Remembering Faces

Remembering faces requires several different brain regions on both side of the brain, and all children need to mature in their recognition of faces. The anatomical complexity of facial recognition and memory means that there are many different ways these cognitive tasks can be affected. This means it is developmentally normal for young children to not be as quick as adult distinguishing faces, and problems remembering or recognizing faces can occur from very different causes.

The right prefrontal area here is important for remembering faces (nonverbal), but the left prefrontal area is seems to be necessary for integrating and making meaning of both the emotional and visual aspects of faces.



Memory for Faces
Post: Developmental Changes in Face Perception

Collecting with Kids

Think about the post on beauty yesterday, collections are a wonderful way for some children to linger and enjoy the beauty of many different types of things. Even young children love studying objects closer with magnifying glasses and microscopes (the inexpensive Intel microscope is great for this). Collections can be unorganized or organized, and natural or man-made. Antiques Roadshow can also be a surprising hit with your children, and introduce them different periods in history, inventions, and art. Check out Smithsonian's nice site for Kids & Collecting.



Smithsonian IdeaLabs: Amazing Collections

Kids, Cynicism, and All-or None

Check out this link to a press release about cynicism in children. Children as young as 7 can be cynical and attribute motives to selfishness or lying. But there is another unspoken take-home point from this. At this age, children are also more likely to judge others in all-or-none terms... (for instances, as a liar or bad). Or in other words, children are less likely to see people as complex, ambiguous, or realistic mixtures of good and bad. Care needs to be taken to help children to gradually acquire this deeper and integrative view of others as well as themselves.

Kids and Cynicism

The Neurobiology and Motivating Power of Beauty

"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful." - Henri Poincare

Beauty is a powerful motivating and organizing factor for many creators and innovators, and when we look to see what is distinctive about the brain's experience of beautiful things, we see that beauty activates a part of the brain associated with reward.



So if we are parents or teachers or curriculum designers trying to help young people really find or develop their talents or prepare themselves for their future life's work, we we really should be doing is help them find things that they find beautiful. And when they find it, we can help by giving them space and time and help (if necessary) to think and study more deeply.

Beauty is Its Own Reward pdf>

The Movie Star Mathematician

You don't see someone like this every day - hollywood actress Danica McKellar solves math problems for fun and co-authored the Chayes-McKellar-Winn theorem.

(HT: PGlist)
NYT:Beautiful Boolean?
danicamckellar.com
Percolation and Gibbs State Multiplicity...pdf

'What' and 'Where' in the Auditory System

Here's a link to a recently published article about 'what' and 'where' auditory pathways. It seems that pathways that carry messages about what sounds are are at least partially separable from pathways carrying information about where sounds are coming from.

Children or adults with auditory processing disorders are often seen as being 'strong visual learners', or worse, thought to be slow (miss auditory information a lot), 'ADD'-ish (auditory attention is worse than visual attention), or on the autism spectrum (difficulty understanding the musical, emotional content, or other associations of speech). Because verbal teaching is the dominant style in school, students with undiagnosed auditory processing disorders are particularly at-risk.

Sometimes auditory processing disorders run in families, but auditory pathways are also quite vulnerable to injury with prematurity or even mild birth injury.

Central auditory processing disorders are difficult to diagnose in very young children, but it's important for peripheral hearing to be tested in even very young children. Children with even mild hearing loss are at significant risk for failing at least one grade in school.
Auditory What-Where

Hearing What We Expect to Hear

The helpful tidbit in this paper is that our brains are wired to hear what we expect to hear - in categories. When training the ear (for instance for phonological challenges in reading disabilities or learning a foreign language), it is more important to train "between-category differences than within-category differences"- or training particularly difficult or ambiguous sounds at the boundaries between different categories, will be most helpful for helping the ear to hear. Sound Categories Research Paper pdf

Article Link - International Paper on IQ, Creativity, Curriculum

IQ, Creativity, Curriculum

Efficacy of Working Memory Training for ADHD

Exciting research from Sweden finds that a 5 week computer-based training program in visual working memory, resulted in 60% of non-medicated children diagnosed with ADHD no longer meeting clinical criteria. The Karolinska researchers have already founded a biotech company and a collaborative U.S. based project (NYU) is in the works.

Check out the Scientific American article here. This latest article is not yet available under free access, but an earlier paper by this group involving working memory training can be seen here. Their company is Cogmed.

Why is the the United States so behind in computer-based training for memory and attention? Good question. Even fairly simple behavioral treatment (the Multimodal Behavioral treatment study involved social skills teaching at a summer camp, no working memory training) seems to be as effective as high dose stimulant medication.

Also, Toronto schools have begun to introduce working memory training techniques in the classroom. Some of these methods would be easy to implement here in the U.S. at home or at schools.

(HT: Rob Sperry)

NAEP - The Nation's Report Card - National Assessment of Educational Progress - NAEP

Good news for younger children on the Nation's Report card. 9 year olds appear to making significant gains in reading and mathematics, but the gains certainly flatten out by age 17.



For mathematics, a favorable trend was also seen at age 13, but the 17 year olds' dip occurred again.



High school dropout rates may also be as high as 30-40%, though, and this number may climb if students can't meet state requirements.

NAEP - The Nation's Report Card
NAEP Press release
Fudging High School Graduation Statistics

SENG Highlights: Parenting, Attention, and Self-Regulation

Some highlights from the SENG (sengifted.org) conference:

Judith Roseberry (President, California Association for the Gifted):
- Advice to parents - don't abdicate your role as parents just because your kids are smart. Don't be afraid to use your authority and have your rules respected.
- Empower your children with words, role plays, and socially appropriate behaviors. Allow them to question authority, but teach them socially acceptable ways like: "Mrs. Hill. Have I done something to offend you. You seem angry to me." Role play, and go with them, but have them speak for themselves.
- Teach your children certain phrases: "In my opinion," "What evidence do you have..."
-Support children in gifted programs who don't seem to be achieving - don't kick them out of the program, but troubleshoot
- To parents: "Don't ever let us teachers ever tell you that we know your child better than you..."

Paul Beljan (President of American Board of Pediatric Neuropsychology, Co-Author MisDiagnosis & Dual Diagnosis):
- Attention and Working Memory can be trained
- Don't just say, "don't do this" - give children a positive alternative - "don't do this, do this instead..."
- Dr. Beljan described a coaching and discipline program that he playfully called the 'Zen of Bean Sorting' - Children are given a calming and pleasant sensory task when they lose control or can't regulate their impulses. Privileges are suspended until the beans are sorted.
- "There's a difference between discipline and punishment."
- For time-outs, don't use a clock. Use the same words every time. "When you're quiet, you can come out."
- Scaffold situations so children can avoid catastrophic failure
- After tantrums or bad behavior, make sure the child rectifies any situation he created ("shows he has his rational mind back")
- Be careful how you talk. Be instructive with requests - "Put this in your room", not "Can you pick this up?"
- There were many more pearls...fortunately a book by Dr. Beljan is in the works!

Resisting the Cave - Kids and Media Addiction

This USA Today article reports on the increasing trend for children to spend most of their free time playing video games, watching TV, or surfing on the Internet. Outside events tend to be scheduled, and children are six times more likely to play a video game than ride a bike.

"I call him the caveman because he never leaves his room," says one father. "He comes out now and then for dinner, but he can't eat with us. He has to get back to his game."

The consequences are many - a loss of family time (never give up the family dinner), less face-to-face sharing and conversation, less 'downtime' - important for relaxation, incubating ideas, certain creative pursuits, less time with nature, physical activity, building, and tinkering.

Sometimes a little 'popcorn' for the brain is OK for a brain break, but children can also get caught up in immersive quality of the media, and not know when to quit. If you're a media junkie, try turning off the media yourself. Think about growing up some family traditions - a family walk after dinner, family game night, cooking together, reading books outloud together, building things or playing music together.

Childhood Moving Indoors
Hitting the Off Button
Family that Plays Together
BlueSuitMom.com

Brain Break: Planarity Puzzle (Spatial)

Planarity

Back from New Mexico - SENG

We got back from SENG (Social & Emotional Needs of Gifted Children) in New Mexico and had a terrific time. The kids program was terrific (Gifted Teachers from New Mexico took the children to the Atomic Museum, Natural History, Planetarium, as well as ran group sessions on Learning Styles and Building a Robot) as were some conference talks, and got to meet some very interesting people with great ideas for education and parenting. We got in late tonight, so will catch up blogging (including Conference highlights) tomorrow!

Just the Facts, M'aam - Creativity in Fact Lovers

Maybe you know one of these fact lovers or maybe you are one yourself. It's all to easy to dismiss fact lovers as trivia geeks, hyperfrontal-types, or Asperger folk, but the truth is, a strong knowledge of facts can make the essential difference in innovative or ground-breaking work, and expertise at acquiring and retaining facts may mean that education should take on a different purpose.

One example of an avid fact aficionado is Isaac Asimov. Asimov voraciously read books his whole life long, and he wrote nearly 500 books over the course of 40 years. Many have referred to him as a very 'non-visual' writer and he himself had made this comment about visual thinking:

"You may have heard the statement: 'One picture is worth a thousand words.' Don't you believe it...As soon as it becomes necessary to deal with emotions, ideas, fancies- abstractions in general - only words will suit."

In fact, Asimov's series of "How did we find out about..." is really an extraordinary collection of children's books. Each is only about 60 pages long, but well written and quite creative in its charting of the course of scientific discovery. It's a great book for kids because it talks about the whys and hows and serendipities of science, and it makes the questions and pursuit of knowledge seem attainable. When science is only taught from the standpoint of 'we know this now', students may be discouraged from thinking that they could actually find out anything new. Asimov's series includes topics such as germs, lasers, microwaves, blood, the round earth, and much more. It's great summer reading. We found the books at the library (did you know the microscope inventor Leeuwenhoek was not really a scientist, but a janitor who like tinkering around with lenses?).

One of Asimov's real gifts was being able to recognize and organize interesting facts in simple but compelling ways. Creativity is not just making something completely new, but it is also an ability to see in facts, what others haven't been able to see.

SENG Conference in New Mexico, See You July 14th

We're headed off to the SENG (Social and Emotional Needs of Gifted Children) Conference, so we'll be taking a break from blogging for the next week. Our kids have been doing some last minute learning about New Mexico geology, Los Alamos, the Anasazi, and Billy the Kid. It'll be fun.

The speakers also look terrific - this is one keynote's description..."Alisa's Cuban-born father was placed in the fourth grade when he arrived in the U.S. at age fifteen, because he spoke no English; he went on to become a famed professor of Latin American sociology. Alisa, now the top-selling Latina novelist in the U.S., was failed out of freshman English by a high school English teacher for not following rules. And Alisa's son was recently misdiagnosed as autistic because he did not ift in at preschool, preferred sprinkler systems to toy cars, and had taught himself to read..."

Remembering in Different Ways

Check out the variation in patterns of brain activation among test subjects trying to recall items from a previously displayed word list. The best performer was S.C., and this subject also had the most intense activation and reproducibility in her testing 5 months later. The blue arrows indicate the right parietal area (imagery, attention), whereas the green arrows indicate more conventional prefrontal working memory areas.



We've included a snapshot from "musical imagery" in pianists for comparison. The last link below is a paper which shows that the parietal and prefrontal areas can be strengthened (and the fMRI signals more activated) with memory training involving mneumonics.

Individual Differences in Retrieval fmri pdf
Musical Imagery
Working Memory Training fMRI pdf

More Computer Classes Urged for Kids

Students may be feeling the crunch of declining numbers of computer science teachers. Computer teaching in the elementary school years is often relegated to keyboarding. What students should be doing is learning how to organize and problem solve using computer-based instruction.

Excerpt from article:"If the teachers only know word processing, he said, "that's all their class is going to get."

This exhortation is particularly relevant given a Stanford study showing that having a home computer was associated with 6 points higher math and 4 points higher reading (controlled for parent education level) on the Stanford Achievement Test (3rd graders). The definite no-no was a TV in a child's bedroom. This was associated with 8 points lower on math and 7 points lower on reading.

More Computer for Kids:
TV bad, Computer Good for Kids

Medical School Testing Lawsuit Passes Hurdle

For those of you who are following the lawsuit involving university students suing for testing accommodations on the MCAT, we've heard that they've recently passed a hurdle. The Court ruled that "that California has a legitimate local interest in ensuring that California residents take the MCAT with all the accommodations required by California law." The AAMC intends to vigorously continue the fight. Check out the AAMC's response too.

MCAT Litigation: Victory for Students with Disabilities
AAMC Responds

Flashes from the Past: A Lover of Words...

His father died when he was 4 years old, leaving him, his mother, and a younger brother to fend for themselves. His mother remained ambitious, making the decision to homeschool him (teaching him Latin, French, English, drawing, botany, and piano) in the hopes of having him admitted to the best grammar school in the city. He didn't get in at age 7, but he tried again at age 8, and got in.

From an early age, he loved words and loved to read. He started to read at 4 and his mother provided him with a steady supply of Arthurian legends, fairy tales and George MacDonald's Curdie books. By age 11, he was learning Greek and Shakespeare, and became fascinated by reading The Canterbury Tales in its original Middle English. He also loved to play around with and make up words. His young mother died from diabetes when he was just 12 years old, but he and his brother were fortunate to be adopted by a parish priest, a family friend.

This young man's love of words continued to grow as he progressed through school, and corresponded in made up languages with two cousins. One language, "Animalic" consisted only of animal names. Apparently, "Dog nightingale woodpecker forty" meant "You are an ass."

Here's a limerick he wrote to his cousin in the imaginary language "Nevbosh":

Dar fys ma vel gom co palt "Hoc
Pys go iskili far maino woc?
Pro si go fys do roc de
Do cat ym maino bocte
De volt fact soc ma taimful gyroc!"

The translation:

There was an old man who said "How
Can I possibly carry my cow?
For if I were to ask it
To get in my basket
It would make such a terrible row!"

Who was this budding philologist? This was J.R.R. Tolkien, later Oxford Professor and literary scholar, and author of The Hobbit, Lord of the Rings, and Silmarillion, among others. He often said he thought of names he liked first, then put them in stories.

Throughout his life, he was close to all of his children and told them stories to help them fall asleep. Many were apparently never recorded, but some were collected together for books that were published posthumously. The story of Roverrandom was told by him after one of his sons had lost a favorite toy on a vacation.

Tolkien often mentioned that everything he knew, he owed to his mother who died so young, and her deep religious faith. Quote, "However by name a Tolkien, I have the taste, talents and education of a Suffield.”

Tolkien Biography
Planet-Tolkien.com

Advantages of Bilingual Language Learning

Is there any advantage to picking up a foreign language as a child? That depends. It's important to be aware that bilingual children have significant extra hurdles in the early years of their schooling. Gifted bilingual children are underrecognized, and some are even mistakenly thought to be learning disabled.

But for those are able to become fairly proficient at two languages, this hard work appears to pay off one's entire life span. The study below shows that bilingualism reduces age-related decline in working memory and the slower response times! In other studies, there's a suggestion that "successful" bilinguals have stronger flexibility of thinking, higher 'creativity', and better problem solving ability. When you think about it, young bilingual children get much more intensive practice with inferences, and multiple word meanings.



Now that being said, the choice of whether to add a second language at a young age should be made individually. Children struggling with auditory processing, fundamental language disability, or working memory limitation should consider a foreign language waiver. Also realize that all languages are not alike. Some languages (like Spanish, Italian, or American Sign Language) are not as demanding phonetically or spelling-wise as languages like French.

Improved Cognitive Control Among Bilinguals
Bilingualism Press Release
Challenges with Young Bilingual Children

Happy Fourth of July!

Howstuffworks "How Fireworks Work"
The Chemistry of Fireworks

Spatial But Not Visual Thinking

There are many different types of spatial thinking, but a lot of confusion that visual and spatial gifts are the same. They're not. Spatial abilities can be visual -but they can also be distinct - and even at odds with visual ability. Spatial ability is particularly challenging to train because it may be the most abstract and 'non-conscious' style of learning.

Spatial thinking may involve personal experience, memories of movements or manipulations, or relationships of parts. It may involve sight, but also sound, touch, and more amorphous sensations. Spatial reasoning may involve a sequence of ideas, possibilities, or objects, or inductive leaps (Aha!) based on previously seen or experienced patterns.

In this interesting study above, researchers from Max Planck find different steps of coordination that the brain goes through when it performs a spatial reasoning task -
"V is left of X. X is left of Z. So V is left of Z" The first step involves occipital-temporal areas (visual /auditory overlap - premise considered), then the prefrontal cortex becomes activated (integration), then prefrontal and parietal lobes (multisensory, spatial) become active in the final 'validation' stage.

Spatial thinking and reasoning are hard to teach didactically, because they are best learned by direct experience, internalization and positing or rules, abstraction (thinking), and experimentation. No wonder that tweakers are ideal spatial learners.

Think of the paradox that comes with spatial thinking - the best way to 'train' is to work both with hands-on and non-hands-on approaches (abstraction, visualization). In fact, it's probably wise to make sure creative spatial thinkers get plenty of both types of practice (working with models and manipulatives, but also not working with models and manipulatives to imagine and problem solve).

So does this picture of spatial thinking encompass too much? We don't think so. What is not spatial thinking? It's not words and doesn't have to be visual images.

We've added some interesting links we stumbled upon for spatial teaching and reasoning. This is probably obvious to many of you, but strong spatial thinkers are necessary in almost all scientific and technical domains (including video gaming and software design of course), design and graphics, architecture, the military, mathematics, and more.

Spatial Reasoning Resources
Spatial Reasoning and Cognition:
NCTM: Cubes and Drawings
More Student Spatial Activities
Dyslexia & Talent: Visual-Spatial
Problem Solving Spatial Geometry

A Challenge to Autism Statistics: Three Reasons....

This paper is likely to cause quite an uproar. Read the full paper at the link below. This group has taken on the notion of an autism epidemic. While some of their points about the morph'ing of definitions over time are fair (current behavioral checklist guidelines stink), they ignore the fact that are many children out there who are unable to keep up with 'regular' activities of childhood language and social interaction.

Today many children are being mis- or over-diagnosed, but many do have neurologic issues, and they need specific interventions for their particular problems.

Three Reasons Not to Believe in an Autism Epidemic

Teaching Optimism

Some children seem to be born more pessimistic than others, but optimism can also be systematically taught. And a child with a higher degree of optimism is more likely to resist depression, be health physically, persist at difficult tasks, and succeed in school and later life. In fact, children with high 'optimism' scales are more likely to outperform in college what their SAT and achievement scores would predict.

The picture below shows that students with higher anxiety scores are more likely to have lower levels of amygdala activation when viewing photographs of 'happy faces.' Of interest too, the higher anxiety subjects were still within normal ranges of personality.



Gifted children may also especially prone to existential depression, and studies of gifted children have shown that gifted students may react more intensely than average-ability students to frustration. Studies of stress and burn-out in gifted students suggest that key factors can be an inappropriate level of intellectual stimulation ('underload' or 'overload' as Hoekman et al. have recently commented).

One helpful book offering a step-by-step program to improve a child's optimism is Dr. Seligman's The Optimistic Child. It provides practical instruction on how to encourage children to see failures and setbacks as temporary, limited, and impersonal.

Seligman's Optimism Program
Happy Faces fMRI
Optimism article

Hoekman, McCormick, Barnett, 2005. The Important Role of Optimism in a Motivational Investigation of the Education of Gifted Adolescents, Gifted Child Quarterly, Spring 2005 (not online).

Science Fiction Links

Science fiction can be used to teach creative and critical thinking, social, biological, and physical sciences, art, math, literature, technology, history, and futurism.

Yale Science Fiction
Physics, Art, Literature, Mathematics
University of Kansas Center for the Study of Science Fiction
SCIFI.COM in Classroom
Sci Fi forYounger Readers
Course Study of Science Fiction
Tamora Pierce Gifted Readers Sci Fi List
Science in Science Fiction
Science fiction & Real Technology
HHMI Biology Through Science Fiction

Flashes from the Past: "Do not let this boy in your school..."

His principal had taken the time to write a letter saying, "Do not let this boy in your school under any circumstances," but as he recalled, "... I got in the car and drove up there and got in time for registration. When I reached the desk, they looked at me and said, "We told you not to come." I said, "I know you did, but I didn't think you meant it."

He was a kid who "stayed in trouble all the time," and he was frequently expelled for pranks and insubordination. Although he managed to wrangle his way into the university, he rarely went to classes (although enjoyed reading in the library) and dropped out after 2 years. He went into the National Guard, but was court-martialed for leaving the base without permission to visit a girlfriend, whom he later married.

But he did love to write. In response to a interviewer's question, "How did you get interested in writing?, he said "I'm sure my interest began in an interest in reading, which then was translated into an interest in writing...I was about 11 years old. I won a copy of "David Copperfield." Up to that time I'd read the "Bobbsey Twins" and then "Tom Swift" and the "Rover Boys" and "Tarzan," but since I got this as a prize, I decided I should read it. I found a world that was realer than the world I lived in, unlike these Tarzan and other books. This was a whole other world, and it was a world of art. I couldn't have defined it as that, but, one thing, I knew "David Copperfield" better than anybody I knew in the real world, including myself...I remember vividly having that reaction to that book "David Copperfield." I think most writers probably have that experience."

Who was this? This was Shelby Foote, who died just this past Monday at the age of 88. Shelby Foote was best known as the lyrical historian on Ken Burns' Civil War documentary. Foote's Civil War: A Narrative has been ranked as No. 15 on the Modern Library's list of the century's 100 best English-language works of nonfiction. He really did have a way with words.

"Of all the passions of mankind, the love of novelty most rules the mind. In search of this, from realm to realm we roam. Our fleets come loaded with every folly home." - Shelby Foote

Shelby Foote Interview
Shelby Foote Biography

Math Education Links

We came across these excellent links at Kevin Karplus' website. His brief comments on the sites are also helpful - we demo'ed ALEKS and were disappointed as well. EPGY math may also not allow enough opportunity to return to subjects. Do you have experiences with these programs? If so, please post comments if you get a chance.

Karplus' Math Ed Links

Javits Funding NAGC Alert

The NAGC has sent out an alert to contact your senator about Javits funding for Gifted education. The appropriations committee meets July 12.

Javits Funding NAGC

Training Visual Perception - More Than Meets the Eye

Trends in Cognitive Sciences has a nice review on the 'top-down' cognitive direction of visual perception. We see more when we are expecting to see more. It's like this gray and black picture below. At first glance, we may not recognize it, but with further inspection we can fill in and organize what we see into a figure.



Many people are aware of these sorts of 'eye tricks' in the form of optical illusions. But, visual perception has extensive relevance to many aspects of learning, expertise, and some forms of disability.

Perceptual learning is big news because it highly trainable and involves 'rewiring' the brain. Computer-based programs are ideal for perceptual training, but existing commercial programs are fairly simplistic, although that probably won't be for long.

Training in visual perception has powerful implications for many groups and conditions, including athletes, workers who require visual discrimination as part of their occupations (quality control, air traffic controllers, umpires, chemists, architects, engineers etc.), visual experts (artists, bird watchers, antique appraisers, chess masters etc.), and children and adults who have conditions such as dyslexia, nonverbal learning disabilities, visual distractibility, prematurity (periventricular leukomalacia), or autism.

What can you do now, if you have a child with visual perceptual problems? First look for visual factors that may improve or detract from their visual ability. Vary the light intensity, color, and visual crowding. Could there be a problem with seeing movement? If so, slow it down. Try simplifying visual settings to see if it helps their visual search or orientation. Use words and touch to help them correct visual errors, spatial mistakes or size distortions. Have them draw and build, and give them plenty of time to study and compare what they see with what they perceive in terms of space. Many adults are able to compensate very well for visual perceptual problems, but they had to learn it gradually.

Visual Perceptual Learning
Cutting through the Clutter -PLos brief
The Principles of Artistic Illusions
Visual Shape Learning pdf

Geek Brain Break: Interactive Mathematics Puzzles

Interactive Mathematics Miscellany and Puzzles

Free Online U.S. Report Teaching Children with ADHD

There are other free downloadable publications at this government site: for instance, Helping Your Child Become a Reader, Helping Your Child Learn Math, Helping Your Child with Homework...

Fed Report Teaching Strategies ADHD

East meets West: Fundamental Differences in Math Teaching

We finally got a chance to read Liping Ma's Knowing and Teaching Elementary Mathematics, and Wow, what a book! This book (Ma's PhD thesis) used interviews with U.S. and Chinese mathematics teachers to compare approaches and understanding about basic elementary mathematics: subtraction with regrouping, multidigit number multiplication, division by fractions, and explorations of new knowledge. Her findings have direct and practical implications for teachers, parents, and tutors.

Key Findings:

- U.S. teachers tend to focus on procedures rather than understanding the conceptual foundations of basic math operations(in one testing situation, 83% U.S., 14% Chinese used procedural knowledge only)

- Impaired conceptual knowledge impaired U.S. teachers' abilities to understand student mistakes and apply math reasoning to new problems or scenarios.

- U.S. teachers' use of manipulatives could be misapplied, for instance, removing the need for a child to understand regrouping, rather than illustrating principles regrouping or borrowing.

-U.S. teachers showed less flexibility and alternative problem solving than their Chinese counterparts.

-U.S. teachers seemed more likely to introduce entertaining or visually appealing aspects of math calculations, but sometimes at the expense of accurate conceptual teaching.

Example: "One thing I would do is....put either an apple, orange or whatever, in the spaces...I mean it could be some weird thing, even pictures of elephants. I do not care what it was. But the children memorized this and they said, oh I remember that [my teacher] said do not put anything there because that is where the orange was or that was the apple...Just put something different there so that it will hit their eye."

- Some Chinese teachers regularly showed a math problem with errors on the board, and challenging students to 'find the problem' and 'summarize the rule'. A discussion would then follow about the correct underlying concept.

- Only 43% U.S. math teachers arrived at the correct answer to: 1 3/4 divided by 1/2 compared to 100% of the Chinese teachers. Problems included over-reliance on a mneumonic (without conceptual understanding), a lack of alternative ways to solve the problems, and limited analogical understanding. For the latter, for instance, U.S. teachers tended to rely on pizza-type examples for fractions, but became stumped with dividing by the 1/2.

- Finally, U.S. teachers also fared poorly in a scenario of a student suggesting a novel theory that increasing the perimeter of a closed figure would necessarily increase the area. 9% accepted the theory without a doubt, 78% would not have conducted any mathematical investigation ("I'd try to look it up in a book"), and only 13% would have investigated the claim. Only 1 teacher out of the 23 was able to solve the answer. In comparison, of the Chinese teachers, 8% accepted the claim outright, 70% arrived at the correct answer, and the remaining at least tried with mathematical reasoning, but solved the problem incorrectly.

Clearly we have a long way to go with teaching conceptual foundations in math. Bravo, for the math teachers at NCTM for taking a hard look at the book, and considering reforms.

(HT:artofproblemsolving.com)

NCTM: Comparing U.S. and Chinese Elementary Math

Thinking It Over: Combining Analytical Thinking and Imagery

When we make decisions based on risk, it matters whether the possibilities are framed in a positive or negative light, what risks are matched to possible benefits. People are likely to opt for 'certain' rather than 'risky' options when only good outcomes are offered, but tempted to make riskier choices confronted with two negative possibilities. This pattern of decision making has always been a bit perplexing because the choices (certain-good, risky-bad) seem to be somewhat contradictory. There are different possible reasons for this (see the paper for more discussion below) - but one theory posits a compromise between desire to make a good decision and desire to minimize cognitive effort, while the other suggests a compromise betweens fears and wishes of an individual.

This recent study found the cognitively 'easy' choice for a certain positive gain matched well with fmri activation data. The negative condition required more brain work under both conditions, and that also showed more imagery area activation (blue arrows) than the simplest positive-certain condition. Imagery, it seems, is very important in making decisions under uncertain conditions.



Analysis and Imagery in Framing Decisions

Sci Am: Math without Words

Here's a Scientific American article about Numerical Reasoning independent of words: Sci Am: Math without Words

The Extra Work of Multiple Word Meanings and Word Play

This figure shows you the extra work with multiple word meanings. Although sometimes we see parents or teachers who are concerned that a child's difficulty in getting jokes is due to autism, it takes a lot more brain work to figure out words that have several possible meanings, and it is also an ability that improves with age.

We just excerpted two key figures, but the main point to notice is that ambiguous words take more 'frontal' activity and right hemispheric activity- keeping different possibilities in mind, generating alternatives, and then choosing one on the basis of the best fit or pattern. Many children have difficulty with figuring out word meanings - sometimes it is developmental, sometimes it is attentional or memory related, and it can occur in many different kids with language challenges.



Multiple word meanings come up all the time in English, and we probably need to quiz kids more to see if they really understand the meaning. Some of the links below may be helpful to some of you. Word play sites are also good practice for speech fluency, prosody, and of course, just for fun.

Ambiguous Words and fMRI
Multiple Word Meanings-Elementary
Powerpoint Elementary Multiple Word Meanings
List Multiple Meanings
Fun With Words
Puns@Web English Teacher

Super Smart? Denver Post Article

Super Smart?

Essential Questions Site U.S. History

Since we're going to be doing U.S. History next year homeschooling, we've been looking for a site like this. Excellent links too.
Essential Questions U.S. History

For Kids, Actions Speak Louder Than Words - Different Site for Word Generation

In this very interesting study from Washington University St Louis, Schlaggar and his group find that children use action and movement-related areas of the brain to generate words. This is a nifty study because the investigators matched children and adults who showed an equivalent performance. So we are really seeing how kids (age 7-10) use their brains differently from young adults. The word generation trials involved several different ways to generate words - matching verbs with nouns (car & drive), rhymes (cat-hat), and opposites (up-down).



What you can see is that adults (red) tended to use their 'classic' left hemispheric language area to generate words, while kids (blue) were using their right occipitotemporal region, a region involved in multisensory imagery for action and movement. So it seems children are closer to the 'source', associating words with direct sensations and imagery, while adults have gone on to file word knowledge away in their word definition library.

Children, Word Generation, and fMRI
Action Imagery in the Brain

Math and Learning Disabilities Links

Found some nice links for Math and Learning Disabilities in a course syllabus at Johns Hopkins University. Some of them are rather technical, but show us how many different ways math performance can be affected by a disability or individual cognitive challenges.

Mathematics and Learning Disabilities
Course Syllabus JHU
Developmental Dyscalculia

Analogical Thinking and Imagery in Problem Solving

Analogical thinking has always played a powerful role in scientific innovation, but now the contribution of multimodal imagery is also becoming clearer.

Some 20 or so years ago, John Clements found that analogies played an important role in the problem solving abilities of scientists. Given a physical problem involving coiled springs, he videotaped and interviewed them as the were able to figure the problems solution. The analogies that the scientists used usually bore some functional or structural similarity to the unsolved problem, but several observations were notable: the solutions were not sudden (some only solved the problem after an hour or more), most adopted analogies only tentatively at first, the analogies seemed to based on structural or functional features, and most of the work seemed to be involved with testing and challenging the favored analogy. Ultimately the correct answer was arrived at by associational and inferential conclusions, rather than deduction.

Now in this latest paper from John Clements, he has become interested in the role of personal dynamic / kinesthetic imagery in bridging the analogical concept and physical problem. Hand gestures and movements seemed important for representing forces, and visualizations (combined with gestures) were important for reaching final conclusions.

Studies such as these are an interesting look into the problem solving process and they offer interesting questions as to the best ways to expose students to these approaches in their school training. There are variety of successful problem solving traits of these scientists - persistence with a problem, willingness to suspend judgment, flexibility to possibilities, and facility with personal imagery.

We also included some research papers which looked at the introduction of analogical teaching in science classrooms. There are some differences presenting experts vs. novices with analogies - many experts love analogies because they start off with a richer foundation of knowledge. Analogies help you if you already have a lot of information because it simplifies and groups what you already know. However, for the novice, analogies might just seem to be a pattern to be memorized - and so the likelihood that it will be learned as it should be as a tool for other situations is unlikely.

The first chemistry paper below looks at an obviously very creative teacher who explores many analogies with chemical events in his classroom. But the concern would be that he adopts too many different and non-specific analogies that his students don't get a chance to test it out or see how the analogy could lead to particular predictions or testable hypotheses.

Finally, as a brain break, if you're interested, check out the funny 'bad analogies' link in student writing or the winning entries in the 'bad fiction' of Bulwer Lytton ("It was a dark and stormy night..." below.

Clement's Study of Analogy in Problem Solving
Analogy in Chemistry
Analogical Strategic Reasoning in Management
Multiple Models in Chemistry
Metaphors and Analogies in Scientific Thinking
Bad Analogies
The Bulwer-Lytton Fiction Contest

Flashes from the Past: "He was a bit of a dud in math..."

In school, he seemed to be a bit of a dud in math, and in fact he was held back one year when he had trouble learning mental math. He was rescued in his teenage years when an insightful teacher realized he needed more time.

"I used to take these maths tests which were supposed to be done in one period and it took me not just that period but the next one which was a play period and somethimes the one beyond that before I finished the test. And it was only then that I started to do well."

Who was this super-slow thinker? This was Roger Penrose, now mathematician and physicist, discoverer of Penrose tilings, and author of many original thoughts in geometry, relativity, quantum mechanics, and theories of consciousness. It seems that if you are a slow thinker, you may still think well.

Offered Penrose, "My own way of thinking is to ponder long and I hope deeply on problems and for a long time which I keep away for years and years and I never really let them go. I'm pretty tenacious when it comes to prob"People think of these eureka moments and my feeling is that they tend to be little things, a little realisation and then a little realisation built on that."

And "...these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about."

Penrose Interview