Abstract
We have investigated the various approaches taken by first-year university students (n approximate to 550) when asked to determine the direction of motion, the constancy of speed, and a numerical value of the speed of an object at a point on a numerical linear distance-time graph. We investigated the prevalence of various well-known general graphing difficulties, such as graph-as-picture errors and slope-height confusion. We established that two-thirds of our students could determine the direction of motion with respect to a reference point, just under 80% could determine that the speed is constant, and just under 20% of our students could correctly determine the value of the speed; in the latter case, about half of the students divided the two coordinates. Three stable categories of correctly explaining the constancy of speed emerged from the data. We found that the reason given for determining that the speed of the object was constant did not correlate with successfully determining a value for the speed. We have established that technical difficulties such as determining the slope of any linear graph did not explain the poor performance. By comparing the answers to similar questions on water level versus time graphs, we were able to establish that context dependence and incorrect prior learning are likely to play a role. Post-test data are used to confirm the validity of the categorization and support the conclusion that being able to determine the slope of a y, x graph and having a correct qualitative understanding of a distance-time graph is not sufficient to correctly determine a value for the speed. DOI: 10.1103/PhysRevSTPER.9.010107
Highlights
In this paper we investigate the approaches taken by first-year university undergraduate students when asked questions on numerical distance-time graphs
We found that the method by which students find a numerical value for the speed at an instant is independent of the reasoning by which they determined that the speed was constant. (By contrast, less than 2% of students who said the speed was not constant determined the speed correctly.)
Having concluded that possible technical issues alone cannot explain the low fraction of students who can correctly determine a value for the speed from a linear distance-time graph, we investigated a closely analogous question on water level versus time graphs
Summary
In this paper we investigate the approaches taken by first-year university undergraduate students when asked questions on numerical distance-time graphs. We asked students to determine in what direction an object was moving and whether its speed was constant, and to find a numerical value for the speed at a particular instant. We asked the students to engage with a graphical representation of uniform motion, to differentiate between distance and speed, to use (implicitly or explicitly) the idea of a limit, and to use an algorithm for determining the slope of a graph. We have investigated whether there was a context dependence to the approaches our students took.
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