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Unpublished MST thesis, University of Maine, August, 2008.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.