e-assessment (f)or learning

I have posted before about the difficulties that students have with fractions and the problems that this causes. Many others recognise the same difficulty.

On a related point, students also have problems with reciprocation, and sometimes it is simply that they don’t recall that x^-2=1/x²

So the analysis of the question shown on the right should not be too surprising. The question is very well answered, but the ‘correct’ option that students are least likely to select is the one shown highlighted (top right). This is present in about 86% of all answers, but all the other correct options are present in more than 90% of answers.

The question shown was originally planned to assess students’ ability to estimate, but since we can’t prevent them from using a calculator, I adapted it to test calculator use as well.

43% of the analysed 14943 responses were correct, and the errors made were depressingly familiar:

8.1% were numerically correct but expressed to the nearest order of magnitude not to 1 significant figure.

3.1% were numerically correct but expressed to 2 significant figures.

In 2.9% of responses, the square root on the numerator had only been applied to the first number (4 in the example shown)

2.9% had used 10 to the plus 6 instead of 10 to the minus 6 in the denominator (which may have been caused by dividing rather than multiplying by 10 to the minus 6).

So it remains the simple things that cause the problems. Sig figs, calculator use, precedence…