Hawkins et al. on vector addition

Jeffrey M. Hawkins, John R. Thompson, Michael C. Wittmann, Eleanor C. Sayre, and Brian W. Frank

Students' Responses To Different Representations Of A Vector Addition Question

AIP Conf. Proc. -- October 24, 2010 -- Volume 1289, pp. 165-168
2010 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3515188

We investigate if the visual representation of vectors can affect which methods students use to add them. We gave students one of four questions with different graphical representations, asking students to add the same two vectors. For students in an algebra-based class the arrangement of the vectors had a statistically significant effect on the vector addition method chosen while the addition or removal of a grid did not. ©2010 American Institute of Physics

Springuel Ph.D.: Cluster analysis in kinematics and the FMCE

Applying Cluster Analysis to Physics Education Research Data
R. Padraic Springuel, 2010

One major thrust of Physics Education Research (PER) is the identification of student ideas about specific physics concepts, both correct ideas and those that differ from the expert consensus. Typically the research process of eliciting the spectrum of student ideas involves the administration of specially designed questions to students. One major analysis task in PER is the sorting of these student responses into thematically coherent groups. This process is one which has previously been done by eye in PER. This thesis explores the possibility of using cluster analysis to perform the task in a more rigorous and less time-intensive fashion while making fewer assumptions about what the students are doing. Since this technique has not previously been used in PER, a summary of the various kinds of cluster analysis is included as well as a discussion of which might be appropriate for the task of sorting student responses into groups. Two example data sets (one based on the Force and Motion Conceptual Evaluation (FMCE) the other looking at acceleration in two-dimensions (A2D) are examined in depth to demonstrate how cluster analysis can be applied to PER data and the various considerations which must be taken into account when doing so. In both cases, the techniques described in this thesis found 5 groups which contained about 90% of the students in the data set. The results of this application are compared to previous research on the topics covered by the two examples to demonstrate that cluster analysis can effectively uncover the same patterns in student responses that have already been identified.

Recommended Citation
Springuel, R. Padraic, "Applying Cluster Analysis to Physics Education Research Data" (2010). Electronic Theses and Dissertations. 1086.
http://digitalcommons.library.umaine.edu/etd/1086

Black Ph.D.: Air resistance problems, resources, and epistemic games

Katrina E. Black

Multiple Perspectives on Student Solution Methods for Air Resistance Problems

Physics education researchers use many frameworks to observe and analyze student understanding in physics - each is useful for understanding and explaining particular student behaviors. In this dissertation, I focus on two: difficulties and knowledge in pieces. In the difficulties paradigm, researchers focus on identifying specific topics or questions that pose challenges to students without making claims regarding underlying cognition. In the pieces paradigm, the focus is on describing the structure of student ideas, which are often found to be developed on-the-fly, easy to change, and can be described as made up of chunks of knowledge that are not inherently correct or incorrect. I use both video and written data collection methods and the difficulties and pieces theoretical frameworks to examine aspects of students' solutions to first-order separable differential equations in an air-resistance context. I uncover several difficulties students have when applying boundary conditions, and develop a new graphic, the consistency plot, that allows researchers to track individual student responses over time. Additionally, using air resistance as a context, I expand upon resources, a model of student thinking that falls into the pieces paradigm. I both expand the resources model directly and make connections between it and other modes of analysis present but less common in physics education research: epistemic games, gesture analysis, conceptual blending, and Process/Object theory. Introducing procedural resources as a type of resource allows the resources model to better describe students' problem-solving activities. I give several examples of procedural resources used in the incorporation of boundary conditions, and I show how procedural resources can be organized into facets of epistemic games. I also examine the creation of procedural resources. Drawing from the traditions of gesture analysis, conceptual blending, and Process/Object theory, I consider the internal structure of two procedural resources, Group and Move, and give a plausible path for the creation of the resource Separate Variables.

Black, Katrina E., "Multiple Perspectives on Student Solution Methods for Air Resistance Problems" (2010). Electronic Theses and Dissertations. Paper 1091.

http://digitalcommons.library.umaine.edu/etd/1091

Frank on the stability of students' thinking

Brian W. Frank

Multiple Conceptual Coherences in the Speed Tutorial: Micro-processes of Local Stability
Proceedings of the 9th International Conference of the Learning Sciences (ICLS 2010) - Volume 1, Full Papers, pp.873-881
Published on line at arXiv:1008.3258v1

Researchers working within knowledge-in-pieces traditions have often employed observational approaches to investigate micro-processes of learning. There is growing evidence from this line of work that students' intuitive thinking about physical phenomena is characterized more so by its diversity and flexibility than its uniformity and robustness. This characterization implies that much of the dynamics of students' thinking over short timescales involve processes that stabilize local patterns of thinking, later destabilize them, and allow other patterns to form. This kind of "change" may only involve dynamics by which the system of intuitive knowledge settles into various states without changing the system structure itself. I describe a case study in which a group of college students shift their thinking about motion several times during a collaborative learning activity. Instead of focusing on micro-processes of change, I describe these dynamics in terms of mechanisms that contribute to local stability of students' conceptual coherences.

Wittmann on conceptual blending in wave propagation

Michael C. Wittmann
Using conceptual blending to describe emergent meaning in wave propagation
Proceedings of the 2010 International Conference on the Learning Sciences

Students in interviews on a wave physics topic give answers through embodied actions which connect their understanding of the physics to other common experiences. When answering a question about wavepulses propagating along a long taut spring, students' gestures help them recruit information about balls thrown the air. I analyze gestural, perceptual, and verbal information gathered using videotaped interviews and classroom interactions. I use conceptual blending to describe how different elements combine to create new, emergent meaning for the students and compare this to a knowledge-in-pieces approach.

Hayes and Wittmann on the use of signs

K. Hayes and M. C. Wittmann
The Role of Sign in Students' Modeling of Scalar Equations
The Physics Teacher 48, 246 (2010)

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way are a major source of difficulty for us as instructors. In this paper, we consider just one such difficulty, getting the plus and minus signs correct when setting a net force equal to mass times acceleration. Even in such simple equations, we find that students make common errors in how they connect the mathematics and the physics. Specifically, we have seen college physics students use physical and mathematical reasoning inconsistently when determining signs of terms in equations. The problem seems to lie in how a vector equation gets interpreted into a scalar equation (whose form depends on one's choice of coordinate system).

Springuel Thompson Wittmann correcting a past paper

R. Padraic Springuel, Michael C. Wittmann, and John R. Thompson
Erratum: Applying clustering to statistical analysis of student reasoning about two-dimensional kinematics [Phys Rev. ST Phys. Educ. Res. 3, 020107 (2007)]

In our paper reported previously in this journal, we explored how cluster analysis, a method from data mining used to find natural groupings in data, could be used to categorize the responses given by students on a free-response question about acceleration in two dimensions. In the process of preparing to expand on that work, however, we discovered that our analysis was both incorrect and incomplete. We were incorrect in that we used default settings in our software package and thereby misidentified the distance measure used. We have since determined that this distance was not appropriate for our data coding. Furthermore, we were incomplete in that we were not sufficiently rigorous in our definition of groups of student responses. We have corrected both of these issues.

This is an erratum related to (and nearly longer than!) the paper found here.

Black and Wittmann on Resource Creation in Mechanics

Katrina E. Black and Michael C. Wittmann
Procedural Resource Creation in Intermediate Mechanics
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 97-101
2009 PHYSICS EDUCATION RESEARCH CONFERENCE

A problem in resource theory is describing the creation of new, high-level resources. We model resource creation by analyzing four student groups separating variables in a group quiz setting. The task was to solve an air resistance problem with uncommon initial conditions. We assess the fluency of each group and two observables: use of overt (such as divide, subtract, equals) and covert (such as moving, bringing, or pulling over) mathematical and use of accompanying gestures (such as circling, grabbing, or sliding). For each group, the type of language and gesture used corresponds to how easily they carry out separation of variables. We create resource graphs for each group to organize our observations and use these graphs to model the creation of the procedural resource Separate Variables.

Wittmann, Anderson, and Smith on teaching Newton's Second Law

Michael C. Wittmann, Mindi Kvaal Anderson, and Trevor I. Smith
Comparing Three Methods for Teaching Newton's Second Law
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 301-304
2009 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3266742

As a follow-up to a study comparing learning of Newton's Third Law when using three different forms of tutorial instruction, we have compared student learning of Newton's Second Law (NSL) when students use the Tutorials in Introductory Physics, Activity-Based Tutorials, or Open Source Tutorials. We split an algebra-based, life sciences physics course in 3 groups and measured students' pre- and post-instruction scores on the Force and Motion Conceptual Evaluation (FMCE). We look at only the NSL-related clusters of questions on the FMCE to compare students' performance and normalized gains. Students entering the course are not significantly different, and students using the Tutorials in Introductory Physics show the largest normalized gains in answering question on the FMCE correctly. These gains are significant in only one cluster of questions, the Force Sled cluster.

Hawkins, Thompson, and Wittmann on persistence of methods used to add vectors

Jeffrey M. Hawkins, John R. Thompson, and Michael C. Wittmann
Students Consistency of Graphical Vector Addition Method on 2-D Vector Addition Tasks
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 161-164
2009 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3266704

In a series of ten two-dimensional graphical vector addition questions with varying visual representations, most students stuck to a single solution method, be it correct or incorrect. Changes to the visual representation include placing vectors on a grid, making the vectors arrangements symmetric, varying the separation between vectors, and reversing the direction of either vector. We discuss the questions asked of students and their responses, emphasizing the results of one student who did change solution methods during an interview. ©2009 American Institute of Physics

Smith, Christensen, Thompson on entropy, engines, and cycles

Trevor I. Smith Warren M. Christensen and John R. Thompson
Addressing Student Difficulties with Concepts Related to Entropy, Heat Engines and the Carnot Cycle
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 277-280
2009 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3266735

We report the rationale behind and preliminary results from a guided-inquiry conceptual worksheet (a.k.a. tutorial) dealing with Carnot's efficiency and the Carnot cycle. The tutorial was administered in an upper-level thermodynamics course at the University of Maine. The tutorial was implemented as the third in a three-tutorial sequence designed to improve students' understanding of entropy and its applications. Initial pre- and post-tutorial assessment data suggest that student understanding of heat engines and the Carnot cycle improved as a result of tutorial instruction

Hayes MST: Language, discourse, and problem solving

Kate McCann Hayes
A qualititative analysis of student behavior and language during group problem solving
Unpublished MST thesis, University of Maine, August, 2009.

In guided-inquiry group problem solving, students experience shifts in understanding: potential "a-ha" moments where ideas fall into place and things suddenly make sense. To characterize students’ behavior, activities and language as they interact, we use video and transcript of students working in an Intermediate Mechanics class. Key elements of discourse, such as the words “just” or “anyway,” or false starts, indicate speakers' expectations about an activity so we identify these elements and track the frequency with which they appear in student discourse, both in total quantity and relative frequency. We use changes in both language and behavior to identify areas of struggle in problem solving followed by a shift in student understanding and expectations. Our methodology can capture very different resolutions in problem solving; in the three areas selected, we find that students come to a genuine resolution following struggle or knowingly accept an insufficient answer.

Recommended Citation

Hayes, Kate, "A Qualitative Analysis of Student Behavior and Language During Group Problem Solving" (2009). Electronic Theses and Dissertations. 1225.

http://digitalcommons.library.umaine.edu/etd/1225

Anderson MST: Three ways of teaching Newton's Second Law

Mindi Kvaal Anderson
Comparing the Effectiveness of Three Unique Research Based Tutorials for Introducing Newton’s Second Law
Unpublished MST thesis, University of Maine, August, 2009

Recent research has shown that guided inquiry tutorials can be effective supplements to traditional methods of teaching. This study examines the learning outcomes of three different tutorials about Newton’s Second Law (NSL): the University of Maryland’s Activity Based Tutorial, the University of Maryland’s Open Source Tutorial and the University of Washington’s Tutorial in Introductory Physics. Specifically, to what extent does a single hour of tutorial impact student learning of NSL? The force and motion conceptual evaluation (FMCE), a multiple-choice assessment instrument, is used to evaluate gains in conceptual understanding in the areas of one dimensional motion and kinematics in introductory physics courses. FMCE pretest and post-test data were collected for each of the three guided inquiry tutorial groups. The data was analyzed by separating the exam into clusters using a template created by Michael Wittmann and later updated by Trevor Smith. Gains for each tutorial group on the NSL portions of the FMCE were compared for students in a first semester algebra-based physics course. Although significant gains were not recorded in overall scores for any particular tutorial group over the others, analysis of the FMCE showed definite improvement areas by tutorial groups for certain curricula.

Recommended Citation

Anderson, Mindi Kvaal, "Comparing the Effectiveness of Three Unique Research Based Tutorials for Introducing Newton's Second Law" (2009). Electronic Theses and Dissertations. 1223.

http://digitalcommons.library.umaine.edu/etd/1223

O’Brien and Thompson on assessing Physics First in Maine

Effectiveness of Ninth-Grade Physics in Maine: Conceptual Understanding

Phys. Teach. 47 (4), 234-239 (2009)

The Physics First movement—teaching a true physics course to ninth-grade students—is gaining popularity in high schools. There are several different rhetorical arguments for and against this movement, and it is quite controversial in physics education. However, there is no actual evidence to assess the success, or failure, of this substantial shift in the science teaching sequence. We have undertaken a comparison study of physics classes taught in ninth- and 12th-grade classes in Maine. Comparisons of student understanding and gains with respect to mechanics concepts were made with excerpts from well-known multiple-choice surveys and individual student interviews. Results indicate that both populations begin physics courses with similar content knowledge and specific difficulties, but when learning concepts, ninth-graders are more sensitive to the instructional method used.

Originally posted at arxiv.org, where a pre-print remains available.

Sayre Wittmann on resource plasticity and coordinate systems

Eleanor C. Sayre, Michael C. Wittmann

Plasticity of intermediate mechanics students’ coordinate system choice
Phys. Rev. ST Phys. Educ. Res. 4, 020105 (2008)

We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.