Mathematical modelling in the primary classroom has long been an area that I have wanted to develop yet didn’t really know how. I’ve seen (and, admittedly, taught) a probably familiar looking lesson many times – ‘word problems’ tagged onto the end of teaching children some concept or other. Underline the important information; decide which operation is needed; calculate; answer the question. Sure, some children get it, but many, as we know, slip through the net.
I first came across Dan Meyer (@ddmeyer) when I watched his TED talk about a year ago. Recently, I had the chance to attend one of his workshops and even though his work is very much aimed at teaching the secondary age range, I felt that there was plenty that could be applied to improve mathematical modelling in primary schools.
The problem with word problems
Here’s a typical word problem that requires some mathematical modelling that you might find in a primary classroom:
A rectangle has a length of 15cm and a width of 8cm. What is the area of the rectangle?
There will definitely be some children that have trouble decoding and comprehending this. The literacy demand may play some role in children being unable to work trough this type of problem. All the necessary information is given from the outset which is not how the world tends to work. The purpose of the problem comes last. The child will read some words without knowing the purpose for it until the end. Children may be given a whole raft of almost identically worded problems with slightly changed numbers.
One way of addressing these problems
How to address these problems? Dan Meyer’s blog post explains in good detail, but here’s a simplified version to get started with. First, remove the literacy demand and make the context concrete. Image or video works great here. Ask “What questions pop into your head?” I’d have a question ready that I’d like children to work on, but children may think of questions that have some mileage. Make sure children know the question that they’ll be working on – the purpose comes before any of the maths or specific information. Ask “What information is needed to answer this question?” With skilful further questioning, make children work for the necessary information, revealing it when they have shown an understanding of what it may be used for or why it is important. Once they have the information they need, it’s time for the maths. Make sure that they know how to do what they need to do. Model; generate success criteria and get them to practise as necessary before returning to the problem. Children will soon have an answer – have ready a few related but different questions as opposed to repetitively worded problems.
My next few posts will be some examples of these principles that I have tried out.