# Category Archives: mathematical misunderstandings

## Significant figures and decimal places

Following the finding that students struggle with significant figures and decimal places, we added a question that tested fairly basic rule-based understanding (of stuff that I thought we were teaching quite well in the Maths for Science book). The question … Continue reading

## x to the minus 1 = 1 over x. OK?

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 … Continue reading

## Yet more problems with significant figures, using a calculator for scientific notation and precedence

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 … Continue reading

## More on significant figures

I’ve said before that students are not good at giving answers to an appropriate number of significant figures. But what do they do wrong? The question shown on the left provides some insight. The correct three options are B, C … Continue reading

## Significant figures and rounding

I’ve posted before about the difficulties students seem to have with significant figures and rounding. This post adds some data, to give you an appreciation of the size of the problem. The data are for the question shown on the left … Continue reading

## Scientific notation

The question shown on the right is quite well answered even though it is on the formative-only practice assessment. Errors when they do occur are mostly as I’d have predicted – 4.5% of responses give the wrong sign in the power … Continue reading

## Is the answer 6, 9, 300 or 11809.8?

It was the analysis of question such as the one above that led to one of my early insights into mathematical misunderstandings. I discovered then that a common answer to this question was 11809.8. This is caused by students finding 310 and then … Continue reading

## Formative or summative logarithms

I’ve posted before about the fact that whilst students usually engage quite well with formative-only iCMA questions, when the going gets tough, they are inevitably more likely to guess than is the case when the mark counts. When I eventually get … Continue reading