Illogical numbers hurt students

Danish number names to blame for kids’ bad maths results, say researchers

The Danish number names are too confusing for kids learning maths, says a neuro mathematics researcher, proposing that Danes adopt the numeral system used by their Scandinavian neighbours in Sweden and Norway.

In Danish, counting above 50 is centred around a base 20 number system, called ‘vigesimal’, whereas most languages use the much simpler decimal numeral system, which is based on 10.

The Danish number 50, for example, is halvtreds (short for halvtredje sinds tyve) – or to say it numerically, 2.5 x 20. 

This and further complications with Danish numerals has inspired researcher Lisser Rye Ejersbo and her colleagues at the University of Aarhus to propose that Danes adopt a simpler way of talking about numbers. She suggests a decimal-based system such as the Swedish one, where 50 is femti (five ten).

“The Danish numbers are a hurdle for children trying to learn mathematics,” she told science weekly Ingeniøren. “If you don’t fully understand how the numbers are positioned in relation to the words, you’ll have trouble understanding numbers in general. The names of Danish numbers say nothing about the numbers themselves.”

That, according to Ejersbo, is one explanation for Danish kids’ bad maths results, highlighted in the recently published Programme for International Student Assessment (PISA).

“What sets the Danish usage apart is that we say the numbers in reverse order, and that’s not logical for the kids.” The Danish 71, for instance, is called enoghalvfjerds (1 and 3½ x 20).

In France they also use old vigesimal names, but theirs is in the right order – as with the French number 91 (quatre-vingt-onze), which is 4 x 20 + 11.

She pointed out that some Danish teachers have started telling the smallest school kids the number names in Swedish to make it easier for them to understand numbers.

The Danish Language Council has backed the proposal, but the council doubts if such a change would work in practice.

“It would be great if we could change the Danish number names,” said Margrethe Heidemann Andersen, a researcher at the language council. “But it wouldn’t work because once we have learned the number names, we have internalised them to such a degree that replacing them would probably cause even more confusion.”