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Parenting版 - Stanford neuroscience -- Using symmetry to learn about numb
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话题: symmetry话题: students话题: stanford话题: brain话题: negative
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a*****g
发帖数: 19398
1
Stanford neuroscience research identifies more effective way to teach
abstract math concepts to children
A new study shows that students who use symmetry to learn about numbers tap
into critical brain circuits. The approach appears promising in improving
math skills in general.
By Edmund L. Andrews
(Courtesy AAALab@Stanford)
Building on new discoveries about how the brain grapples with abstract
mathematics, researchers at Stanford Graduate School of Education (https://
ed.stanford.edu/) have developed a classroom strategy for teaching children
the often baffling concepts surrounding negative numbers.
The new strategy recruits the brain's use of visual symmetry to make sense
of the physical world, and it could have profound implications for the way
elementary schools teach math.
Using symmetry appears to have helped not just in teaching children about
negative numbers but in improving their ability to solve higher-level math
problems they haven't seen before.
"Learning about negative numbers is one of the first times that kids learn
about abstract numbers - it's a gateway to more abstract learning,'' said
Jessica Tsang, a Stanford researcher and lead author of a new study with
Daniel Schwartz and Kristen Blair of Stanford and Laura Bofferding of Purdue
University.
The study marks the latest and most concrete result of a five-year project
that bridges the gap between new insights from neuroscience and the testing
of new classroom teaching tools for fourth-graders in the San Francisco Bay
Area. It is published in the current issue of the journal Cognition &
Instruction. [SEE http://www.tandfonline.com/doi/abs/10.1080/07370008.2015.1038539?journalCode=hcgi20#.VaF1ECgQiS0 ]
Researchers have long thought that the brain harnesses and adapts "perceptuo
-motor" capacities to make sense of abstract ideas.
For the purposes of making sense of math, the most widely studied of these
capacities has been the ability to compare physical magnitudes such as size.
Over the past 15 years, neuroscientists have confirmed that the same region
of the brain that assesses physical magnitudes is also key to comparing the
magnitudes represented symbolically by numerals.
Three years ago, the Stanford researchers proposed that the brain actually
re-purposes several additional capabilities, such as sequencing and ordering
, to solve math problems. In this project, the researchers focused on the
brain's ability to process visual symmetry.
In 2012 the researchers found that most adults identified the midpoint
between a negative number and a positive number more easily if the integers
were more symmetric about zero.
For example, people were faster computing the mid-point of 6 and -4 than 8
and -2, even though both pairs of digits were displayed in the same
locations on a video screen. Moreover, using functional magnetic resonance
imaging, the authors found that visual symmetry-coding regions of the brain
became more active for the more symmetric pairs.
Given that the adult brain recruits symmetry circuits for conceptual math
problems, the researchers hypothesized that helping young students engage
this native ability would improve their mathematics learning.
For the new study, the authors created a guide and tools that incorporate
ideas about using symmetry to teach negative numbers. As intuitive as it
might seem for people to rely on symmetry as a way to make sense of the
world, few curricular materials now used for teaching math make explicit use
of it.
The researchers then tested the tools with students and compared the results
to those of other students who were taught with the existing approaches.
One of the new classroom teaching tools was a specially designed hands-on
manipulative device. Students worked with a magnetic plastic strip that was
numbered. To solve the problem 3 + -2, students attached three magnetized
blocks to the right of zero and two blocks to the left of zero. The
manipulative further included a hinge at zero, the point of integer symmetry
. Students folded the two sides together, and the number of extra blocks on
either side gave the answer, in this case +1. The hinge at zero helped
students recruit their native abilities with symmetry, and the numbers on
the little platform helped them coordinate the sense of symmetry with the
symbolic digits.
After four hours of instruction spread over three weeks, the researchers
documented encouraging results.
First, the children quickly applied the hands-on lessons with symmetry to
build new strategies for solving abstract problems involving symbolic digits
. When the symmetry students were asked to add up a string of negative and
positive numbers, for example, many used a balancing strategy to simplify
the problem.
Some paired up negative and positive numbers that would add up to zero and
cancel each other out. Others clustered the positive and negative integers
on separate sides, which made the balance between the positives and
negatives more apparent.
Second, students were likely to incorporate symmetry as an almost automatic
part of their thinking. That's important, said Tsang, because many skills -
such as decoding words in reading - are more effective when they become
instantaneous and reflexive.
But the biggest surprise was on what educational researchers call "
generativity" - the tendency of students to apply the ideas of symmetry on
their own to problems they haven't encountered before.
As it turned out, students who learned to rely on symmetry didn't simply do
better than other students on the material they had just been taught. They
also did better on topics that they hadn't yet studied, such as making sense
of negative fractions and solving pre-algebraic problems.
"The big difference was that the symmetry instruction enabled students to
solve novel problems and to continue learning without explicit instruction,"
said Schwartz, who holds the Nomellini & Olivier Professorship in
Educational Technology at Stanford. "By untangling how the brain comes to
know mathematics, we helped with a major goal of education - putting
children on an upward trajectory of future learning."
---------------------------
SIDEBAR PHOTO: As part of a four-hour curriculum on integers, fourth-grade
students played games using a special number line that could be folded in
half at the zero point, allowing the symmetry between positive and negative
quantities to stand out.
--------------------------
This research was funded by the National Science Foundation and the Marcus
and Marianne Wallenberg Foundation.
--------------------------
a*****g
发帖数: 19398
2
所谓 symmetry 其实还是 spatial thinking
看看明年我和西北大学这边研究的结果会不会更有趣。

tap
children

【在 a*****g 的大作中提到】
: Stanford neuroscience research identifies more effective way to teach
: abstract math concepts to children
: A new study shows that students who use symmetry to learn about numbers tap
: into critical brain circuits. The approach appears promising in improving
: math skills in general.
: By Edmund L. Andrews
: (Courtesy AAALab@Stanford)
: Building on new discoveries about how the brain grapples with abstract
: mathematics, researchers at Stanford Graduate School of Education (https://
: ed.stanford.edu/) have developed a classroom strategy for teaching children

f**********n
发帖数: 29853
3
继续支持安安猪,有没有考虑哪天为本版小孩上一堂课?

【在 a*****g 的大作中提到】
: 所谓 symmetry 其实还是 spatial thinking
: 看看明年我和西北大学这边研究的结果会不会更有趣。
:
: tap
: children

i**e
发帖数: 19242
4
天生的
marginal improvement
可以慢慢地把脑子研究清楚,找到why
但是找到how,让每个娃娃生的都具备藤苗的特质,可能性接近零

【在 a*****g 的大作中提到】
: 所谓 symmetry 其实还是 spatial thinking
: 看看明年我和西北大学这边研究的结果会不会更有趣。
:
: tap
: children

x**8
发帖数: 4844
5
安安猪好像不好听.改叫安娜皮革吧? 哈哈.

【在 f**********n 的大作中提到】
: 继续支持安安猪,有没有考虑哪天为本版小孩上一堂课?
a*****g
发帖数: 19398
6
文章摘要——
How can children's natural perceptuo-motor skills be harnessed for teaching
and learning mathematical structure? We address this question in the case of
the integers. Existing research suggests that adult mental representations
of integers recruit perceptuo-motor functionalities involving symmetry.
Building on these findings, we designed a hands-on curriculum that
emphasizes symmetry to teach integer concepts to fourth graders. Compared to
two control conditions, children who went through the experimental
curriculum showed evidence of incorporating symmetry into their mental
representations of integers and performed higher on problems beyond the
scope of instruction, including negative fractions and algebra-readiness
problems. Gains did not come at the expense of basic integer computation
skill. This study has direct practical implications, as current integers
curricula generally omit symmetry. The research demonstrates an approach to
designing instruction that involves identifying perceptuo-motor
functionalities underlying numerical cognition and creating learning
activities to recruit them. (PsycINFO Database Record (c) 2015 APA, all
rights reserved) (journal abstract)

tap
children

【在 a*****g 的大作中提到】
: Stanford neuroscience research identifies more effective way to teach
: abstract math concepts to children
: A new study shows that students who use symmetry to learn about numbers tap
: into critical brain circuits. The approach appears promising in improving
: math skills in general.
: By Edmund L. Andrews
: (Courtesy AAALab@Stanford)
: Building on new discoveries about how the brain grapples with abstract
: mathematics, researchers at Stanford Graduate School of Education (https://
: ed.stanford.edu/) have developed a classroom strategy for teaching children

a*****g
发帖数: 19398
7
我想的是把围棋数学发展到全美国全世界呢。
一个足够好的东西才能支撑这样大的局面。

【在 f**********n 的大作中提到】
: 继续支持安安猪,有没有考虑哪天为本版小孩上一堂课?
a*****g
发帖数: 19398
8
娃的素质,其实是和同时代的人比,更是和它自己的以往相比。
每个人都提高素质,就不仅仅是上好大学,还有好的人生

【在 i**e 的大作中提到】
: 天生的
: marginal improvement
: 可以慢慢地把脑子研究清楚,找到why
: 但是找到how,让每个娃娃生的都具备藤苗的特质,可能性接近零

f**********n
发帖数: 29853
9
当然,理解,并支持你。
我的想法是,现在互联网技术很发达,也许你给大家的小孩免费远程上一课,影响就更
加大了。小孩如果有兴趣,可以让他的老师和你联系啥的。
当然,这个得看你能不能挤出时间来。

【在 a*****g 的大作中提到】
: 我想的是把围棋数学发展到全美国全世界呢。
: 一个足够好的东西才能支撑这样大的局面。

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话题: symmetry话题: students话题: stanford话题: brain话题: negative