences between expert and novice problem solvers, knowledge of those differences typically does not provide enough detail to help instructors understand why some students seem to learn physics while solving problems and others do not. A critical issue is how students access the knowledge they have in the context of solving a particular problem. In this paper, we discuss our observations of students solving physics problems in authentic situations in an algebra-based physics class at the University of Maryland. We find that when these students are working together and interacting effectively, they often use a limited set of locally coherent resources for blocks of time of a few minutes or more. This coherence appears to provide the student with guidance as to what knowledge and procedures to access and what to ignore. Often, this leads to the students failing to apply relevant knowledge they later show they possess. In this paper, we outline a theoretical phenomenology for describing these local coherences and identify six organizational structures that we refer to as epistemic games. The hypothesis that students tend to function within the narrow confines of a fairly limited set of games provides a good description of our observations. We demonstrate how students use these games in two case studies and discuss the implications for instruc-tion.

Sabella & Redish, Am J Phys (2007)

Knowledge Organization and Activation in Physics Problem Solving

M. Sabella & E. F. Redish, Am J Phys, 75, p 1017-1029 (2007).

Abstract: Conceptual knowledge is only one aspect of a good knowledge structure: how and when knowledge is activated and used are also important. In this paper, we explore knowledge organization in the context of the resources model of student thinking through observations of student problem-solving behavior on a mechanics task that integrates the concepts of force, motion, and energy. We document in detail that both introductory and advanced students may have knowledge structures with local coherences that may inhibit their access to additional useful knowledge. These results suggest that instructors and researcher need to pay increased attention to how and when students use what they know as well as to what they know.

Redish, Scherr & Tuminaro, The Physics Teacher (2006)

Reverse Engineering the Solution of a "Simple" Physics Problem: Why learning physics is harder than it looks

E. F. Redish, R. E. Scherr & J. Tuminaro, published in a slightly abbreviated version in The Physics Teacher, 44, p 293 (May 2006).

Abstract:  Problem solving is the heart and soul of most college physics and many high school physics courses. The “big idea” is that physics tells you more about a physical situation than you thought you knew — and you can quantify it if you use fundamental physical principles expressed in mathematical form. Often, the results of your problem solving can lead you to understand and rethink your intuitions about the physical world in new and more productive ways. As a result, physics is a great place (some of us would claim the best place) to learn how to use mathematics effectively in science.

As physics teachers, we often stress the importance of problem solving in learning physics. Unfortunately, many of our students appear to find problem solving very difficult. Sometimes they generate ridiculous answers and seem satisfied with them. Sometimes they can do the calculations but not interpret the implications of the results. Sometimes, despite apparent success in problem solving, they seem to have a poor understanding of the physics that went into the problems.1 We give them explicit instructions on how to solve problems (“draw a picture,” “find the right equation,” …) but it doesn’t seem to help.

We might respond that they need to take more math prerequisite classes, but in the algebra-based physics class at the University of Maryland, almost all of the students have taken calculus and earned an A or a B. Many of them have been successful in classes such as organic chemistry, cellular biology, and genetics. Why do they have so much trouble with the math in an introductory physics class?

As part of a research project to study learning in algebra-based physics,2 the Physics Education Research Group at the University of Maryland videotaped students working together on physics problems. Analyzing these tapes gives us new insights into the problems they have in using math in the context of physics. One problem is that they have inappropriate expectations as to how to solve problems in physics (some of it learned, perhaps, in math classes). This is discussed elsewhere.3 A second problem seems to lie with the instructors. As instructors, we may have misconceptions about how people think and learn, and this has important implications about how we interpret what our students are doing.

In this paper, we want to consider one example of students working on a physics problem that showed us in a dramatic fashion that we had failed to understand the work the students needed to do in order to solve an apparently “simple” problem in electrostatics. Our critical misunderstanding was failing to realize the level of complexity that we had built into our own “obvious" knowledge about physics.

Hammer, Elby, Scherr & Redish, Transfer of Learning: Research and Perspectives (2004)

Resources, framing, and transfer

D. Hammer, A. Elby, R. E. Scherr & E. F. Redish, in Transfer of Learning: Research and Perspectives, J. Mestre (Ed.) Information Age Publishing: Greenwich, CT (2005), pp. 89-119.

Abstract: As researchers studying student reasoning in introductory physics, and as instructors teaching courses, we often focus on whether and how students apply what they know in one context to their reasoning in another. But we do not speak in terms of “transfer.” The term connotes to us a unitary view of knowledge as a thing that is acquired in one context and carried (or not) to another. We speak, rather, in terms of activating resources, a language with an explicitly manifold view of cognitive structure. In this chapter, we describe this view and argue that it provides a more firm and generative basis for research.

In particular, our resources-based perspective accounts for why it is difficult, and perhaps unnecessary, to draw a boundary around the notion of “transfer”; provides an analytical framework for exploring the differences between active transfer involving metacognition and passive transfer that “just happens”; helps to explain many results in the transfer literature, such as the rarity of certain kinds of transfer and the ubiquity of others; and provides an ontological underpinning for new views of transfer such as Bransford, Schwartz, and Sears’ (this issue) “preparation for future learning.”

Redish, Proceedings of International School of Physics (2004)

A Theoretical Framework for Physics Education Research: Modeling Student Thinking

E. F. Redish, in Proceedings of the International School of Physics, "Enrico Fermi" Course CLVI, E. F. Redish and M. Vincentini (Eds.) IOS Press, Amsterdam (2004).

Abstract: Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations and through which different theoretical models of student thinking can be compared. Much that is known in the behavioral sciences is robust and observationally based. In this paper, I draw from a variety of fields ranging from neuroscience to sociolinguistics to propose an over-arching theoretical framework that allows us to both make sense of what we see in the classroom and to compare a variety of specific theoretical approaches. My synthesis is organized around an analysis of the individual’s cognition and how it interacts with the environment. This leads to a two level system, a knowledge-structure level where associational patterns dominate, and a control-structure level where one can describe expectations and epistemology. For each level, I sketch some plausible starting models for student thinking and learning in physics and give examples of how a theoretical orientation can affect instruction and research.

Bao & Redish, UMD preprint (2001)

Model Analysis: Assessing the Dynamics of Student Learning

L. Bao & E. F. Redish, University of Maryland preprint (Mar 2001).

Abstract: In this paper we present a method of modeling and analysis that permits the extraction and quantitative display of detailed information about the effects of instruction on a class’s knowledge. The method relies on a cognitive model of thinking and learning that represents student thinking in terms of patterns of association in long-term memory structures that we refer to as schemas or mental models. As shown by previous research, students frequently fail to recognize relevant conditions that lead to appropriate uses of their mental models and, as a result, can use multiple models inconsistently to treat problems that appear equivalent to an expert. Once the most common mental models have been determined via qualitative research, they can be mapped onto probing instruments such as a multiple-choice test. We have developed Model Analysis to analyze the results of these instruments that treats the student as if he/she were in a mixed state – a state which, when probed with a set of scenarios under diverse contextual settings, gives the probability that the student will choose a particular mental model to analyze the scenario. We illustrate the use of our method by analyzing results from the Force Concept Inventory, a research-based multiplechoice instrument developed to probe student’s conceptual understanding of Newtonian Mechanics in a physics class. Model Analysis allows one to use qualitative research results to provide a framework for analyzing and interpreting the meaning of students’ incorrect responses on a well-designed research-based multiple-choice test. These results can then be used to guide instruction, either for an individual teacher or for developers of reform curricula.

Redish, Am J Phys (1994)

Implications of Cognitive Studies for Teaching Physics

E. F. Redish, Am J Phys, 62, 796-803 (1994). (html version)