Master these multiple representations to help students access abstract concepts, activate prior knowledge and build confidence

Children passing through four entrance barriers

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Why use just one representation when four offer learners more entry points to understanding?

It’s always satisfying when everyone in the class understands what I have taught them and I can see they have made progress in the lesson. I’m sure that this is the case for every teacher. However, as science teachers, we have the added difficulty of teaching abstract concepts that learners can find hard to understand and relate to. So, it is highly rewarding when they finally demonstrate that they get it.

It allows me to use targeted questions to bring pupils on board

I also want to ensure that what I teach caters for everyone in the classroom as part of an inclusive curriculum. One way to achieve this is through the multiple representation approach; something experienced physics teacher and associate teaching professor at the University of Cambridge, James de Winter, illustrated when I attended an Ogden Trust conference. Multiple representations offer more than one way to demonstrate the concept at hand, giving pupils several entry points into the topic and a variety of ways to understand the abstract.

What are the representations?

I developed a four-pronged approach with Jim Henderson, my mentor in a programme for early career teachers. The representations are:

Verbal – the written version of the concept. Ideal for revealing the context of the problem.

Mathematical – equations, formulas and numbers to represent quantitative information.

Graphical – a line graph, bar chart or pie chart of the same concept to help predict relationships between variables and demonstrate the nature of those relationships.

Diagrammatic – a sketch or diagram of the concept to represent qualitative information.

Multiple entry points

I developed a four-pronged approach with Jim Henderson, my mentor in a programme for early career teachers. The representations are:

Verbal – the written version of the concept. Ideal for revealing the context of the problem.

Mathematical – equations, formulas and numbers to represent quantitative information.

Graphical – a line graph, bar chart or pie chart of the same concept to help predict relationships between variables and demonstrate the nature of those relationships.

Diagrammatic – a sketch or diagram of the concept to represent qualitative information.

For example, using the abstract concept of dynamic equilibrium, I begin with a verbal description of what it is. This is especially useful in classes requiring more support as it allows me to use targeted questions to bring pupils on board, so they contribute to the discussion. I then move into the mathematics and use whole integers so pupils can manipulate them more easily. I allow time for them to navigate the other representations, going around the class to facilitate the discussion and provide prompts. At other times, I do one representation and get pupils to do the rest by filling in a blank table or explaining a concept to one another.

You can also provide the four representations as a grid and, beneath that, add prompts to guide learners’ thinking. For example, in the mathematical approach, what symbol do you need to show dynamic equilibrium? What does that mean in terms of the rate of the forward and backward reaction? How can you represent that graphically? The various representations allow pupils to develop competency in different parts of the brain and activate prior knowledge.

Feedback and impact

I have used the approach with classes of varying attainment ranging in age from 11 to 16 and it has had a positive impact on students. The multiple representations enable learners to engage with the material more deeply as it gives them multiple ways to access and grasp abstract concepts.

The four representations enhance one another, which further develops learners’ understanding. The verbal complements the diagrammatic and the mathematical complements the graphical.

The scope of the multiple representation approach is vast. However, you should think hard about the representations you choose. Could they confuse learners and make them inaccurately infer things? It is important that each of the four representations convey the same concept, but just approach it in a different way.

Find more on making abstract concepts accessible

Mustafa Mahmoud