There’s really no such number as “point three seven five.” Yet that’s how a lot of students say .375, and a big reason for this is that a lot of teachers say it that way too—me included until I realized this perpetuated students’ difficulties with decimals.

So from that point on, I stopped saying “point” and instead referred to decimal numbers correctly—“three-hundred seventy-five thousandths,” for example—and insisted students do so too. And not only did their grasp of decimal place value improve as a result, but so did their computational skills. Even better, they became much more proficient at something that trips kids up as much as anything: converting between decimals, fractions, and percents!

Look for more on decimal-fraction-percent conversions in a future post. For now, though, make it a point to stop saying point when referring to decimals (including mixed numbers—i.e., go with “and” rather than “point;” example: read 15.03 as “fifteen and three hundredths”).

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3 Responses to An Important Point About Teaching Decimals

Good point here, Dave. I think we have to watch a lot of our math vocabulary so our students can perform better. For example, in algebra I often notice students will say “subtract both sides from five” when trying to solve an equation such as 2x + 5 = 15. They mean subtract five from both sides and that is what they do operationally but they said it wrong. I will stop and ask them to look at it and even talk it out if needed so they will say “subtract five from both sides”. Little details but I do believe they make a difference.

This seems like a good way to introduce students to the concept of the part to the right of the “.” as being a fraction. At some point (forgive the pun!), they do have to learn the ‘mathematical’ way of saying them though. Otherwise, recurring decimals and irrational numbers such as pi may cause problems! This type of approach may also cause confusion if you are working in the metric system, i.e. outside the US! How would you say 12.4cm, for example?

Oh, and Jim, as I am sure you know, in your example 5-(2x+5)=5-15, so the students’ statement is valid as a step towards solution, even if it’s not an accurate statement of the operation they are actually performing. Unless they are conceptualizing -2x = -10 (which seems very unlikely)! If I had students who said this, I’d actually take them through what they’d said and show them that it was valid, but not what they meant. Mathematics, more than one way to skin a cat, as the saying goes… 😉

Good point here, Dave. I think we have to watch a lot of our math vocabulary so our students can perform better. For example, in algebra I often notice students will say “subtract both sides from five” when trying to solve an equation such as 2x + 5 = 15. They mean subtract five from both sides and that is what they do operationally but they said it wrong. I will stop and ask them to look at it and even talk it out if needed so they will say “subtract five from both sides”. Little details but I do believe they make a difference.

This seems like a good way to introduce students to the concept of the part to the right of the “.” as being a fraction. At some point (forgive the pun!), they do have to learn the ‘mathematical’ way of saying them though. Otherwise, recurring decimals and irrational numbers such as pi may cause problems! This type of approach may also cause confusion if you are working in the metric system, i.e. outside the US! How would you say 12.4cm, for example?

Oh, and Jim, as I am sure you know, in your example 5-(2x+5)=5-15, so the students’ statement is valid as a step towards solution, even if it’s not an accurate statement of the operation they are actually performing. Unless they are conceptualizing -2x = -10 (which seems very unlikely)! If I had students who said this, I’d actually take them through what they’d said and show them that it was valid, but not what they meant. Mathematics, more than one way to skin a cat, as the saying goes… 😉

Good point (forgive me too) about irrational numbers. And I hadn’t thought about the metric system. So how would you say 12.4 cm– convert to mm?