Redish & Gupta, GIREP Conference Presentation (2009)

Making Meaning with Math in Physics

Edward F. Redish and Ayush Gupta

Contributed paper presented at GIREP2009, Leicester, UK, August 20, 2009.

Physics makes powerful use of mathematics, yet how this happens is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive knowledge structures. But because of the way the cognitive system builds expertise, instructors who are expert physicists may have difficulty in unpacking their well-integrated knowledge in order to understand the difficulties novice students have in learning their subject. Despite the fact that students may have previously been exposed to ideas in math classes, the addition of physical contexts can produce severe barriers to learning and sense-making. In order to better understand student difficulties and to unpack expert knowledge, we adopt and adapt ideas and methods from cognitive semantics, a sub-branch of linguistics devoted to understanding how meaning is associated with language. We illustrate this with examples spanning the physics curriculum.

Redish & Bing, GIREP Conference Poster (2009)

Using Math in Physics: Warrants and Epistemological Frames

Edward F. Redish and Thomas J. Bing

Prepared in conjunction with Symposium, “Mathematization in Physics Lessons: Problems and Perspectives”, R. Karam and G. Pospiech, organizers. GIREP meeting, Leicester, UK, 18. August, 2009.

Abstract: Mathematics is an essential component of university level science, but it is more complex than a straightforward application of rules and calculation. Using math in science critically involves the blending of ancillary information with the math in a way that both changes the way that equations are interpreted and provides metacognitive support for recovery from errors. We have made ethnographic observations of groups of students solving physics problems in classes ranging from introductory algebra based physics to graduate quantum mechanics. These lead us to conjecture that expert problem solving in physics requires the development of the complex skill of mixing different classes of warrants – the ability to blend physical, mathematical, and computational reasons for constructing and believing a result. In order to analyze student behavior along this dimension, we have created analytical tools including epistemic frames and games. These should provide a useful lens on the development of problem solving skills and permit an instructor to recognize the development of sophisticated problem solving behavior even when the student makes mathematical errors.

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Redish & Sayre, GIREP Conference Poster (2009)

Resources: A Theoretical Framework for Physics Education

Edward F. Redish and Eleanor C. Sayre

Poster presented at GIREP2009, Leicester, UK, August 2009

Abstract: The Resources Framework (RF) is a structure for creating phenomenological models of high-level thinking. It is based on a combination of core stable results selected from educational research phenomenology, cognitive neuroscience, and behavioral science. As a framework (as opposed to a theory), it provides ontologies -- classes of structural elements and their behaviors -- rather than providing specific structures. These ontologies permit the creation of models that bridge existing models of knowledge and learning, such as the alternative conceptions theory and the knowledge in pieces approach, or cognitive modeling and the socio-cultural approach. Structurally, the RF is an associative network model with control structure and dynamic binding. As a phenomenological and descriptive framework, it does not (yet) create mathematical models from low-level elements. This poster outlines the RF and shows how it gives new ways of looking at traditional issues such as transfer, concepts, ontologies, and epistemology.

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