How would you say the decimal number 0.173 out loud? For me, it feels natural to say, ‘zero point one seven three’. But other ways of verbalising decimals may be more helpful for children when they are first learning. Jing Tian, Assistant Professor of Psychology at Fordham University in New York, says that understanding decimals is essential for studying advanced mathematics and science, and that mastering them is critical for academic and career success. But it’s also important in everyday life, she says, for example, when we measure materials for crafts, weigh foods for cooking, and make financial decisions.

## What are different ways to verbalise decimal numbers?

While my approach is to name each digit in turn, Tian explains that we can also verbalise decimals by labelling the place of each digit. There are two ways to do so: One is to use a decomposed label, expressing the number 0.173 as ‘one tenth, seven hundredths, and three thousandths’. Another is to use a common-unit label: ‘one hundred and seventy-three thousandths’. Both of these are place-value labels, and they have often been treated by researchers as interchangeable in the past. In Tian’s recent research, however, she has found that the language used to express decimal numbers makes a difference in how children understand those numbers.

“The language used to express decimal numbers makes a difference in how children understand those numbers.”

Three ways to label decimal numbers
How would you say 0.173 out loud?
• Point one seven three
This is a point label. Each digit is named in turn.
• One tenth, seven hundredths, and three thousandths
This is a decomposed label, a type of place-value label.
• One hundred and seventy-three thousandths
This is a common-unit label, another type of place-value label.

## What are the benefits of different labels for decimal numbers?

In a study run by Tian and her colleagues, 10- to 12-year-olds were taught to use one of the three labels to express decimals. While I start the point label by saying ‘zero’, for simplicity it was not verbalised in the study. Tian does not expect this makes a difference to children’s learning. Each child was randomly assigned to use one of the labels in a one-on-one training session lasting 10 to 15 minutes. In a test administered after the training session, children who used one of the place-value labels performed better than those who used the point label – but in different ways.

Children who were taught to use decomposed labels had a better understanding of the role of zero in decimals. “Children often mistakenly believe that adding a zero to the end of a decimal changes its value,” Tian says. For example, they often think that 0.173 is different from 0.1730. It is also common for them to believe that adding a zero to the beginning of a decimal does not change its value; they conclude, incorrectly, that 0.0173 is the same as 0.173. These misconceptions arise because this is how whole numbers work. But children who learned to use decomposed labels were less likely to have these misconceptions, probably because they had paid closer attention to the place of each digit.

Children who were taught to use common-unit labels benefited in a different way: They were better at judging the overall magnitude of decimal numbers. For example, they found it easier to compare 0.61 and 0.59, probably because they were focusing less on individual digits and more on overall magnitude, Tian explains. Comparing the tenths digits (6 and 5) and comparing the hundredths digits (1 and 9) leads to different answers. “So focusing on individual digits will hurt performance,” says Tian.

Since there was no test of long-term benefits, it is possible that these were only short-term gains. However, the authors expect that if children continued to use the place-value labels, they would develop a better conceptual understanding of decimals.

## How should teachers verbalise decimal numbers?

While both types of place-value labels helped children to gain a better understanding of decimal numbers, the point label showed no specific benefit. Tian therefore suggests using place-value labels in the classroom, choosing one type or the other depending on the context. Teachers might use decomposed labels when teaching about the role of zero, to show children that the place of each digit is important. Common-unit labels could be used when kids need to evaluate the magnitude of decimal numbers.

“Language is an important part of mathematics.”

Although using the point label – my approach – did not prove helpful in boosting children’s understanding of decimals, this type of label is often used in daily life. Becoming familiar with expressing decimal numbers in this way would help children better understand the decimals they encounter outside the classroom.

Language is an important part of mathematics. Verbalising decimals in the best way for each context could help children master decimals, and ultimately help them enjoy maths, as Tian does: “I love the simplicity and complexity of mathematics,” she says. Language matters for how children learn decimals, and thinking carefully about how it is used in the classroom could help unlock the principles of maths for children.

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