You may think the sign of a good teacher lies in their ability to provide engaging real life examples for abstract concepts. But a new study by Jennifer Kaminski and colleagues at Ohio State University, suggests that when it comes to maths, it’s probably best to keep things abstract.
Students were taught the rules governing mathematical relations between three items in a group. All students were able to learn these, but crucially only those taught using abstract symbols were able to transfer what they’d learned to a novel, real-life situation. Students taught with the metaphorical aid of water jugs, slices of pizza or tennis balls in a container, were unable to transfer what they’d learned.
Another experiment compared the effectiveness of a purely abstract teaching approach with an approach that provided concrete examples first, followed by an abstract illustration. Students in the purely abstract condition outperformed their peers who were given the concrete/abstract mix.
Kaminski’s team said that although concrete examples might be more engaging, it seems they may also constrain students’ ability to transfer relevant knowledge to a different situation.
The researchers concluded: “If a goal of teaching mathematics is to produce knowledge that students can apply to multiple situations, then presenting mathematical concepts through generic instantiations, such as traditional symbolic notation, may be more effective than a series of ‘good examples’.”
Kaminski, J.A., Sloutsky, V.M., Heckler, A.F. (2008). LEARNING THEORY: The Advantage of Abstract Examples in Learning Math. Science, 320(5875), 454-455. DOI: 10.1126/science.1154659