Archive for: August, 2010

Developmental Origins of Numerical Cognition

Aug 16 2010 Published by under Blogging on Peer-Reviewed Research

Nearly everyone has heard of developmental dyslexia - a learning disorder characterized by poor reading skills despite otherwise sufficient schooling - but have you heard of developmental dyscalculia? Many people have not. Today begins a week-long series on this lesser-known learning disorder. First, we'll consider some potentially innate mechanisms of numerical cognition that give rise to more complex mathematics.

In his 1933 novel Miss Lonelyhearts, Nathanael West writes, “Numbers constitute the only universal language.” Humans have a natural tendency to classify and quantify objects and events around them. Numbers and arithmetic are so basic to the human experience that children develop a basic sense of number and mathematical relations without explicit instruction.

Developmental Building Blocks
ResearchBlogging.orgIn the 1960s, Piaget proposed a three-stage sequence to number acquisition. In stage one, children do not understand one-to-one correspondence of objects – that is, when shown an array of five white jelly beans, they cannot match them to the proper number of black jelly beans. In stage two, an instinctive one-to-one correspondence emerges where children begin to grasp the fundamental idea of equivalence in number, but only if the two sets of objects are equal in all dimensions (number and density, for example). The third stage child understands equivalence more fully, not being fooled by a change in density (i.e. physical proximity of each item in a set) to think that the number of jelly beans has changed.

A stage two child would not consider the two rows of dots as equivalent, since they have different densities.

While Piaget was a great experimentalist, many of his experiments were critically flawed (he experimented on his own children!), and development in general probably doesn't proceed along in a series of stages. More recently, in a more sophisticated series of experiments involving the brief presentation of arrays of dots on a screen, Xu and Spelke demonstrated that six-month-old infants were able to discriminate between eight and sixteen, and between sixteen and thirty two. However, the infants did not discriminate eight dots from twelve or sixteen from twenty four. Starkey and Cooper demonstrated that infants were unable to discriminate four from six dots, in a similar experiment. The findings suggest that infants can discriminate to 2:1 ratios such as 16:8 and 32:16, but not 3:2 ratios such as 12:8 or 6:4. Critically, these dot arrays were presented too quickly for the infants to count them (and even so, infants aren't yet able to explicitly count, since counting requires language); instead, some other mental process was engaged in order to quickly estimate the number of items in the array.

A second set of experiments by Lipton and Spelke sought to determine whether this finding was limited to the visual field, or also applied to auditory input. Infants heard sequences of sounds from a right-side and left-side speaker. The infants were again sensitive to 2:1 ratios (16 and 8 sounds) but not 3:2 ratios (12 and 8 sounds). These findings suggest that representations of approximate numerosities are independent of sensory modality or stimulus format.

In a third set of experiments, Spelke and Xu repeated their dot-array experiments with smaller numbers of dots: arrays of either one versus two dots, or two versus three dots. The findings of these studies indicated that although infants treat large numbers of visible items as a set, they appear to treat small numbers of visible items as individual objects, and not as a set of objects with a cardinal value.

Taken together, these experiments (and many others) suggest that very early in development, infants are able to engage at least two cognitive mechanisms that contribute to numerical cognition: an approximate large number system, and an exact small number system (for up to 3-4 objects).

From Numerosity to Mathematics
Most children eventually acquire four primary mathematical abilities without explicit instruction:
(1) numerosity, which is the ability to determine the quantity of items in a set without counting;
(2) ordinality, which is a basic understanding of "more than" and "less than" relationships between sets of objects;
(3) counting, which is the ability to determine how many items are in a set using a system of symbolic representation – a preverbal counting system has been observed, as well as a language-based system; and
(4) simple arithmetic, which is an understanding of and sensitivity for increases (addition) or decreases (subtraction) from a set. (Geary, 1995)

Unlike basic number abilities, calculation ability represents an extremely complex cognitive process, and requires explicit instruction. The loss of the ability to perform calculation tasks resulting from neuropathology is known as acalculia or acquired dyscalculia, which is an acquired disturbance in computational ability. The developmental defect in the acquisition of numerical abilities, on the other hand, is usually referred to as developmental dyscalculia, or simply dyscalculia.

This was the first in a week-long series on developmental dyscalculia.

Get Your Literature On
Xu, F. (2000). Large number discrimination in 6-month-old infants Cognition, 74 (1) DOI: 10.1016/S0010-0277(99)00066-9

Starkey, P., & Cooper, R. (1980). Perception of numbers by human infants Science, 210 (4473), 1033-1035 DOI: 10.1126/science.7434014

Lipton JS, & Spelke ES (2003). Origins of number sense. Large-number discrimination in human infants. Psychological science : a journal of the American Psychological Society / APS, 14 (5), 396-401 PMID: 12930467

Geary DC (1995). Reflections of evolution and culture in children's cognition. Implications for mathematical development and instruction. The American psychologist, 50 (1), 24-37 PMID: 7872578

3 responses so far

The Development of Causal Reasoning: On Optimal Search in the A-not-B task

Aug 16 2010 Published by under Forget What You've Read!, From the Melodye Files

I am a horribly forgetful girl.

Which is a funny thing to say, really, because I’m not quite sure whether it’s my memory that’s bad or my attention.  Recently, for instance, I spent several hours searching for my phone to no avail, only to find (the following morning) that I had left it in my underwear drawer.  It reminded me of when I left my driver’s license in the refrigerator with my passport; or the time I put a bowl of ice-cream in the oven for safekeeping.

It is desperately hard to ‘find’ things again once I’ve committed such an error, because there is simply no logical way to retrace my steps.  “Ah yes, the oven!  A perfect place to stow the ice-cream…”

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9 responses so far

Blind Item: Developmental Learning Disorders

Aug 15 2010 Published by under Blind Item

Nearly everyone has heard of developmental dyslexia, a learning disorder characterized by poor reading skills despite otherwise sufficient schooling. But there is another developmental learning disorder, characterized by poor achievement in mathematics, despite otherwise sufficient education. Tomorrow begins a week-long series on this lesser-known learning disorder.

One point to the first individual who identifies the proper name for this developmental (i.e. not acquired) disorder in the comments.

Image source: Scientific American

11 responses so far

Open Lab Update

Aug 14 2010 Published by under Odds 'n Ends

Bora publishes the full list of submissions for Open Lab every week on Monday. I will be publishing it somewhat less often.

Note: if you have recently moved your blog, please e-mail me the corrected URLs for your entries

The list is growing fast - check the submissions to date and get inspired to submit something of your own - an essay, a poem, a cartoon or original art.

The Submission form is here so you can get started. Under the fold are entries so far, as well as buttons and the bookmarklet. The instructions for submitting are here.

Check out the list - you might be surprised to find your blog in the list, if someone else submitted your posts. And please don't feel shy about submitting your own pieces!

You can buy the last four annual collections here. You can read Prefaces and Introductions to older editions here.

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Is The Child The Father of the Man?

One of the fundamental themes (and a continuing debate) in developmental psychology concerns the continuity or discontinuity of temperament and personality from infancy through the rest of a child’s life and into adulthood.

Some researchers believe that they have found evidence for the continuity of relatively stable personality traits through development. Despite the clear importance of environmental stressors and other random events, the evidence seems fairly clear that the personality traits that dictate the response pattern to such life events in adulthood is fairly predictable based on early childhood temperament.

ResearchBlogging.orgSchwartz and colleagues, in 2003, investigated amygdalar responses to novelty in adults who had been previously classified as inhibited or uninhibited at age two. (The amygdala, a part of the limbic system, has been shown to be involved in the processing of emotional information.) Children classified as inhibited tend to be shy around people, objects, or situations which are unfamiliar, while uninhibited children tend to approach or even seek out novel people, objects, or situations. They hypothesized that there would be neural differences between the two groups, particularly in response to novel versus familiar faces. The hypothesis was confirmed for this sample, as the two groups had different responses to the stimuli in this fMRI study. One interpretation of these results is that there is continuity in temperament at least to early adulthood, although only a longitudinal study could truly address that question. This study found a correlation between early temperament categorization and adult amygdala activity, which leaves open several possible alternative interpretations.

Caspi, in 2000, gave somewhat more convincing longitudinal evidence that there is developmental continuity of temperament, using data from the Dunedin longitudinal study. In general terms, he found that undercontrolled (uninhibited) three year olds grew up to become impulsive, unreliable, and antisocial, while inhibited three year olds became unassertive and depressed, and had less social support.

More specifically, undercontrolled toddlers were rated by teachers and parents as having more externalizing problems at age 5, 7, 9, and 11. In adolescence (age 13 and 15), the undercontrolled toddlers continued to have externalizing behavior problems, and they showed more internalizing problems as well. The inhibited children had significantly more internalizing problems than the undercontrolled or control groups.

By age 18, the undercontrolled children were low on traits designed to measure constraint. In self-descriptions, terms used included “reckless” and “careless”, and they indicated low harm avoidance. They scored high on negative emotionality measures. They also reported high aggression and alienation. Much of these findings are consistent with the findings from early adolescence. The inhibited children were low on the constraint measurements, and low in positive emotionality. They self-reported high self-control, high harm avoidance, and low aggression. They also reported low social potency – that is, they shied away from leadership roles. Informant ratings at age 21 were consistent with these self-ratings at age 18. Finally, by age 21, undercontrolled children were involved in conflicted relationships; inhibited children had significantly higher social support. Similar significant patterns were also found by age 21 for employment, psychopathology, and criminal behavior.

Ultimately, a considerable amount of data from these studies and others suggest that adult personality is indeed predictable from childhood temperament, but that still does not explain why this is so. A more comprehensive view, accounting for biological, cognitive, emotional, social, and environmental factors, is necessary. Despite the fact that random life encounters cannot be predicted, stable differences in personality likely influences how such events are subjectively experienced.

Image Source

Schwartz, C. (2003). Inhibited and Uninhibited Infants "Grown Up": Adult Amygdalar Response to Novelty Science, 300 (5627), 1952-1953 DOI: 10.1126/science.1083703

Caspi, A. (2000). The child is father of the man: Personality continuities from childhood to adulthood. Journal of Personality and Social Psychology, 78 (1), 158-172 DOI: 10.1037//0022-3514.78.1.158

3 responses so far

The Politics of Ideas : Hauser Gone Wild

Aug 11 2010 Published by under Forget What You've Read!

Well...I had been planning on saving this post for a rainy day, somewhere far, far down the yellow brick road.  And then --as fate would have it-- the Marc Hauser story broke.  All over my windscreen.  For those of you who have somehow missed the train-wreck in progress, these headlines should clue you in:

"Harvard morality researcher investigated for scientific misconduct" (Nature News)

"Investigation of scientist’s work finds evidence of misconduct, prompts retraction by journal" (Boston Globe)

"Harvard U. Finds Evidence of Scientific Misconduct by Professor" (Chronicle of Higher Ed.)

(New Scientist even decided to dub it #Hausergate.  Ha.)

Hauser is -- as I'm sure many of you already know -- a big name in the field and has collaborated with even bigger names : among them, Noam Chomsky, Gary Marcus, Susan Carey, Antonio Damasio, and dozens more.  If you read his publications list, it's a veritable who's who of psychology today.  Which begs the question -- how did no one know this was going on?

It's the wrong question to ask.  Because -- in all honesty -- people must have known, and they must have known for a while.

Harvard, I can assure you, did not want to put one of their own out to dry.  They have one of the best psychology departments in the world and this is the worst press imaginable.  And in all seriousness -- what university wants to lead one of its best and brightest to the gallows, while admitting, shame-faced, to being cuckolded the entire time?  That it took them three years to finally oust him is telling.

All I can say is : it must have been egregious.

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42 responses so far

Eat Yer Spinach! ...and other tales from Bangkok

Aug 10 2010 Published by under Blogging on Peer-Reviewed Research

As was pointed out this past weekend, even Cookie Monster readily admits that fruits and vegetables (especially eggplant, for Dr. Cookie) are important components of any healthy diet. Yet children and adults routinely consume far fewer servings of fruits and vegetables than are recommended. Recent data from Thailand suggests that preschoolers and school-age children eat less than one serving each of fruits and vegetables daily, more than seventy percent below the minimum recommendation. Since early dietary habits tend to persist into adolescence and adulthood, it follows that an intervention in early childhood could have a major effect on future health and life quality by adulthood.

ResearchBlogging.orgA group of researchers from Mahidol University in Bangkok designed an intervention program to teach healthy eating habits to children in kindergarten (age 4-5). The program consisted of 11 activities, each 30-40 minutes long, implemented during school hours over the course of eight weeks.

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10 responses so far

A Thinking Machine: On metaphors for mind

The real question is not whether machines think but whether men do. The mystery which surrounds a thinking machine already surrounds a thinking man.”–B. F. Skinner.

The study of mind begins with a metaphor.

In the 20th century (and now on into the 21st) the metaphor that has dominated our study of mind is the computational metaphor.  The mind, they say, is like a computer.

But in what way like a computer?  In what respect, and in which dimensions?

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24 responses so far

Blind Item: Cookie Monster!

Aug 08 2010 Published by under Blind Item

As a child, my favorite googley-eyed muppet on Sesame Street was Cookie Monster. For those not in the know, chocolate chip cookies are his favorite kind and oatmeal cookies are his second favorite. Showing awareness of healthier habits, since 2006 he has said that cookies are "a sometime snack" and that he also enjoys fruits and eggplant.

But Cookie Monster didn't always love cookies. In one song, he revealed what name his parents had given him, before he discovered his love for cookies.

One point to the person who correctly identifies Cookie's original name in the comments of this post. An additional point for identifying the individual who first provided Cookie's voice, for over thirty years. Remember: No googling for the correct answers! The first correct answer for each question wins. Winners need not answer both questions to earn points.

As a reminder, you can keep track of all blind items and trivia questions, and keep score, by clicking on the Trivia Scorecard and Rules page, above.

16 responses so far

What You Missed: This Week's Series on Delay of Gratification

Aug 08 2010 Published by under Links Best Served Cold, What You Missed

This week, we did a series on Delay of Gratification and Walter Mischel's classic cookie task.

If you're just getting started now, the best place to begin is with Jason's hilarious video post on the task itself.  Then onto the series:

1.  The Room: Self Control and the Classic Cookie Task

2. A Cognitive Primer: Cognitive Control and Neural Architecture

3. The Defenestration of Cookie: Throwing Cognitive Control out the Window?

4. Does Self Control Determine Class?

5. In Sum, Dear Reader

From the Melodye Files, there was a bittersweet tale of tears and triumph, circa 1989.  Then downloaded straight from Jason's brain, we had a fascinating look at historical perspectives on social development.   You might also enjoy our writerly blind item on a bed-wetting British essayist (for the curious, the answer is revealed at the end of the comments).

Still hungering for more?

Last year, Jonah Lehrer did an engaging piece for the New Yorker on Walter Mischel that should intrigue.  And given all the talk about class that got bandied about, you may be interested in hearing about "The Persistence of Poverty," by philosopher Charles Karelis (link is to Mind Hack's write up, which is a great starting point).

My friend, Jason K., has also rightly pointed out the excellent work of Harvard economist Roland Fryer, and in particular his papers "It May Not Take a Village: Increasing Achievement Among the Poor" and "Are High-Quality Schools Enough to Increase Achievement Among the Poor? Evidence from the Harlem Children’s Zone."

Signing off from the city of angels,

Melody & Jason

One response so far

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