I’m currently advising a team of teachers who have taken great care to make sure they all use the same representations of a problem. They use the same symbols, have agreed on what kind of diagrams they use, even sketch the problems using the same blue print. They are pretty proud that they have gone to all that trouble to make sure their students don’t get confused. And they got pretty confused themselves when I suggested that they might not be doing their students a favor.

Why would I say that? Well, because evidence suggests it. For example the paper “An Overview of Recent Research on Multiple Representations” by Rosengrant et al., 2007.

The authors compare multiple representations of the same problem (for example text, sketch, motion/free-body/… diagram, graph, computer simulation, mathematical equation). And they find that the more representations students get to know when they learn new content, the easier they learn the content and the easier it is for them to interpret other representations later.

Students who, on an exam, used representations in addition to the mathematical representation that was given to think about a problem, have higher grades. But only if their representations are correct! If students construct incorrect representations (like incorrect free body diagrams), they actually have a lower chance to correctly solve the problem than if they did not draw a representation.

When posing problems, this applies as well. The same student might be able to answer a text-based question, but not an isomorphic question when it is posed as a vector diagram.

Hence, learning multiple representations might be confusing in the very short run, but in the long run students need to learn to deal with them anyway. And representations are important for student learning – if students can construct a different representation of a given problem, they are likely to be able to solve it.

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David Rosengrant, Eugenia Etkina, & Alan Van Heuvelen (2007). An Overview of Recent Research on Multiple Representations AIP Conference Proceedings Volume 883 DOI: 10.1063/1.2508714

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