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3岁幼儿也可能学数学
Kids may be ready for math earlier than you think
http://www.washingtonpost.com/local/education/quick-whats-bigge
By Lyndsey Layton, Published: December 17
摘要：研究发现，3岁的幼儿就可以理解数字的含义。
这个报告发现了一个重要的情况：儿童认数字比用实物的教具更有效。
这个和我的教育理念基本一致——
人大脑本身在小数目是可以实例化的，而大的数目要用抽象的方式对待。
美国数学教育界过于强调用“实例”教育，损伤了孩子的数学抽象能力。
Children as young as 3 can understand the meaning and value of multi-digit
numbers and might be more ready for direct math instruction when they begin
formal schooling than previously believed, according to new research by
developmental psychologists.
“Contrary to the view that young children do not understand place value and
multi-digit numbers, we found that they actually know quite a lot about it,
” said Kelly Mix, a professor of educational psychology at Michigan State
University and a lead investigator on the study.
“They certainly haven’t mastered it, but the new insight is that they can
pick up on patterns, start to make inferences, and they’re starting
kindergarten with a lot more partial knowledge than what people have
believed,” said Mix, who worked with Richard Prather and Linda Smith, both
of Indiana University.
The research comes as teachers, policymakers and government officials have
been increasingly dismayed by U.S. students’ math performance on
internationally benchmarked exams. This month, the results of a well-
regarded international exam placed U.S. teenagers at below average in math
compared with their counterparts in 64 other countries and economies.
Educators and researchers have long assumed that children do not have the
capacity to fully understand place value and to accurately compute multi-
digit numbers until at least second grade. The ability to add and subtract
multi-digit numbers is a gateway skill, an important prerequisite for higher
-order math.
Researchers had dismissed the abilities of younger children to handle multi-
digit numbers because they make frequent errors. But Mix said those kinds of
errors are often “intelligent” mistakes that belie at least a partial
grasp of the underlying math.
What’s more, young learners can be taught to improve their calculations,
she said.
Funded with a $1.5 million grant from the U.S. Education Department and
published this week in the journal Child Development, the research examined
how well children ages 3 to 7 could identify and compare two- and three-
digit numbers.
In one experiment, children were shown two numbers, such as 36 and 306, and
were asked to name the larger number. They had a 50-50 chance of being
correct. After the first several tries in which they guessed no better than
chance, the kindergartners grew increasingly accurate. First- and second-
graders did better than 50-50 from the start.
The researchers tested about 200 children from ethnically diverse, middle-
income communities in Michigan and Indiana.
One surprising finding of the research was that when children were asked to
compute with numerals, they performed significantly better than when they
were given “manipulatives” — learning tools they could hold in their
hands, such as blocks — or were shown visual arrays of numbers, such as
dots in a box.
Classrooms across the country are stocked with “manipulatives” for
children in younger grades, and educators have thought that young children
have an easier time learning math if they can visualize or touch quantities.
But that’s not so, Mix found.
“They can learn math faster with .?.?. numerals, which is counterintuitive,
” she said. “We’ve always believed that younger children needed to learn
through concrete models. But it turns out they can do it faster with
symbolic numbers.”
Very young children learn math because they are continually exposed to multi
-digit numbers, whether from telephone numbers or price tags. Mix said they
might begin to understand numbers from language because adults are
continually talking about numbers, whether they are commenting on a calendar
, asking their children to push a number in an elevator or looking for a
room number in an office building.
While the research suggests that kindergartners are ready for multi-digit
math instruction, Mix said educators should take a balanced approach.
“A lot of educators believe strongly in the power of play in kindergarten
and even first grade,” she said. “And I believe that, too. Kids need lots
of time to discover and explore. I wouldn’t say we should teach second-
grade math in kindergarten. But there is a risk in the other extreme, too.
If you believe kindergartners are oblivious to the symbol system and we have
to gradually introduce it, you’re missing out on the fact that they’re
already picking it up.”
? The Washington Post Company
Kids may be ready for math earlier than you think
http://www.washingtonpost.com/local/education/quick-whats-bigge
By Lyndsey Layton, Published: December 17
摘要：研究发现，3岁的幼儿就可以理解数字的含义。
这个报告发现了一个重要的情况：儿童认数字比用实物的教具更有效。
这个和我的教育理念基本一致——
人大脑本身在小数目是可以实例化的，而大的数目要用抽象的方式对待。
美国数学教育界过于强调用“实例”教育，损伤了孩子的数学抽象能力。
Children as young as 3 can understand the meaning and value of multi-digit
numbers and might be more ready for direct math instruction when they begin
formal schooling than previously believed, according to new research by
developmental psychologists.
“Contrary to the view that young children do not understand place value and
multi-digit numbers, we found that they actually know quite a lot about it,
” said Kelly Mix, a professor of educational psychology at Michigan State
University and a lead investigator on the study.
“They certainly haven’t mastered it, but the new insight is that they can
pick up on patterns, start to make inferences, and they’re starting
kindergarten with a lot more partial knowledge than what people have
believed,” said Mix, who worked with Richard Prather and Linda Smith, both
of Indiana University.
The research comes as teachers, policymakers and government officials have
been increasingly dismayed by U.S. students’ math performance on
internationally benchmarked exams. This month, the results of a well-
regarded international exam placed U.S. teenagers at below average in math
compared with their counterparts in 64 other countries and economies.
Educators and researchers have long assumed that children do not have the
capacity to fully understand place value and to accurately compute multi-
digit numbers until at least second grade. The ability to add and subtract
multi-digit numbers is a gateway skill, an important prerequisite for higher
-order math.
Researchers had dismissed the abilities of younger children to handle multi-
digit numbers because they make frequent errors. But Mix said those kinds of
errors are often “intelligent” mistakes that belie at least a partial
grasp of the underlying math.
What’s more, young learners can be taught to improve their calculations,
she said.
Funded with a $1.5 million grant from the U.S. Education Department and
published this week in the journal Child Development, the research examined
how well children ages 3 to 7 could identify and compare two- and three-
digit numbers.
In one experiment, children were shown two numbers, such as 36 and 306, and
were asked to name the larger number. They had a 50-50 chance of being
correct. After the first several tries in which they guessed no better than
chance, the kindergartners grew increasingly accurate. First- and second-
graders did better than 50-50 from the start.
The researchers tested about 200 children from ethnically diverse, middle-
income communities in Michigan and Indiana.
One surprising finding of the research was that when children were asked to
compute with numerals, they performed significantly better than when they
were given “manipulatives” — learning tools they could hold in their
hands, such as blocks — or were shown visual arrays of numbers, such as
dots in a box.
Classrooms across the country are stocked with “manipulatives” for
children in younger grades, and educators have thought that young children
have an easier time learning math if they can visualize or touch quantities.
But that’s not so, Mix found.
“They can learn math faster with .?.?. numerals, which is counterintuitive,
” she said. “We’ve always believed that younger children needed to learn
through concrete models. But it turns out they can do it faster with
symbolic numbers.”
Very young children learn math because they are continually exposed to multi
-digit numbers, whether from telephone numbers or price tags. Mix said they
might begin to understand numbers from language because adults are
continually talking about numbers, whether they are commenting on a calendar
, asking their children to push a number in an elevator or looking for a
room number in an office building.
While the research suggests that kindergartners are ready for multi-digit
math instruction, Mix said educators should take a balanced approach.
“A lot of educators believe strongly in the power of play in kindergarten
and even first grade,” she said. “And I believe that, too. Kids need lots
of time to discover and explore. I wouldn’t say we should teach second-
grade math in kindergarten. But there is a risk in the other extreme, too.
If you believe kindergartners are oblivious to the symbol system and we have
to gradually introduce it, you’re missing out on the fact that they’re
already picking it up.”
? The Washington Post Company
