Experienced teachers will be familiar with the feeling of disappointment when, two weeks after you have taught a mathematical concept, you are met with blank gazes, furrowed brows and question marks when you return to it. We often ask ourselves why children have not managed to retain the facts they could so easily recall before.
One answer may be that we are not giving children enough models and images on which to hang their newly learned concepts. How often do we use practical resources with all key stage 2 primary children, not just those with special educational needs?
When I questioned a group of nine- to 11-year-olds about learning recently, I found a clear difference between those who had a deep understanding of the number system and those whose understanding was based on simple recall of facts.
The main difference in these children's learning journeys was that some had been exposed to a range of models and images throughout their school lives, whereas others had relied on their ability to recall and follow procedures from worksheets without truly understanding why something worked. Children in the latter category had consequently become manipulators of digits, unable to apply the concepts and procedures they had picked up to new problems. These children had learned to be calculators rather than mathematicians.
The problem arises because many teachers believe that children should be content with pencil and paper in the later stages of primary school and no longer working with practical resources. But why should we starve older students of the rich experiences we so frequently provide for younger pupils?
Such resources are undoubtedly useful for supporting lower-attaining students but we must not forget to use them with more-able children, too. There are lots of helpful resources that, if used well, will open the door to allow children to learn a new concept. Such practical experiences also mean that they are more likely to retain the knowledge.
A new model
I was recently introduced to Derek Haylock and Anne Cockburn's connective model of learning maths. This outlines how mathematical understanding depends on four different elements: symbols, language, images and concrete examples.
Try dividing your display board into the four sections and pin up some examples from each segment, including some of the practical resources you have used and pictures of the group using them. These act as a visual reminder of what the children have learned, meaning that the board becomes a prompt to enable further independent work.
I have also recently discovered the bar model, a popular visual resource used in Singapore. Essentially, this involves a simple strip of paper being used to represent the "whole", which can then be cut into sections to answer questions featuring division, ratio, proportions, fractions, whatever you like. Children divide their "whole" to find out how much each segment of the bar is worth.
This is a great example of how a resource can provide a practical experience without compromising the maths that should be taking place. It's also simple, cheap and easy to prepare - perfect for busy teachers.
Numicon (inset, below) is another great resource that can be used with all ages and abilities. It is a multi-sensory piece of equipment consisting of coloured shapes that represent numbers. I use it regularly with more-able children to teach them decimals.
Representing numbers in varied ways like this should be a key feature of a resource-rich classroom. Such approaches can even be used to liven up everyday tasks.
One example of this is how I get my students to represent each day's date and how many of them are in class with concrete resources. They use, say, Numicon to make the number, and the discussion about tens, units, place value, more and less gives them the opportunity to practise using mathematical vocabulary. It is a great way to informally assess what each child knows about the number system.
In an educational landscape of constant testing, we are all too familiar with the phrase: "If only I had more time I could." On a busy Monday morning or an exhausted Friday, it is overwhelmingly easy to pull out that worksheet you have used before, or photocopy the tried-and-tested activity that always does the job.
But weigh up your options - deep and meaningful learning takes time. Shallow learning wastes time as you will only be going over it again six weeks down the line. So get creative. Dust off your counters, dig out your arrow cards and remind yourself just how fun and practical maths can be.
Rebecca Misselbrook is assistant headteacher at White Meadows Primary Academy in Littlehampton, West Sussex
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