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发帖数: 19398 | 1 美国儿童的数学教育——How are our children doing in Math?
http://www.philly.com/philly/education/How_are_our_children_doi
摘要：
英语影响了孩子的最基本数学能力
“Our education system is not designed to create and shape a math brain.”
建议：
Teaching a math hierarchy from non-symbolic to symbolic to patterns and
relationships and ultimately to conceptual understandings.
正文：
Of 57 industrialized nations that participated in a 2011 Trends in
International Math and Science Study (TIMSS), United States fourth graders
ranked 11th place. Not bad. Even better was that 8th graders ranked 9th of
56 countries. But, by age 15, in a Program for International Student
Assessment (PISA, 2009), American students were in 31st place out of 65
participating countries.
“The longer our children are in school, the further behind they fall from
their counterparts in other nations,” announced Dr. Steven G. Feifer last
week to a group of Temple University faculty and graduate students, as well
as area school psychologists attending the university’s annual Education
and School Psychology conference.
Examining the data from the three studies, Dr. Feifer found that American
students did well early because they were taught how to get the answers.
Fourth graders were tested on knowledge of numbers, geometric shapes and
measures. Eighth graders were quizzed on numbers, algebra, data and chance,
and geometry.
Student performance went downhill when as high school sophomores they were
expected to directly apply mathematical principals. Math is “not so much
about crunching numbers as it is about applying it to the real world,” Dr.
Feifer explained.
Dr. Feifer, professor and research scientist at George Washington University
in Washington, D.C., is a neuropsychologist known for his work in the field
of learning disabilities. As keynote speaker at the conference he outlined
brain-based possibilities for why the United States lags behind, especially
to Asian countries.
National Science Board statistics report enrollment in science and
engineering programs is expanding 10 times faster in China. Nearly 2/3 of
Chinese undergraduate students earn math, science, or engineering degrees
compared to just 1/3 of U.S. and there has been a 10 percent decline in
science and engineering graduate school enrollment of American students in
the past decade while foreign graduate student enrollment is up 35 percent.
Americans fall short on how much time they actually spend in school as well
as on Math instruction. The U.S. has a 180 day school year compared to South
Korean with 220 and 243 in Japan. School days are 10-12 hours compared to
shorter days in the U.S. which also often allots only about 45 minutes a day
to math with science being rotated in using time blocks. And much of the
way Americans are taught math historically focuses on answers more than
process or translation to real world problem solving, Dr. Feifer says.
But, these aren’t the only differences.
Dr. Feifer believes brain neuropsychology is partially responsible for
holding back Americans from mathematical excellence. In the brain, a number
is “seen” as a word first and that word is long and gets longer as we add
quantity. For example, we see “twenty” instead of 20. Then “twenty five”
instead of 25. Chinese numbers are brief allowing for more efficient memory
. (i.e. 4=si, 7=qi) By age four, chinese students can count to 40, U.S.
student to 15, simply because of word length.
Also, most Asian languages have linguistic counting systems past ten (ten-
one, ten-two, etc.) whereas English deviates from the base-10 system (
Campbell & Xue, 2001) with an over-complicated number system. “We struggle
because building number connections centered around a base-10 system is
crucial in the development of mathematical efficiency when problem solving,
” Dr. Feifer says.
To take math beyond word level, another part of the brain encodes a number
as a fixed symbol representing a quantity that can be sequenced in a
particular order. This encoding starts the process needed to go beyond rote
memory to solving mathematical equations. An 11th grader taking trigonometry
relies on rote memory as well as a working knowledge of mathematical
process to get the answer right.
Getting the answer right is key but also the greatest setback for American
students who have often been taught to be right much more than being curious
about why it is right. “There is a difference between getting answers and
facilitating mathematical knowledge,” says Dr. Feifer. “Our education
system is not designed to create and shape a math brain.”
To change that, math instruction would benefit from adding multiple methods
of problem solving, including verbal and visual-spatial approaches, taught
with the processing center of the brain in mind.
“We also need to go for depth not breadth,” he adds, citing a Mathematical
Advisory Panel 2008 report that recommends streamlining curriculums to
bring topics to closure before moving on to another. He concurs with the
Panel’s suggestion on teaching a math hierarchy from non-symbolic to
symbolic to patterns and relationships and ultimately to conceptual
understandings.
This understanding takes math to a third “math coding” level in the brain,
one of “nirvana” says Dr. Feifer, when the brain can actually achieve
qualitative judgement. A simple explanation of this is that a number can now
be judged as larger or smaller, “9” is bigger than “4”, creating a math
sense and number intimacy that finally makes it all real and transferrable.
“It’s when you find you can quickly take 10 percent of an $80 restaurant
check and halve that to come up with a 15 percent tip,” he explains. It is
such a habit today to figure a tip using a calculator or tip sheet that we
are robbed of number sense, he explains, as well as the pleasure of doing it
ourselves. Asian countries don’t allow calculator use until much later and
then only to check answers, he adds.
Just as wisdom is a “cognitive sophistication over time”, says Dr. Feifer,
math should be no different. The more that is learned about neuropsychology
and learning, the more teachers can incorporate new approaches and increase
flexibility within their teaching to build up American math and science
esteem. |
