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Doing Fractions “In Chinese” ?!

Friday, March 5th, 2010

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I was so excited to discover that in Malcolm Gladwell, his recent book, Outliers, presents a bunch of new research on learning math!

There’s so much good stuff in there that I can’t even begin to tell you all about it. But one thing that struck me in particular was Gladwell’s discussion of the cultural differences between Asian and Western attitudes towards learning math. (You can read an excerpt from the chapter here.)

To start, language differences give Asians a linguistic advantage. In Asian languages, numbers are more transparent. For example, when an English speaker has to do mental math, they need to translate words into numbers first. Before we add “forty-three” to something else, we have to break it down into “four tens and a three.” By comparison, in Chinese the word for “forty-three” is already broken down: “four-tens-three.”

Similarly, we say “three-fifths” to describe a fraction in English. But the Chinese for the same number literally translates as, “out of five parts, take three”: the definition of how a fraction works is built in. These linguistic differences make calculation easier in Asian languages. And because it’s easier to figure out what things mean just from the words, there’s an attitude that it’s normal to be able to figure math out.

This creates what Gladwell calls a “virtuous circle”: because the names for numbers are a little bit easier to understand, arithmetic is a little bit easier to do, which means that maybe students like math a little bit more, which means that maybe they take more math classes and ultimately achieve more in math. In contrast, Western children, by third and fourth grade, start to feel that “math doesn’t seem to make sense; it’s linguistic structure is clumsy; and its basic rules seem arbitrary and complicated.” And the trouble begins…

When I mentioned this to my friend, the Future Doctor Jones, she said, “We’re stuck with this language! What are we supposed to do with it?” Her question is valid—if I tell my tutoring students to say “two-tens-seven” for 27, will they just get beat up on the playground for talking crazy numbers?

So recently I was working with a fifth grader on fractions, and I casually mentioned that in Chinese, they say fractions like, “out of four parts, take one,” instead of “one-fourth.”

I was totally surprised when later in the lesson, this same student spontaneously started saying fractions “the Chinese way.” “Out of seven parts, take four!” “Out of two parts, take one!” When I slipped up and said, “Out of two parts take five,” she corrected me immediately, which meant she completely understood the concept.

Most importantly, she didn’t want to stop doing fractions. She was begging for more!

I’m grateful to my student for spontaneously showing me how we, as English-speakers, can adopt a “Chinese” way of thinking about numbers.

Related Articles:
I cried myself to sleep over my math homework
The Downside of Always Telling Students to Try Harder (1)
The Downside of Always Telling Students to Try Harder (2)
Malcolm Gladwell on Math and Persistence (1)

8 Comments on “Doing Fractions “In Chinese” ?!”

  • Sue VanHattum on March 6th 12:01 pm

    Thanks for intriguing me, as usual! Unfortunately, it looks like that Gladwell link isn’t the whole chapter, just the first page of it.

  • Rebecca Zook on March 9th 11:58 pm

    Thank you for being intrigued! I appreciate you pointing out that the Gladwell link isn’t the whole chapter. I didn’t realize it was an excerpt. I’ll fix that in the post. (And I think you would really love his book Outliers if you want to read the whole thing.)

  • QueerSilver on March 9th 5:05 pm

    I learned math in both Chinese and English since I went to a Chinese school. We had a regular math class and we have a Chinese math class. Concepts are all similar but I do find that there is a disconnect and I guess it confused me a lot so I can’t say I’m in any way better at math but reading this re-sparked my interest in re-learning Chinese math for what it is. Who knows? Maybe now that I could make sense of more things, I could actually catch up with my math skills.

  • Rebecca Zook on March 9th 11:51 pm

    Thanks for your comment! That’s really interesting. I’ve worked with a couple students who learned math in a second language, but it just seemed to make them super-confused. (Which made me question my plan, if I ever have kids, to raise them multilingual.) It sounds like if you went to a Chinese school that maybe you grew up speaking both Chinese and English? Anyway, I heartily support your efforts to catch up with your math skills! 🙂

  • Hao Ye on March 23rd 1:51 am

    I think this is an excellent example of how some teachers teach math as though it is a separate language with its own rules, when many of the concepts have intuitive definitions that aren’t typically explained. In addition to your example with fractions, why the standard multiplication algorithm works and what it has to do with place value is probably another big thing that isn’t emphasized as much as it should be.

  • Rebecca Zook on March 29th 10:29 pm

    Hao Ye, thanks so much for sharing your thoughts! It’s great to “meet” you. I am really interested in finding ways to explain the intuitive concepts that aren’t typically explained. I’d love to hear more of your thoughts on the standard multiplication algorithm and place value!

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  • Melvin Goldstein on August 24th 2:29 pm

    Numbers are the Supreme Court of science. However Godel proved that we may not prove everything. Science needs numbers. There must be Science and Physics Foibles!!

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