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(Math) Math Made Easy

 
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adedios
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Location: Angel C. de Dios

PostPosted: Sun Nov 27, 2005 9:19 am    Post subject: (Math) Math Made Easy Reply with quote






Math Made Easy: Study Reveals 5-year-olds' Innate Ability
By Ker Than
LiveScience Staff Writer
posted: 16 September 2005
10:05 am ET

Young children can perform certain kinds of math operations before ever
receiving any kind formal math training, a new study reports.

The finding suggests children have an inborn intuition about math that
could be used to make learning the real thing in school less painful.

Ask a 5-year old child whether the sum of 13 and 17 is greater or less
than 50 and chances are you'll just get a funny look. But the same
problem could be presented another way, as a visual problem, and this is
what the researchers did.

In one experiment, the children saw 13 blue dots on a computer screen;
those were covered, and then they saw 17 blue dots and were forced to
keep the running tally in their heads. Then they were shown 50 red dots
and asked whether there were more blue dots or red dots.

Presented this way, the children answered correctly about two-thirds of the
time that there were more red dots than blue dots.

Sight and sound

In another experiment, the children were asked to compare the number of
blue dots on the screen with audible beeps that represented red dots.

Again they were generally able to determine which was more, suggesting
they have an abstract notion of numbers that spans multiple sensory
modalities, just like adults.

"What's central about numbers for us as adults is that we can apply a
number like 7 to a diverse number of things," said Elizabeth Spelke, a
psychologist at Harvard University and the principal investigator of the
study. "We can say that there are seven dots but also that a horn honks
seven times. Although these are different in their sensory qualities, the
numbers are the same."

Past studies performed on infants and non-human primates suggests that
these abilities are present even before the age of 5.

"The experiments of the infants and the monkeys, I think, make it
extremely likely that these abilities are inborn," Spelke said.

While mathematical intuitions have been demonstrated before, the
surprising result of this study is that the children could tap into these
abilities to solve the types of arithmetic problems they might encounter in
school.

Avoiding torture

In the United States, a child's first encounter with math is often in
elementary school, and for some, perfecting the ability to add and
subtract, multiply and divide will be a long and torturous process.


"A lot of children find symbolic arithmetic quite difficult and tedious, yet the
children loved our tasks," Spelke told LiveScience. "They were games, the
children were very happy to play them, and they were also they were
good at them."

The children did math without even realizing it.

Spelke stresses that more studies will be needed, but she believes
teachers could use this knowledge to increase children's confidence in
their own math abilities and to make math more fun and engaging.

Abstract ways of teaching math could also be used to ease children into
the more difficult symbolic forms of math they will encounter and which
they will have to eventually master.

"What our study shows is that children have a fundamental understanding
of addition and of numbers and we hope to harness that ability to enhance
mathematic instruction," Spelke said.

The finding is detailed in the Sept. 12 issue of the journal for the
Proceedings of the National Academy of Sciences.

************************************************************
Additional Topics:


[See a graphic of experiments.]

http://www.livescience.com/php.....+tasks%3A+(a)+comparison+of+visual+quantities+(b)+addition+of+visual+quantities+(c)+compa%20

“Knowing” Math May Be Easier Than Learning It

http://www.jyi.org/news/nb.php?id=556

Big Answers from Little People

http://homepage.mac.com/ddobbs.....ition.html

Education Revealed: How the brain calculates

http://news.bbc.co.uk/1/hi/education/337328.stm

Math is fun

http://www.mathsisfun.com/

GAMES

http://www.mathsisfun.com/games/index.html
http://www.mathsisfun.com/games/games-2.html
http://www.mathsisfun.com/games/games-3.html


Last edited by adedios on Sat Jan 27, 2007 3:14 pm; edited 1 time in total
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adedios
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PostPosted: Wed Mar 22, 2006 9:01 pm    Post subject: Scientists Discover The Part Of The Brain that Does Math Reply with quote

Source: California Institute Of Technology

15 March 2006

Scientists Discover The Part Of The Brain That Causes Some People To Be Lousy In Math

Most everyone knows that the term "dyslexia" refers to people who can't keep words and letters straight. A rarer term is "dyscalculia," which describes someone who is virtually unable to deal with numbers, much less do complicated math.

Scientists now have discovered the area of the brain linked to dyscalculia, demonstrating that there is a specific part of the brain essential for counting properly. In a report published in the March 13 issue of the Proceedings of the National Academy of Sciences (PNAS), researchers explain that the area of the brain known as the intraparietal sulcus (IPS), located toward the top and back of the brain and across both lobes, is crucial for the proper processing of numerical information.

According to Fulvia Castelli, a postdoctoral researcher at the California Institute of Technology and lead author of the paper, the IPS has been known for years as the brain area that allows humans to conceive of numbers. But she and her coauthors from University College London demonstrate that the IPS specifically determines how many things are perceived, as opposed to how much.

To explain how intimately the two different modes of thinking are connected, Castelli says to think about what happens when a person is approaching the checkout lines at the local Trader Joe's. Most of us are impatient sorts, so we typically head for the shortest line.

"Imagine how you really pick the shortest checkout line," says Castelli. "You could count the number of shoppers in each line, in which case you'd be thinking discretely in terms of numerosity.

"But if you're a hurried shopper, you probably take a quick glance at each line and pick the one that seems the shortest. In this case you're thinking in terms of continuous quantity."

The two modes of thinking are so similar, in fact, that scientists have had trouble isolating specific networks within the IPS because it is very difficult to distinguish between responses of how many and how much. To get at the difference between the two forms of quantity processing, Castelli and her colleagues devised a test in which subjects performed quick estimations of quantity while under functional MRI scans.

Specifically, the researchers showed subjects a series of blue and green flashes of light or a chessboard with blue and green rectangles. The subjects were asked to judge whether they saw more green or more blue, and their brain activity was monitored while they did so.

The results show that while subjects are exposed to the separate colors, the brain automatically counts how many objects are present. However, when subjects are presented with either a continuous blue and green light or a blurred chessboard on which the single squares are no longer visible, the brain does not count the objects, but instead estimates how much blue and green is visible.

"We think this identifies the brain activity specific to estimating the number of things," Castelli says. "This is probably also a brain network that underlies arithmetic, and when it's abnormal, may be responsible for dyscalculia."

In other words, dyscalculia arises because a person cannot develop adequate representations of how many things there are.

"Of course, dyscalculics can learn to count," Castelli explains. "But where most people can immediately tell that nine is bigger than seven, anyone with dcyscalculia may have to count the objects to be sure.

"Similarly, dyscalculics are much slower than people in general when they have to say how many objects there are in a set," she adds. "This affects everyday life, from the time when a child is struggling to keep up with arithmetic lessons in school to the time when an adult is trying to deal with money."

The good news is that the work of Castelli and her colleagues could lead to better tools for assessing whether a learning technique for people with dyscalculia is actually working. "Now that we have identified the brain system that carries out this function, we are in a position to see how dyscalculic brain activities differ from a normal brain," Castelli says.

"We should be in a position to measure whether an intervention is changing the brain function so that it becomes more like the normal pattern."

The article is titled "Discrete and analogue quantity processing in the parietal lobe: A functional MRI study." Castelli's coauthors are Daniel E. Glaser and Brian Butterworth, both researchers at the Institute of Cognitive Neuroscience at University College London.
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adedios
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Joined: 06 Jul 2005
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PostPosted: Thu Aug 10, 2006 8:57 am    Post subject: Baby Brains are Wired For Math Reply with quote

Baby Brains are Wired For Math

By Sara Goudarzi
LiveScience Staff Writer
posted: 08 August 2006
04:04 pm ET



Next time someone complains about arithmetic being hard, math lovers can defend themselves by saying "even a six-month-old can do it."

Through monitoring the brains of infants, researchers confirmed that infants as early as six months in age can detect mathematical errors, putting to rest a debate that has been ongoing for over a decade.

A team of scientists from the United States and Israel exposed 24 infants to a videotaped puppet show. They used the puppets for addition and subtraction while observing the reaction of the babies.

For example, they started the show with two dolls. Before the show ended, a doll was removed and then the infant's vision was blocked with a screen. When the screen was taken away, either one doll was left, as expected, or two dolls, which would not be mathematically correct.


For the full article:

http://www.livescience.com/hum.....fants.html
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adedios
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PostPosted: Wed Jul 25, 2007 10:11 am    Post subject: Hand gestures dramatically improve learning Reply with quote

University of Rochester
25 July 2007

Hand gestures dramatically improve learning

Kids asked to physically gesture at math problems are nearly three times more likely than non-gesturers to remember what they’ve learned. In today’s issue of the journal Cognition, a University of Rochester scientist suggests it’s possible to help children learn difficult concepts by providing gestures as an additional and potent avenue for taking in information.

“We’ve known for a while that we use gestures to add information to a conversation even when we’re not entirely clear how that information relates to what we’re saying,” says Susan Wagner Cook, lead author and postdoctoral fellow at the University. “We asked if the reverse could be true; if actively employing gestures when learning helps retain new information.”

It turned out to have a more dramatic effect than Cook expected. In her study, 90 percent of students who had learned algebraic concepts using gestures remembered them three weeks later. Only 33 percent of speech-only students who had learned the concept during instruction later retained the lesson. And perhaps most astonishing of all, 90 percent of students who had learned by gesture alone—no speech at all—recalled what they’d been taught.

Cook used a variation on a classic gesturing experiment. When third graders approach a two-sided algebra equation, such as “9+3+6=__+6” on a blackboard, they will likely try to solve it in the simple way they have always approached math problems. They tend to think in terms of “the equal sign means put the answer here,” rather than thinking that the equal sign divides the problem into two halves. As a result, children often completely ignore the final “+6.”

However, even when children discard that final integer, they will often point to it momentarily as they explain how they attacked the problem. Those children who gestured to the number, even though they may seem to ignore it, are demonstrating that they have a piece of information they can’t reconcile. Previous work has shown that the children with that extra bit of disconnected knowledge are the ones ready to learn, which suggests that perhaps giving children extra information in their gesture could lead to their learning.

Cook divided 84 third and fourth graders into three groups. One group expressed the concept verbally without being allowed to use gestures. The second group was allowed to use only gestures and no speech, and the third group employed both. Teachers gave all the children the same instruction, which used both speech and gesture.

After three weeks, the children were given regular in-school math tests. Of those children who had learned to solve the problem correctly, only a third of the speech-only students remembered the principles involved, but that figure rose dramatically for the speech-and-gesture, and the gesture-only group, to 90-percent retention.

“My intuition is that gestures enhance learning because they capitalize on our experience acting in the world,” says Cook. “We have a lot of experience learning through interacting with our environment as we grow, and my guess is that gesturing taps into that need to experience.”

Cook plans to look into how gesturing could be implemented effectively in classrooms to make a noticeable improvement in children’s learning.

“Gesturing does have one clear benefit,” Cook adds. “It’s free.”
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