Eleanor C. Sayre,

Plasticity: Resource Justification and Development

Unpublished Ph.D. dissertation, University of Maine, 2007

Physics education research is fundamentally concerned with understanding the processes of student learning and facilitating the development of student understanding. A better understanding of learning processes and outcomes is integral to improving said learning. In this thesis, I detail and expand upon Resource Theory, allowing it to account for the development of resources and connecting the activation and use of resources to experimental data. Resource Theory is a general knowledge-in-pieces schema theory. It bridges cognitive science and education research to describe the phenomenology of problem solving. Resources are small, reusable pieces of thought that make up concepts and arguments. The physical context and cognitive state of the user determine which resources are available to be activated; different people have different resources about different things. Over time, resources may develop, acquiring new meanings as they activate in different situations. In this thesis, I introduce "plasticity," a continuum for describing the development of resources. The plasticity continuum blends elements of Process/Object and Cognitive Science with Resource Theory. The name evokes brain plasticity and myelination (markers of learning power and reasoning speed, respectively) and materials plasticity and solidity (with their attendant properties, deformabihty and stability). In the plasticity continuum, the two directions are more plastic and more solid. More solid resources are more durable and more connected to other resources. Users tend to be more committed to them because reasoning with them has been fruitful in the past. Similarly, users tend not to perform consistency checks on them any more. In contrast, more plastic resources need to be tested against the existing network more often, as users forge links between them and other resources. To explore these expansions and their application, I present several extended examples drawn from an Intermediate Mechanics class. The first extended example comes from damped harmonic motion; the others discuss coordinate system choice for simple pendula. In every case, the richness of student reasoning indicates that a wealth of resources of varying plasticity are in play. To analyze the encounters, a careful and fine-grained theoretical approach is required.

Recommended Citation

Sayre, Eleanor C., "Plasticity: Resource Justification and Development" (2007). Electronic Theses and Dissertations. 1107.

http://digitalcommons.library.umaine.edu/etd/1107

## 2007-08-31

### Sayre Ph.D.: Resource justification and development

Labels: coordination classes, mathematics, PhD, plasticity, resources, Sayre

## 2007-08-24

### Pollock, Thompson, and Mountcastle on Variables in PV diagrams

E.B. Pollock, J.R. Thompson, D.B. Mountcastle

Student Understanding of the Physics and Mathematics of Process Variables In P-V Diagrams

Physics Education Research Conference Proceedings 2007

Students in an upper-level thermal physics course were asked to compare quantities related to the First Law of Thermodynamics along with similar mathematical questions devoid of all physical context. We report on a comparison of student responses to physics questions involving interpretation of ideal gas processes on P-V diagrams and to analogous mathematical qualitative questions about the signs of and comparisons between the magnitudes of various integrals. Student performance on individual questions combined with performance on the paired questions shows evidence of isolated understanding of physics and mathematics. Some difficulties are addressed by instruction.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 168-171

2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820924

Labels: mathematics, Mountcastle, papers, pers, Pollock, thermo, Thompson

### Mountcastle, Bucy, Thompson on Probability and Uncertainty

D.B. Mountcastle, B.R. Bucy, J.R. Thompson

Student Estimates of Probability and Uncertainty in Advanced Laboratory and Statistical Physics Courses

Physics Education Research Conference Proceedings 2007

Equilibrium properties of macroscopic systems are highly predictable as n, the number of particles approaches and exceeds Avogadro's number; theories of statistical physics depend on these results. Typical pedagogical devices used in statistical physics textbooks to introduce entropy (S) and multiplicity () (where S = k ln()) include flipping coins and/or other equivalent binary events, repeated n times. Prior to instruction, our statistical mechanics students usually gave reasonable answers about the probabilities, but not the relative uncertainties, of the predicted outcomes of such events. However, they reliably predicted that the uncertainty in a measured continuous quantity (e.g., the amount of rainfall) does decrease as the number of measurements increases. Typical textbook presentations assume that students understand that the relative uncertainty of binary outcomes will similarly decrease as the number of events increases. This is at odds with our findings, even though most of our students had previously completed mathematics courses in statistics, as well as an advanced electronics laboratory course that included statistical analysis of distributions of dart scores as n increased.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 152-155

2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820919

Labels: Bucy, mathematics, Mountcastle, thermo, Thompson

### Van Deventer and Wittmann on math and physics vectors

J. Van Deventer and M.C. Wittmann

Comparing Student Use of Mathematical and Physical Vector Representations

Physics Education Research Conference Proceedings 2007.

Research has shown that students have difficulties with vectors in college introductory physics courses and high school physics courses; furthermore, students have been shown to perform worse on a vector task with a physical context when compared to the same task in a mathematical context. We have used these results to design isomorphic mathematics and physics free-response vector test questions to evaluate student understanding of vectors in both contexts. To validate our test, we carried out task-based interviews with introductory physics students. We used our results to develop a multiple-choice version of the vector test which was then administered to introductory physics students. We report on our test, giving examples of questions and preliminary findings.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 208-211

2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820935

Labels: kinematics, mathematics, Mechanics, papers, Van Deventer, Wittmann

### Black and Wittmann on the epistemic games in integration

K.E. Black and M.C. Wittmann

Epistemic Games in Integration: Modeling Resource Choice

Physics Education Research Conference Proceedings 2007.

As part of an ongoing project to understand how mathematics is used in advanced physics to guide one's conceptual understanding of physics, we focus on students' interpretation and use of boundary and initial conditions when solving integrals. We discuss an interaction between two students working on a group quiz problem. After describing the interaction, we briefly discuss the procedural resources that we use to model the students' solutions. We then use the procedural resources introduced earlier to draw resources graphs describing the two epistemic game facets used by the students in our transcript. ©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 53-56

2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820945

Labels: Black, epistemic games, mathematics, Mechanics, papers, resources, Wittmann

### Bucy PhD: Thermo, Entropy, and Partial Differentials

Brandon R. Bucy

Investigations of Student Understanding of Entropy and of Mixed Second-Order Partial Derivatives in Upper-Level Thermodynamics

Unpublished Ph.D. dissertation, August 2007

Labels: Bucy, mathematics, PhD, thermo