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Topic: math and language

Wait … that’s where algebra comes from?

Tuesday, February 15th, 2011

A statue of mathematician al-Khwarizmi

Ben Blum-Smith has a great article up about how certain key mathematicians first explored and refined the concept of negative numbers.

In his article, Blum-Smith dives into original historical source texts (in translation) to explore how the historical process of developing negative numbers parallels how each of us comes to understand negative numbers when we encounter them for the first time.

One of my favorite parts was learning that the title of one of the texts, Kitab al-Jabr wa-l-Muqabala, aka The Compendium on Calculating by Completion and Reduction by Muhammad ibn Musa al-Khwarizmi, is the origin of the word “algebra.”

Al-Jabr = algebra. AICH!!! So AWESOME!!!

And the treatise’s author, al-Kwarizmi? That’s where the term “algorithm” comes from. SO COOL!!!!!

Topic: math and language

Doing Fractions “In Chinese” ?!

Friday, March 5th, 2010


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.

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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)