News in Science

Abstract maths easier, not harder

Frustrated maths students may have a good excuse. Some teaching methods meant to make maths more relevant may be making it harder to understand, US researchers say.

They say students who are taught abstract maths concepts fare better in experiments than those taught with real-world examples.

Adding extra details makes it hard for students to extract the basic mathematical concepts and apply them to new problems, they say.

"We're really making it difficult for students because we are distracting them from the underlying maths," says Jennifer Kaminski from Ohio State University, whose study appears today in the journal Science.

The findings cast doubt on the widely used practice of using friendly, concrete examples to teach abstract maths concepts.

For example, a teacher might use a bag of coloured marbles to explain probability, or teach a formula about distance with the classic example of two trains departing from different cities and travelling at different speeds.

"The danger with teaching using this example is that many students only learn how to solve the problem with the trains," Kaminski says.

Symbols or examples?

To find out the best methods of teaching basic maths concepts, the researchers conducted several experiments using college students in which some students were taught concepts using basic symbols, while others were taught with concrete examples.

For example, they studied different approaches at teaching the basic mathematical property of commutativity.

This means that you can switch up the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5.

Some students learned the concepts using generic symbols. Others were taught with concrete examples such as pictures of measuring cups filled with liquid, or slices of pizza or tennis balls in a container.

While all of students mastered these concepts easily, the students who first learned maths concepts using abstract symbols were better able to transfer that learning to other problems when tested.

End of real-world examples?

That is not to say story problems should disappear.

Kaminski says story problems offer a good way to test whether a student has mastered the abstract concept.

"Story problems aren't out, but they are probably not the way we want to go about introducing concepts or problem solving," she says.

"That would be best done through symbolic maths."