The Case for Dynamic Models of Learners' Ontologies in Physics

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, pp. 285-321. [Link to Article on the Journal Page]

On static and dynamic ontologies

1. Hammer, D., Gupta, A, & Redish, E. F. (2011). On static and dynamic ontologies. The Journal of the Learning Sciences, 20 (1), 163-168.

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.

(List of references)

Redish, Cooke, Dobbins, & Hall, GIREP Conference Poster (2009)

Transforming the Physics Education of Undergraduate Biology Students in Introductory Physics and Biology Courses

Edward F. Redish, Todd J. Cooke, Heather D. Dobbins, and Kristi L. Hall

Poster presented at GIREP2009, Leicester, UK, August 2009.

Abstract: In 2003, the US National Academy of Sciences issued the BIO 2010 report that called for the increased incorporation of mathematics, physics, and chemistry into undergraduate biology curriculum, and for a corresponding increase in the biological relevance of introductory science courses for biologists. This initiative has led to widespread interdisciplinary efforts that are transforming the way mathematics and chemistry is taught to US biology students, but it has not prompted comparable reform in physics. There appear to be a number of reasons for this lag. Many Physics faculty are hesitant about pruning and reorganizing traditional content and may not be familiar with the content that biologists feel is relevant and useful, while many Biology faculty are hesitant about including physics in their biology classes explicitly. At the University of Maryland, a group of physicists and biologists have started working together to better understand the roadblocks to implementing a coordinated revision of our introductory biology and physics courses for biology students. The challenges facing this effort occur at a variety of levels. 1) Introductory physics for biologists is often a “cut-down” version of introductory physics for engineers. As such, it inherits some inappropriate approaches. For example, it introduces the second law of Thermodynamics via heat engines and ignores chemical energy. This approach is inappropriate because organisms cannot convert temperature gradients into useful metabolic energy, whereas other forms of physical and chemical energy are continually being transformed in biological systems. 2) Introductory biology classes typically are “fact-based”, relying on extensive reading and focusing on concept mastery, including introducing the student to many different terms, processes, and relationships, while physics courses are structured to emphasize complex reasoning from a small set of fundamental laws and principles. 3) Physics classes rely heavily on problem-solving and are over the past decade have developed extensive active-engagement learning pedagogy, whereas biology courses still tend to rely heavily on direct lecture and protocol-based laboratories. 4) Biology classes tend to use mathematics to represent qualitative dependences, while physics classes treat math as a fundamental reasoning tool. Our poster presents examples and suggestions for bridging these gaps. Our goal is to initiate a widespread discussion among physicists and biologists regarding the physics challenge in the BIO 2010 initiative.

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.

(List of references.)

Tuminaro & Redish, PER Conference Proceedings (2003)

Understanding Students' Poor Performance on Mathematical Problem Solving in Physics

J. Tuminaro & E. F. Redish, Proceedings of the Physics Education Research Conference, Madison, WI (Aug 6-7, 2003).

Abstract: Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) Students lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. Many physics faculty assume that the lack of mathematical skills is the problem. We present evidence suggesting that the major source of students’ errors is their failure to apply the mathematical knowledge they have or to interpret that knowledge in a physical context. Additionally, we present an instructional strategy that can help students employ the mathematical knowledge they already possess.

Redish, Wittmann, Bao & Steinberg, NARST Annual Meeting (1999)

The Influence of Student Understanding of Classical Physics when Learning Quantum Physics

E. F. Redish, M. C. Wittmann, L. Bao & R. N. Steinberg, Research on the Teaching and Learning of Quantum Sciences, NARST Annual Meeting, Boston, MA (1999).

Abstract: Understanding quantum mechanics is of growing importance, not just to future physicists, but to future engineers, chemists, and biologists. Fields in which understanding quantum mechanics is important include photonics, mesoscopic engineering, and medical diagnostics. It is therefore not surprising that quantum is being taught more often to more students starting as early as high school. However, quantum mechanics is difficult and abstract. Furthermore, understanding many classical concepts is prerequisite to a meaningful understanding of quantum systems.

In this paper, we describe research results of two examples of the influence of student understanding of classical concepts when learning quantum mechanics. for each example, we describe difficulties students have in the classical regime and how these difficulties seem to impair student learning of quantum concepts. We briefly discuss how these difficulties can be addressed.

Obviously the examples described in this paper are not intended to be exhaustive. Instead, we have two objectives. The first is to highlight the importance of having a strong conceptual base when learning more advanced topics in physics. The second is to illustrate the importance of continuously and systematically probing student learning by using the tools of physics education research.

Wittmann, Steinberg & Redish, Int J Sci Ed (2003)

Understanding and Affecting Student Reasoning about Sound Waves

M. C. Wittmann, R. N. Steinberg & E. F. Redish, International Journal of Science Education, 25(8), p 991-1013 (2003).

Abstract:Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.

Gupta, Hammer & Redish, Proceedings for the International Conf for the Learning Sciences (2008)

Towards a Dynamic Model of Learners' Ontologies in Physics

A. Gupta, D. Hammer & E. F. Redish, Proceedings of the International Conference for the Learning Sciences, Issue 8 [ISSN: 1814-9316]. (2008)

Redish, Talk: AAPT National Meeting (2001)

What can astronomy education learn from physics education research?

E. F. Redish, Invited talk presented at AAPT National Meeting, San Diego (January 2001). (frame html version)

Redish, Talk: Ganiel Symposium (2001)

Metacognition and instructional design: Theory-driven goals and methods in a large university physics class

E. F. Redish, talk given at Ganiel Symposium, Rehovoth, Israel (September 14, 2001). (frame html version)

Redish, Talk: Conf on Integrating Math and Science Ed Research (2002)

Our Model of how a Student "Works": Does it matter for teaching science?

E. F. Redish, talk given at the Conference on Integrating Science and Math Education Research, Orono, Maine (June 23, 2002). 

Redish, Talk: Physics Colloquium (2003)

Rethinking College Physics: What do we have to offer biology students?

E. F. Redish, talk given as the UMD Physics Department Colloquium, College Park, MD (February 11, 2003). (frame html version)

Redish, Talk: APS-AAPT Joint Regional Meeting (2003)

The Future of Physics Education: Building an Applied Science?

E. F. Redish, Talk given at the APS-AAPT Joint Regional Meeting, Berkeley, CA (November 15, 2003). (frame html version)

Bing & Redish, Conference Proceedings (2008)

Using warrants as a window to epistemic framing

T. J. Bing & E. F. Redish, Proceedings of the Physics Education Research Conference, Edmonton, AB, July 2008, to be published.

Abstract: Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his physics problem solving. We present a short example from the problem solving work of upper level physics students and use it to illustrate the epistemic framing process: “framing” because these students are focusing on a subset of their total math knowledge, “epistemic” because their choice of subset relates to what they see (at that particular time) as the nature of the math knowledge in play. We illustrate how looking for students’ warrants, the often unspoken reasons they think their evidence supports their mathematical claims, serves as a window to their epistemic framing. These warrants provide a powerful, concise piece of evidence of these students’ epistemic framing.

Redish & Hammer, Am J Phys (2008)

Reinventing College Physics for Biologists: Explicating an Epistemological Curriculum

E. F. Redish & D. Hammer, accepted for publication in Am J Phys, (2008). [with supplementary appendix]

Abstract: The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department’s large service courses, serving primarily life-science majors. After consultation with biologists, we re-focused the class on helping the students learn to think scientifically – to build coherence, think in terms of mechanism, and to follow the implications of assumptions. We designed the course to tap into students’ productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials, including Peer Instruction, Interactive Lecture Demonstrations, and Tutorials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations, and we administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.

Redish & Smith, J of Engineering Educ (2008)

Looking Beyond Content: Skill development for engineers

E. F. Redish & K. A. Smith, Journal of Engineering Education, 97, p 295-307 (July 2008). 

Abstract: Current concerns over reforming engineering education have focused attention on helping students develop skills and an adaptive expertise. Phenomenological guidelines for instruction along these lines can be understood as arising out of an emerging theory of thinking and learning built on results in the neural, cognitive, and behavioral sciences. We outline this framework and consider some of its implications for one example: developing a more detailed understanding of the specific skill of using mathematics in modeling physical situations. This approach provides theoretical underpinnings for some best-practice instructional methods designed to help students develop this skill and provides guidance for further research in the area.

Bing & Redish, Am J Phys (2008)

Symbolic manipulators affect mathematical mindsets

T. J. Bing & E. F. Redish, Am J Phys, 76, p 418-424 (2008). (html version)

Abstract: The use of symbolic calculators such as MATHEMATICA is becoming more commonplace among upper level physics students. The presence of such powerful calculators can couple strongly to the type of mathematical reasoning students employ. These tools do not merely offer students a convenient way to perform the calculations they would have otherwise done by hand. We present examples from the work of upper level physics majors where MATHEMATICA plays an active role in focusing and sustaining their thoughts around calculation. These students still engage in powerful mathematical reasoning while they calculate, but struggle because of the narrowed breadth of their thinking. We model MATHEMATICA'S influence as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.

Gupta, Redish & Hammer, PER Conf Proceedings (2008)

Coordination of Mathematical and Physics Resources by Physics Graduate Students

A. Gupta, E. F. Redish & D. Hammer, in Proceedings of the Physics Education Research Conference, Greensboro, NC, July 2007, AIP Conf. Proc, 951, p104-107 (2008). (html version)

Abstract: We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While all the 16 participating students obtained the dielectric function correctly in one of two equivalent expressions, roughly half of them (7 of 16) failed to compute the roots correctly. All seven took the same initial step that led them to the incorrect answer. We note a perfect correlation between the specific expression of dielectric function obtained and the student's success in solving for the roots. We analyze student responses in terms of a resources framework and suggest routes for future research.