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

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

Nagpure MST: Vectors and 2-d acceleration

Bhupendra Nagpure
The effects of reasoning about vector components on student understanding of two-dimensional acceleration
Unpublished MST thesis, University of Maine, August, 2008.

Concepts of motion form the very basis of Newtonian physics and are very important for a sound understanding of more complex physics. In an attempt to explore how students think about kinematical concepts, we have investigated student understanding of acceleration in two-dimensional motion. Our research builds on prior work identifying student difficulties with two-dimensional motion. We focus our investigation on comparing the effectiveness of different instructional strategies at improving student understanding of 2-D acceleration, and the effect of these strategies on student reasoning in particular.

Tutorials in Introductory Physics (TIP), a set of small-group, guided-inquiry curricular materials, have demonstrated improved student conceptual understanding of many physics concepts, including kinematical concepts such as acceleration. One of the tutorials in TIP, Motion in two dimensions, deals explicitly with the concepts of velocity and acceleration during motion on a curved trajectory. In this tutorial, students are guided to think about the "operational definition" of acceleration, which requires subtraction of velocity vectors, a documented difficulty for introductory students. A modified version of TIP materials was developed, which emphasizes the use of "entailed knowledge" of vector components (in the direction of motion and perpendicular to the direction of motion) and the effect on the velocity of each of these acceleration components.

Through free-response surveys and interviews, we categorized the primary reasoning paths that students use to think about two-dimensional acceleration before and after going through the two different tutorials. In addition to recognizing specific, well- documented student difficulties, we compared overall student performance as well as the types of reasoning that are used for both correct and incorrect responses on the tasks administered.

Student performance increases significantly after instruction with either tutorial; furthermore, the modified tutorial produces higher post-test performance than the original tutorial. The prevalence of student reasoning using components is higher on post-tests than on pretests, after instruction with either tutorial. Moreover, the prevalence of component reasoning is higher after the modified instruction than after the original tutorial. Thus, students using component reasoning tend to be correct as well as consistent, implying that their conceptual understanding of acceleration is not only correct but also concrete.

Van Deventer MST: Isomorphic math and physics vector representations

Joel Van Deventer
Comparing student performance on isomorphic math and physics vector representations
Unpublished MST thesis, University of Maine, August, 2008.

We designed isomorphic mathematics and physics free-response vector quizzes to evaluate student understanding of vectors in both contexts. Questions are identical, with only the context of the question changing in each case. To validate our test, we carried out task-based interviews with introductory physics students completing a semester’s instruction. We used our results from the interviews to develop a multiple-choice version of the vector quizzes which was then administered to introductory physics students before and after instruction. Overall, student performance on these isomorphic vector tasks is similar before instruction, different after an initial lecture on vectors in a math context, and different after a semester of instruction in our introductory mechanics course. In general student performance on the math vector tasks, after an initial lecture on vectors in an abstract context, seems to be indicative of performance on the physics vector tasks after a semester of instruction. No general trends were found relating to either the context dependence of the student performance or the responses distributions between individual math and physics isomorphic tasks. We find many students inconsistently apply vector manipulation tools and incompletely apply procedures across different vector tasks and contexts.

Recommended Citation

Deventer, Joel Van, "Comparing Student Performance on Isomorphic Math and Physics Vector Representations" (2008). Electronic Theses and Dissertations. 1348.

http://digitalcommons.library.umaine.edu/etd/1348