I was convinced by the Singapore bar-model when I invigilated the 2016 Key Stage 2 maths reasoning exam. One of my pupils, who I’d come to realise wasn’t going to score well, was faced with this problem:
This is the sort of question many of my pupils struggled with. There is too much to hold in working memory. Yet I watched him answer it.
His strategy is called ‘bar-modelling’ – a problem solving technique developed by a team of maths educators led by Dr Kho Tek Hong in Singapore in the 1980s. The bar-model is an abstract-pictorial representation of the problem. Abstract-pictorial (representing an abstract quantity as a bar) has a lower cognitive load than purely abstract (algebra).
Bar models strip away the surface features of a problem revealing the deep structure. My pupil could see that he needed to add the two short lengths of ribbon and subtract the value from the original length – a multi-step question.
I wondered whether anyone had used bar-model to help learners solve physics problems. It occured to me that many of my key stage 3 and 4 students – those for whom algebra was not yet automatic – would be able to learn how to solve physics problems more efficiently if I could reduce the cognitive load that the algebra adds.
My hypothesis is that understanding concepts in physics is more mathematical than linguistic. The first law of thermodynamics states:
the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.
Which is really algebra in words:
ΔU = Q – W
You’ll never understand the first law of thermodynamics by words alone: you have to use the equation repeatedly to solve problems. But when manipulating the algebra take all of your working memory, learning becomes less efficient.
So I began to use bar-model in my worked examples.
I have been using bar-model surreptitiously in my year 11 lessons – I haven’t drawn specific attention to the bars – I’ve just used them in my modelling, and provided empty bars for the students to use if they chose to.
So far, I’ve noticed two things. First, the students are more willing to give problems a go – previously I have found them reluctant. The second thing I’ve noticed is that they go straight to the correct calculations. Previously, they would often get muddled about what to add, and what to subtract; the bar model seems to have facilitated their choices.
So I have two hypothesis:
- Reducing the cognitive load that algebra adds will make learning more efficient.
- By practising quantitative problems, students develop a richer understanding of physics concepts than by explanation and description alone.
Both hypotheses could be tested.
For more details of bar-modelling: https://mathsnoproblem.com/en/the-maths/teaching-methods/bar-modelling/