Springuel, Thompson, and Wittmann on cluster analysis of vector representations

Springuel, R.P., Thompson, J.R., and Wittmann, M.C.
Applying clustering to statistical analysis of student reasoning about two-dimensional kinematics

We use clustering, an analysis method not presently common to the physics education research community, to group and characterize student responses to written questions about two-dimensional kinematics. Previously, clustering has been used to analyze multiple-choice data; we analyze free-response data that includes both sketches of vectors and written elements. The primary goal of this paper is to describe the methodology itself; we include a brief overview of relevant results.

URL: http://link.aps.org/abstract/PRSTPER/v3/e020107
DOI: 10.1103/PhysRevSTPER.3.020107
PACS: 01.40.Fk, 01.40.gf


Smith and Wittmann on teaching Newton's Third Law

Trevor I. Smith and Michael C. Wittmann
Comparing three methods for teaching Newton’s third law
Phys. Rev. ST Phys. Educ. Res. 3, 020105 (2007)

Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed University of Washington–style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.


Sayre Ph.D.: Resource justification and development

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Unpublished Ph.D. dissertation, University of Maine, 2007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


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

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

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

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

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


Reed MST: SET students' experiences

Dan Reed
Evaluating Factors Contributing to Engineering Technology Students’ Introductory Physics Experience
Unpublished MST thesis, University of Maine, August, 2007.

The UMaine’s introductory algebra-based physics course PHY 107 is dedicated to students from the School of Engineering Technology (SET). These SET students come from a wide range of backgrounds and are studying a hybrid of curricula for an engineer and a technician with a leaning toward engineering. In order to appropriately serve this population we must attempt to understand who these students are.

One of the legends surrounding this group is that their struggles with physics stem from having a lower level of mathematics ability than the typical introductory physics student. Through the use of a math diagnostic, the Force and Motion Conceptual Evaluation (FMCE), an updated version of the Maryland Physics Expectations (MPEX2) survey, and a myriad of student, instructor, and SET Coordinator interviews, I sought to develop a data supported view of the PHY 107 students. In this process, I address current course objectives; the extent students develop toward those objectives; and find which factors correlate with physics conceptual development.

I found that despite SET’s professional concerns, they care most about developing their students’ abilities to make sense of physical and verbal representations of a situation and translate that understanding into meaningful mathematical models. The measure of conceptual development tells the extent to which PHY 107 has developed these skills necessary to build a mathematical model. PHY 107 students only improved !12% of their potential for conceptual development as measured by the FMCE.

Mathematic skill failed to contribute to the PHY 107 students’ conceptual gain , though they do represent the bottom quartile of a typical algebra-based introductory physics course. Of all factors considered in this study, pre- and post-instruction favorable attitudes as measured by MPEX2 coherence and concept cluster scores best-predicted student conceptual development.


Smith MST: comparing reform implementations

Trevor I. Smith
Comparing the Effectiveness of Research-Based Curricula for Teaching Introductory Mechanics
Unpublished MST thesis, University of Maine, May, 2007.

This study examines the effects of implementing various research-based forms of cur- ricula for teaching introductory physics course at the College of DuPage in Glen Ellyn, IL and the University of Maine in Orono, ME. Introductory courses at each of these institutions were modified at each of these institutions over the course of several years. For each course, baseline data were collected during a year in which at least one form of research-based curricula was used. In subsequent years, other research-based curricula were implemented in addition to the baseline treatment at the University of Maine and in place of the baseline treatment at the College of Du- Page. Data collected using the Force and Motion Conceptual Evaluation and the Force Concept Inventory were analyzed using the Model Analysis method developed by Bao and Redish[1] to determine the manner(s) in which the curricular modifica- tions affected students’ conceptual development throughout a course. The results of this analysis show that the majority of curricular changes had little overall effect on students’ conceptual understanding of physics. Several exceptions to this generality are discussed.

Recommended Citation

Smith, Trevor I., "Comparing the Effectiveness of Research-based Curricula for Teaching Introductory Mechanics" (2007). Electronic Theses and Dissertations. 1355.



Moyer MST: Understanding of stem cells

Jon Moyer
A comparative study of how high school students understand stem cells
Unpublished M.S.T. thesis, May 2007

In Spring 2004 an inquiry-based unit on stem cells was developed from chromatin dynamics research at the Jackson Laboratory in Bar Harbor, Maine. The unit was developed according to the backwards design model of curriculum development and implemented in Bangor area high schools in April 2005 and June 2005. With slight modifications, the stem cell unit was re-implemented in June 2006 and tested against a traditional, lecture-based unit.

Open response pre- and post-tests were used to capture initial student conceptions and measure learning gains. Pre-instruction interviews were conducted in order to gain a deeper understanding of pre-test answers. In addition, a two-tailed matched-pair analysis of post-test answers was performed in order to determine the effectiveness of inquiry- based instruction versus lecture-based instruction.

Comparison of pre- and post-tests shows relatively large learning gains after instruction. Analysis of pre-test responses and interview transcripts reveals many misconceptions, such as a fairly widespread belief that abortions are done specifically to obtain stem cells and beliefs that the amount of genetic information of stem cells is different from differentiated cells. Other findings include how students use a variety of terms to describe differentiation and the belief that stem cells are more prevalent early in life and “used up” during development.

The results of the two-tailed, matched-pair analysis for the most part do not indicate statistically significant differences between inquiry- and lecture-based instruction. However, results for a question on controversial aspects of stem cell research imply that the lecture-based instruction was more effective than the inquiry-based instruction at helping students understand the controversy. This result suggests that, given the limited time span of the unit, inquiry-based methods by themselves may not be the most appropriate pedagogy for teaching about controversies in stem cell research. A combination of lecture and inquiry, where the instructor gives a small series of initial lectures before assigning students a genuine inquiry activity, may be a better approach.


Bucy, Thompson, Mountcastle on Partial Differentiation

B.R. Bucy, J.R. Thompson, D.B. Mountcastle
Student (Mis)application of Partial Differentiation to Material Properties
2006 Physics Education Research Conference Proceedings, edited by P. Heron, L. McCullough, and J. Marx, AIP Conference Proceedings 883, 157-160 (2007)

Sayre, Wittmann, and Donovan on resource plasticity

E.C. Sayre, M.C. Wittmann, and J.E. Donovan
Resource Plasticity: Detailing a Common Chain of Reasoning with Damped Harmonic Motion
in P. Heron, L. McCullough, J. Marx (Eds.) Physics Education Research Conference Proceedings 2006, AIP Conference Proceedings 883, 85 (2007).

Coombs MS in Physics on sound as a longitudinal wave

Investigating Student Understanding of Sound as a Longitudinal Wave
Earl C. Coombs, 2007 MS in Physics

The field of physics education research (PER) has highlighted the discrepancy between what is taught during traditional instruction in physics, and what students understand afterward. PER has also provided alternatives to traditional instruction that are research-based and have been shown to be more effective in bringing students’ level of understanding of physics more in line with that of the scientific community. One topic that has received attention is the propagation of sound. We confirmed that students in the introductory algebra-based and calculus-based physics courses at the University of Maine have difficulties with sound propagation similar to those documented by others. We found that a relatively small percentage of the students we interviewed from a calculus-based introductory physics course used the community consensus model of particles oscillating parallel to the direction of propagation. We identified three other mental models used by the interview subjects that have been described previously. The first was a model in which sound is considered to be an entity that passes through the medium without disturbing the particles of the medium. The second was a model in which sound is viewed as an entity that pushes the particles of the medium aside as it propagates. The third was a hybrid model in which the particles of the medium oscillate perpendicular to the direction of propagation. In an extension of the work by previous researchers in this area, we examined students’ ability to predict the points at which the particles of the medium have the maximum and the minimum magnitudes of velocity and displacement from their equilibrium positions. We found that students’ ability to do so was extremely limited. To improve student understanding of sound propagation, we developed an instructional tool in the form of a “tutorial” and evaluated its effectiveness through pre- and post-testing of students enrolled in an algebra-based introductory physics course. The tutorial constructed for this purpose was found to be successful in increasing the number of students that used the community consensus model when answering questions about sound propagation. It was less successful in enabling students to make accurate predictions about particle velocities and displacements.

Recommended Citation

Coombs, Earl C., "Investigating Student Understanding of Sound as a Longitudinal Wave" (2007). Electronic Theses and Dissertations. 314.



Feeley - MST on thinking about gravitational forces

Roger E. Feeley

Identifying student concepts of gravity

unpublished Master of Science in Teaching, 2007

This paper discusses a survey developed to investigate student concepts of "gravity" among AST 109 astronomy students and pre-service K-12 teachers. Survey questions were developed or modified from those in the literature [Berg 1991, Dostal 2005]. Students were questioned on their reasoning about the behavior of objects on the surface of a planetary body (e.g., the Earth or the moon) and the causes of this behavior. Results of the survey successfully elicited student alternate conceptions with various aspects of gravity. These misconceptions include the tendency to attribute gravity to the presence of an atmosphere, and the belief that a threshold amount of gravity, mass, or weight is necessary for free-fall to occur.


Sayre and Wittmann on coordinate systems

Sayre, E.C. and Wittmann, M.C. (2007)
Intermediate Mechanics Students’ Coordinate System Choice
Conference on Research in Undergraduate Mathematics Education 2007. Published online, only. Full conference proceedings available here.


Traxler, Black, and Thompson, PERC Proceedings 2007

Adrienne L. Traxler, Katrina E. Black, and John R. Thompson

Students' Use of Symmetry with Gauss's Law

To study introductory student difficulties with electrostatics, we compared student techniques when finding the electric field for spherically symmetric and non-spherically symmetric charged conductors. We used short interviews to design a free-response and multiple-choice-multiple-response survey that was administered to students in introductory calculus-based courses. We present the survey results and discuss them in light of Singh's results for Gauss's Law, Collins and Ferguson's epistemic forms and games, and Tuminaro's extension of games and frames.

AIP Conf. Proc. -- January 30, 2007 -- Volume 883, pp. 173-176