Language and Mathematical Proficiency

While many are aware that culture and family attitudes strongly influence student achievement, I wonder if many are aware of linguistic impacts on early mathematical proficiency?  And I do not mean how learning in a non-native language impacts learning, as that has been clearly documented and discussed in great length for the good of all second-language students.  My question is broader and applies only to native language speakers.  Specifically, the etymological basis for certain languages potentially offers a competitive advantage to speakers of those languages when it comes to mathematical proficiency.

I find this possibility fascinating.  As someone who grew up reading, chose as his CB radio handle “Bookworm,” and was often called the same by his friends, I love words and their origins.  Academic vocabulary, content vocabulary, and higher level vocabulary, and even idioms regularly flow from me during class.  Each use provides an opportunity to explain the word, or phrase, to students while connecting it among and between mathematics, other subjects, or life circumstances. [1], [2]

Now, back to the mathematical proficiency advantage of certain languages.  David A. Sousa (2008), in “How the Brain Learns Mathematics,” states that “cultural differences in computational ability may have their roots in the words that different cultures use to represent numbers.”  He goes on to explain that given the brain’s limited ability to keep information in short-term memory, native speakers of languages that use more compact words to represent numbers have up to a 50% increase in number memory span.  Sousa (2008) cites the people in Hong Kong who speak the Cantonese dialect of Chinese “have a number memory span of about ten digits, as opposed to the seven in speakers of English and other Western languages.”  He goes on to explain that brain imaging studies of native Chinese speakers “process arithmetic manipulation in areas of the brain different from those of native English speakers.”

Sousa also illustrates how English has “many inconsistencies in its number words,” which make it more complex than Chinese and Japanese whose “number syntax is easy to learn and remember” and the “syntax perfectly reflects the decimal structure,” whereas English does not.  This syntactic difference becomes most apparent around the age of four, when “Chinese children can generally count up to 40, while American children of the same age can barely get to 15, and it takes them another year to get to 40.”  As someone who knows how to count in several languages, to include Chinese and Japanese, as well as French, Spanish, and German, not to mention binary, octal, and hexadecimal back in my engineering days, I appreciate the impact language has on number sense.  The Chinese and Japanese languages follow a logical system when it comes to numbers, which uses the same linguistic algorithm for all numbers whereas English does not.  As an example, the number 15 in Chinese is shi wu, or ten ‘plus’ five, while the number 25 is er shi wu, or two times ten ‘plus’ five.  Both follow a pattern where multipliers such as 10 (shi) are preceded by a factor, such as the two (er) in 25, formerly called a multiplicand, and followed by an addend, such as the five (wu) in 25.  [3]

What all of this brings to mind for me is to what extent does this linguistic advantage accelerate the development of mathematical proficiency for students who speak these languages natively?  Does the advantage fade over time?  Do students born in the US, but whose parents speak Chinese, as an example, at home have the same advantage, assuming they initially learn Chinese?  What about those who do not initially learn Chinese, but do so shortly afterwards, or not at all?

I am fascinated by this topic and line of inquiry.  Anyone who has further information about how native language impacts the development of mathematical proficiency, please comment away!

[1]  CB radios, also known as Citizen’s Band radios, were popular in the 1970’s when I grew up.
[2] While the use of idioms is discouraged when instructing English-language learners, I find that their inclusion, when explained, expands the richness of a students’ experience with our society, language, and words.  Most of my English-only students are not familiar with my sayings, or idioms, so all require a refresher or explanation anyways.  The use of idioms when the listener does not understand its meaning, and no explanation is provided, is not an effective means of communication, hence, discouraged.
[3]  All is not overly simple when counting in Japanese.  The Japanese language makes a distinction for cardinal numbers based on the object being counted, which confused me to no end when visiting Japan.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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4 Responses to Language and Mathematical Proficiency

  1. xiousgeonz says:

    I can’t inform on the brain imagery, but I can tell you that I started noticing in my exploration of math interventions that seemed to have some success that somewhere along the line, incorporating language deeply into the mix happened. Jo BOaler has a chunk of her “What’s Math Got To Do WIth It?” book devoted to the importance of talking about math. The Algebra Project includes learning to express what math means in everyday language and then translating that to the mathematical terms. David Berg’s _Making Math Real_ gets methodical about it — the ones and tens place get their informal, invented names (such as “cheese bits” and “french fries”) and then the math labels are added… and then the connection between the concrete manipulatives, the names, and the symbols are taught and rehearsed to mastery.
    I find when working with students who are struggling that if I ask them “what did you do here?” (say, when they’re adding the same thing to both sides of an algebra problem) they’ll say “I put this here.” They often cannot even begin to tell me what math they did (at first ;)).
    Some of my students are perfectly facile with every day language — and often these folks are helped immensely by plowing that connection in. Others are not so effluvial in their verbosity… so I try to make the connection with more concrete stuff and pictures. (Some have “officially diagnosed” learning disabilities.)


    • Thanks for the suggestions. I have Jo Boaler’s book, so will re-read that portion. I agree that students must be comfortable with manipulatives, names, symbols, diagrams, and other representations to understand mathematics well.


  2. Dave ( also a career changer Math teacher ),a few years ahead of you. says:

    Also, in many oriental cultures, land was scarse, so great precison and attention to detail was necessary for optimal cultivation, including great cooperation among family members. This leads to mathematical proficiency and work ethic. I told you we are on same page, or at least same book. i guess that was an idiom.


  3. Mary Wheeler says:

    I have wondered about this with reading the clock. Do Germans have a different concept of the hour since they say “half ten” while English speakers say “half past ten” or ten thirty. Also, I do know that my Kindergartners have the most trouble with the number 12, as the word gives no clue to the number. Most languages I know are similar; however Italian is closer to two-ten and might be easier. It would be an interesting little study.


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