Abstract
We developed an instrument to systematically investigate student conceptual understanding of the relationships between the directions of net force, velocity, and acceleration in one dimension and report on data collected on the final version of the instrument from over 650 students. Unlike previous work, we simultaneously studied all six possible conditional relations between force, velocity, and acceleration in order to obtain a coherent picture of student understanding of the relations between all three concepts. We present a variety of evidence demonstrating the validity and reliability of the instrument. An analysis of student responses from three different course levels revealed three main findings. First, a significant fraction of students chose ``partially correct'' responses, and from pre- to post-test, many students moved from ``misconception'' to partially correct responses, or from partially correct to fully correct responses. Second, there were asymmetries in responding to conditional relations. For example, students answered questions of the form ``Given the velocity, what can be inferred about the net force?'' differently than converse questions ``Given the net force, what can be inferred about the velocity?'' Third, there was evidence of hierarchies in student responses, suggesting, for example, that understanding the relation between velocity and acceleration is necessary for understanding the relation between velocity and force, but the converse is not true. Finally, we briefly discuss how these findings might be applied to instruction.
Highlights
One of the earliest and most studied areas in physics education research is student understanding of force, velocity, and acceleration
Empirically speaking, to what extent does the correct understanding of the relationship between, say, force and acceleration depend on the correct understanding of another relation, say, between force and velocity? Does the path to correct understanding of these relations empirically occur in steps? If so, what are the steps?
Using acceleration and velocity to illustrate the seven possible combinations of these relationships yields: a~ "" v~ (v~ must be parallel to a~); a~ "# v~ (v~ must be antiparallel to a~); a~ " 0v~ (v~ is zero to a nonzero a~); a~ð""; " 0Þv~ (v~ can be zero or parallel to a~); a~ð""; "#Þv~ (v~ can be parallel or antiparallel to a~); a~ð"#; " 0Þv~ (v~ can be antiparallel to a~ or zero); a~ð""; "#; " 0Þv~ (v~ can be parallel or antiparallel to a~ or zero). Of these seven possible combinations, we found that students rarely if ever considered the physically unnatural possibility of ‘‘can only be opposite or zero’’; usually only six response choices were provided
Summary
One of the earliest and most studied areas in physics education research is student understanding of force, velocity, and acceleration. To more precisely focus the investigation, we will only study student understanding of the relations between the directions of force, velocity, and acceleration in one dimension, and leave the investigation of multiple dimensions and the relations between the magnitudes of these variables for other studies While this investigation included a significant amount of student interviews and open-ended written answers, the bulk of the analysis is based on a multiple-choice test that we developed for this study. The topic of learning progressions has recently generated significant interest in the science education community (e.g., see [13]) and is somewhat relevant to the study in this paper since we examine longitudinal and cross-sectional data on student performance and we are interested in the steps and hierarchies in understanding the relation between the directions of force, velocity, and acceleration. We summarize and discuss how the findings might be applied to the design of instruction aimed at improving student understanding of the relations between the directions of force, velocity, and acceleration
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