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（原文标题－－The Best Language for Math ）
Sept. 9, 2014
【注：刚才遇到一位平时熟悉的美国教育学系的教授．
她说看了这篇文章，以为是我写的．
因为平时我发表的中文对数学教育影响的观点，
以及围棋数学这个游戏对儿童数学能力的影响，
基本上已经覆盖了这篇文章中几位教授的工作．
我说暂时还和文章里面的教授们没有交集，
不过早晚有一天他们会知道围棋数学．】
What's the best language for learning math? Hint: You're not reading it.
Chinese, Japanese, Korean and Turkish use simpler number words and express m
ath concepts more clearly than English, making it easier for small children
to learn counting and arithmetic, research shows.
The language gap is drawing growing attention amid a push by psychologists a
nd educators to build numeracy in small children—the mathematical equivalen
t of literacy. Confusing English word names have been linked in several rece
nt studies to weaker counting and arithmetic skills in children. However, re
searchers are finding some easy ways for parents to level the playing field
through games and early practice.
Differences between Chinese and English, in particular, have been studied in
U.S. and Chinese schools for decades by Karen Fuson, a professor emerita in
the school of education and social policy at Northwestern University, and Y
eping Li, an expert on Chinese math education and a professor of teaching, l
earning and culture at Texas A&M University. Chinese has just nine number na
mes, while English has more than two dozen unique number words.
The trouble starts at "11." English has a unique word for the number, while
Chinese (as well as Japanese and Korean, among other languages) have words t
hat can be translated as "ten-one"—spoken with the "ten" first. That makes
it easier to understand the place value—the value of the position of each d
igit in a number—as well as making it clear that the number system is based
on units of 10.
English number names over 10 don't as clearly label place value, and number
words for the teens, such as 17, reverse the order of the ones and "teens,"
making it easy for children to confuse, say, 17 with 71, the research shows.
When doing multi-digit addition and subtraction, children working with Engl
ish number names have a harder time understanding that two-digit numbers are
made up of tens and ones, making it more difficult to avoid errors.
These may seem like small issues, but the additional mental steps needed to
solve problems cause more errors and drain working memory capacity, says Dr.
Fuson, author of a school math curriculum, Math Expressions, that provides
added support for English-speaking students in learning place value.
It feels more natural for Chinese speakers than for English speakers to use
the "make-a-ten" addition and subtraction strategy taught to first-graders i
n many East Asian countries. When adding two numbers, students break down th
e numbers into parts, or addends, and regroup them into tens and ones. For i
nstance, 9 plus 5 becomes 9 plus 1 plus 4. The make-a-ten method is a powerf
ul tool for mastering more advanced multi-digit addition and subtraction pro
blems , Dr. Fuson says.
Many U.S. teachers have increased instruction in the make-a-ten method, and
the Common Core standards adopted by many states call for first-graders to u
se it to add and subtract. First-graders' understanding of place value predi
cts their ability to do two-digit addition in third grade, according to a 20
11 study of 94 elementary-school children in Research in Developmental Disab
ilities.
The U.S.-Asian math-achievement gap—a sensitive and much-studied topic—has
more complicated roots than language. Chinese teachers typically spend more
time explaining math concepts and getting students involved in working on d
ifficult problems. In the home, Chinese parents tend to spend more time teac
hing arithmetic facts and games and using numbers in daily life, says a 2010
study in the Review of Educational Research by researchers at the Hong Kong
Institute of Education and the University of Hong Kong.
When Chinese preschoolers enter kindergarten, they're ahead of their U.S. co
unterparts in the adding and counting skills typically taught by Chinese par
ents. They're also one to two years ahead on a skill their parents don't tea
ch—placing numbers on a number line based on size, according to a 2008 stud
y of 29 Chinese and 24 U.S. preschoolers by researchers at Carnegie Mellon U
niversity.
In math, one concept builds on another. By the time U.S. students reach high
school, they rank 30th among students from 65 nations and education systems
on international achievement exams, while Chinese and Korean students lead
the world.
The negative impact of English is apparent in a 2014 study comparing 59 Engl
ish-speaking Canadian children from Ottawa, Canada, with 88 Turkish children
from Istanbul, ranging in age from 3 to 41/2 years. The Turkish children ha
d received less instruction in numbers and counting than the Canadians. Yet
the Turkish children improved their counting skills more after practicing in
the lab with a numbered board game, according to the study, co-written by J
o-Anne LeFevre, director of the Institute of Cognitive Science at Carleton U
niversity, Ottawa, Ontario. Turkish students learning to count in their nati
ve language "mastered it more quickly" than the children learning in English
, Dr. LeFevre says.
Dr. LeFevre is among a growing group of researchers exploring how parents ca
n help instill number skills early. Children whose parents taught them to re
cognize and name digits and practice simple addition problems tended to do w
ell on such kindergarten tasks as counting and comparing numbers, says a 201
4 study of 183 children and their parents in the Journal of Experimental Chi
ld Psychology, co-written by Dr. LeFevre.
Board games can offset some of the disadvantages of speaking English, though
only if played in a specific way. Some kindergartners who played a board ga
me with the numbers 1 through 100 lined up in straight rows of 10 improved t
heir performance at identifying numbers and placing numbers on a number line
, according to a 2014 study led by Elida Laski, an assistant professor of ap
plied and developmental psychology at Boston College. The rows of 10 helped
children see that the number system is based on tens.
But the children improved only if researchers had them count aloud starting
with the number of the square where they had landed; if children landed on s
quare 5 and spun a 2, for example, they would count, "6, 7." This skill, cal
led "counting on," is useful in early arithmetic. Kids who counted starting
with "1" for every turn improved their performance only half as much.
Games such as "Chutes and Ladders" can have the same effect if children coun
t on with each turn, Dr. Laski says. Studies show games without numbers in t
he squares, or set up in a winding or circular pattern, such as Candy Land,
don't provide the same benefits.
Just drawing a board game on paper or cardboard and playing it with a presch
ooler a few times can firm up counting skills. "It's definitely more fun tha
n doing a work sheet, and just as valuable," Dr. Laski says.
Children whose parents exposed them to number games and showed they enjoyed
playing with numbers tended to have better skills, according to the 2014 stu
dy co-written by Dr. LeFevre.
Math teacher Andrew Stadel wants to pass on his interest in math to his 4-ye
ar-old son Patrick. A videogame, "Hungry Guppy" by Motion Math, based in San
Francisco, drew Patrick's attention at age 2; players drag together bubbles
with dots to add them, then feed them to a fish. He is now playing its succ
essor for older kids, "Hungry Fish." Patrick is "curious about what numbers
will pair up to make the desired sum," and if he makes a mistake, "there's n
ot a huge penalty and it's not deflating to him," Mr. Stadel says.
Such videogames build fluency in doing calculations, freeing mental energy f
or learning. A game called "Addimal Adventures" by Teachley teaches differen
t strategies for addition, showing "there's more than one way to solve a pro
blem," says Allisyn Levy, vice president of an educational digital-game line
, GameUp, offered by BrainPOP, New York City, a creator of animated educatio
nal content.
Ten-year-old Luke Sullivan of Marietta, Ga., says a game called "Addition Bl
ocks" by Fluency Games of Smyrna, Ga., helped him learn when he started play
ing it two years ago. "You realize it's educational, but then you start to e
njoy it," Luke says.
Sept. 9, 2014
【注：刚才遇到一位平时熟悉的美国教育学系的教授．
她说看了这篇文章，以为是我写的．
因为平时我发表的中文对数学教育影响的观点，
以及围棋数学这个游戏对儿童数学能力的影响，
基本上已经覆盖了这篇文章中几位教授的工作．
我说暂时还和文章里面的教授们没有交集，
不过早晚有一天他们会知道围棋数学．】
What's the best language for learning math? Hint: You're not reading it.
Chinese, Japanese, Korean and Turkish use simpler number words and express m
ath concepts more clearly than English, making it easier for small children
to learn counting and arithmetic, research shows.
The language gap is drawing growing attention amid a push by psychologists a
nd educators to build numeracy in small children—the mathematical equivalen
t of literacy. Confusing English word names have been linked in several rece
nt studies to weaker counting and arithmetic skills in children. However, re
searchers are finding some easy ways for parents to level the playing field
through games and early practice.
Differences between Chinese and English, in particular, have been studied in
U.S. and Chinese schools for decades by Karen Fuson, a professor emerita in
the school of education and social policy at Northwestern University, and Y
eping Li, an expert on Chinese math education and a professor of teaching, l
earning and culture at Texas A&M University. Chinese has just nine number na
mes, while English has more than two dozen unique number words.
The trouble starts at "11." English has a unique word for the number, while
Chinese (as well as Japanese and Korean, among other languages) have words t
hat can be translated as "ten-one"—spoken with the "ten" first. That makes
it easier to understand the place value—the value of the position of each d
igit in a number—as well as making it clear that the number system is based
on units of 10.
English number names over 10 don't as clearly label place value, and number
words for the teens, such as 17, reverse the order of the ones and "teens,"
making it easy for children to confuse, say, 17 with 71, the research shows.
When doing multi-digit addition and subtraction, children working with Engl
ish number names have a harder time understanding that two-digit numbers are
made up of tens and ones, making it more difficult to avoid errors.
These may seem like small issues, but the additional mental steps needed to
solve problems cause more errors and drain working memory capacity, says Dr.
Fuson, author of a school math curriculum, Math Expressions, that provides
added support for English-speaking students in learning place value.
It feels more natural for Chinese speakers than for English speakers to use
the "make-a-ten" addition and subtraction strategy taught to first-graders i
n many East Asian countries. When adding two numbers, students break down th
e numbers into parts, or addends, and regroup them into tens and ones. For i
nstance, 9 plus 5 becomes 9 plus 1 plus 4. The make-a-ten method is a powerf
ul tool for mastering more advanced multi-digit addition and subtraction pro
blems , Dr. Fuson says.
Many U.S. teachers have increased instruction in the make-a-ten method, and
the Common Core standards adopted by many states call for first-graders to u
se it to add and subtract. First-graders' understanding of place value predi
cts their ability to do two-digit addition in third grade, according to a 20
11 study of 94 elementary-school children in Research in Developmental Disab
ilities.
The U.S.-Asian math-achievement gap—a sensitive and much-studied topic—has
more complicated roots than language. Chinese teachers typically spend more
time explaining math concepts and getting students involved in working on d
ifficult problems. In the home, Chinese parents tend to spend more time teac
hing arithmetic facts and games and using numbers in daily life, says a 2010
study in the Review of Educational Research by researchers at the Hong Kong
Institute of Education and the University of Hong Kong.
When Chinese preschoolers enter kindergarten, they're ahead of their U.S. co
unterparts in the adding and counting skills typically taught by Chinese par
ents. They're also one to two years ahead on a skill their parents don't tea
ch—placing numbers on a number line based on size, according to a 2008 stud
y of 29 Chinese and 24 U.S. preschoolers by researchers at Carnegie Mellon U
niversity.
In math, one concept builds on another. By the time U.S. students reach high
school, they rank 30th among students from 65 nations and education systems
on international achievement exams, while Chinese and Korean students lead
the world.
The negative impact of English is apparent in a 2014 study comparing 59 Engl
ish-speaking Canadian children from Ottawa, Canada, with 88 Turkish children
from Istanbul, ranging in age from 3 to 41/2 years. The Turkish children ha
d received less instruction in numbers and counting than the Canadians. Yet
the Turkish children improved their counting skills more after practicing in
the lab with a numbered board game, according to the study, co-written by J
o-Anne LeFevre, director of the Institute of Cognitive Science at Carleton U
niversity, Ottawa, Ontario. Turkish students learning to count in their nati
ve language "mastered it more quickly" than the children learning in English
, Dr. LeFevre says.
Dr. LeFevre is among a growing group of researchers exploring how parents ca
n help instill number skills early. Children whose parents taught them to re
cognize and name digits and practice simple addition problems tended to do w
ell on such kindergarten tasks as counting and comparing numbers, says a 201
4 study of 183 children and their parents in the Journal of Experimental Chi
ld Psychology, co-written by Dr. LeFevre.
Board games can offset some of the disadvantages of speaking English, though
only if played in a specific way. Some kindergartners who played a board ga
me with the numbers 1 through 100 lined up in straight rows of 10 improved t
heir performance at identifying numbers and placing numbers on a number line
, according to a 2014 study led by Elida Laski, an assistant professor of ap
plied and developmental psychology at Boston College. The rows of 10 helped
children see that the number system is based on tens.
But the children improved only if researchers had them count aloud starting
with the number of the square where they had landed; if children landed on s
quare 5 and spun a 2, for example, they would count, "6, 7." This skill, cal
led "counting on," is useful in early arithmetic. Kids who counted starting
with "1" for every turn improved their performance only half as much.
Games such as "Chutes and Ladders" can have the same effect if children coun
t on with each turn, Dr. Laski says. Studies show games without numbers in t
he squares, or set up in a winding or circular pattern, such as Candy Land,
don't provide the same benefits.
Just drawing a board game on paper or cardboard and playing it with a presch
ooler a few times can firm up counting skills. "It's definitely more fun tha
n doing a work sheet, and just as valuable," Dr. Laski says.
Children whose parents exposed them to number games and showed they enjoyed
playing with numbers tended to have better skills, according to the 2014 stu
dy co-written by Dr. LeFevre.
Math teacher Andrew Stadel wants to pass on his interest in math to his 4-ye
ar-old son Patrick. A videogame, "Hungry Guppy" by Motion Math, based in San
Francisco, drew Patrick's attention at age 2; players drag together bubbles
with dots to add them, then feed them to a fish. He is now playing its succ
essor for older kids, "Hungry Fish." Patrick is "curious about what numbers
will pair up to make the desired sum," and if he makes a mistake, "there's n
ot a huge penalty and it's not deflating to him," Mr. Stadel says.
Such videogames build fluency in doing calculations, freeing mental energy f
or learning. A game called "Addimal Adventures" by Teachley teaches differen
t strategies for addition, showing "there's more than one way to solve a pro
blem," says Allisyn Levy, vice president of an educational digital-game line
, GameUp, offered by BrainPOP, New York City, a creator of animated educatio
nal content.
Ten-year-old Luke Sullivan of Marietta, Ga., says a game called "Addition Bl
ocks" by Fluency Games of Smyrna, Ga., helped him learn when he started play
ing it two years ago. "You realize it's educational, but then you start to e
njoy it," Luke says.
