Misconceptions and mathematical misunderstanding
Teaching, Tests and Targets
What, you may ask, have tests and targets to do with mathematical misconceptions and misunderstandings? The answer is “quite a lot” as, unfortunately, it is possible for learners to pass tests with their mathematical misconceptions unchallenged.
The current culture of testing learners frequently, and assessing the effectiveness of their teachers equally often, is affecting the way teachers teach. In the Times Educational Supplement of 22 May 2009 there were at least eight references to the unwanted side effects that testing is having on learners of all ages in English, mathematics and science. For example:
“The bulk of graduates are less prepared for university than they were before mandatory testing.” Nathan Greenfield, concerning Canada.
“Year 6 pupils in particular were too often involved in practising responses to national test questions rather than engaging in exciting science work.” Ofsted Success in Science report, 2008.
“Since SATs ended my daughter says she is now doing fun maths. Shouldn’t all maths be fun when you are 11?” Comment on KS2 SATS from a parent.
It is understandable that teachers’ natural response to tests and targets is to prepare their learners to pass tests, rather than to be able to use their mathematical knowledge in daily life. For example, learners may know how to multiply two numbers together, but they have no idea when it is appropriate to do this in order to solve a mathematical problem.
It seems we have a culture which favours rote learning and success in the short term, rather than fostering deeper learning that will stay with the learner for life.
What can teachers do about this? They are unlikely to be able to change the testing culture overnight, but they can teach in a way that ensures that concepts are understood and not just memorised. The argument is often heard that there is no time to teach in this way. Please try it, because there is! In the long term, it is a better use of time to teach in this way because learners engage with topics in depth and learn for life, rather than “doing” a topic one week and forgetting it the next.
There are many resources available to support teaching in ways that promote understanding. Two of these are:
Improving Learning in Mathematics
Thinking Through Mathematics
Note: Thinking Through Mathematics is no longer available in hard copy, but an online version is expected soon. In the meantime why not try to borrow a copy from a colleague?
Improving Learning in Mathematics: challenges and strategies, Malcolm Swan.