The screenshots below show two variants of the same question. I should start by emphasising that the question is only used formatively – it’s on the Maths for Science Practice Assignment.
The two variants behave very differently and the reason for this has very little to do with student’s understanding. (more…)
The common student error in the question below is somewhat predictable – but I’m not sure why the students make the error that they do.
Whilst 60.4% of responses are entirely correct, 21.7% select the three options that are actually the places where the function rather than its derivative is zero. In the existing version of the Maths for Science End of Module Assignment, this question is assessing the contents of a chapter that some students choose not to study – so it is more than usually likely that a certain percentage of students are guessing, further encouraged by the fact that this is a multiple choice question.
So I’m not sure we can draw many conclusions from the errors that students make on this occasion. But if students really think that dy/dx is zero at the points where the graph crosses the horizontal axis, then they are mistaking the function and its gradient. This is a pretty basic mistake – perhaps a bit like mistaking x to the power of 3 with x times 3. That might be rather interesting.
Working yesterday on the chapter on Graphs and Gradient for the new edition of Maths for Science, I remembered the other student error that I have seen in iCMA questions. When asked to find the gradient of a graph like the one shown below, some students essentially ‘count squares’.
In this case, they would give the rise (actually (170-10) km = 160 km) as 16, since that is how many squares there are vertically between the red lines. By counting squares horizontally, they would give the corresponding run as 28 (which is correct apart from the fact that the units – seconds in this case – have been omitted). So the gradient would be given as 0.57 instead of 5.7 km/s.
A related problem is students measuring the rise and run using a ruler, again rather than reading values from the axes. Perhaps we encourage both these behaviours by making an analogy between the gradient of a line and the gradient of a road. When finding the gradient of a road, we are concerned with actual lengths, not the representations of other things on a graph.
Consider the simple question shown below:
This question is generally well answered, but when students make a mistake, what do they do wrong? (more…)