Archive for: August, 2010

Blind Item : A girl, a rock & a rabbit

Aug 31 2010 Published by under Blind Item

At the beginning of the last decade, a famous linguist wrote :

“To say that “language is not innate” is to say that there is no difference between my granddaughter, a rock, and a rabbit. In other words, if you take a rock, a rabbit, and my granddaughter and put them in a community where people are talking English, they’ll all learn English. If people believe that, then they’ll believe language is not innate. If they believe that there is a difference between my granddaughter, a rabbit, and a rock, then they believe that language is innate.”

Who is s/he?  +1 If you can link to the relevant Ali G episode.  +2 If you can explain why this statement profoundly mischaracterizes the rationalist – empiricist debate in language.  Hint : Scholz & Pullum may have the answer...

9 responses so far

The Long Tail of Language

Aug 31 2010 Published by under Forget What You've Read!, From the Melodye Files

“The truth is rarely pure and never simple.  Modern life would be very tedious if it were either, and modern literature a complete impossibility!”
–Oscar Wilde, The Importance of Being Earnest

My apologies to readers who may be wondering when the promised series would materialize.  The weekend was spent taking snaps of Laura La Rue and drinking double-digit vino in the kitchen with Professor Plum and Miss Scarlet.  If this science-thing doesn’t work out, I’m off to join the jet-set.  I’m still wondering if it’s possible to style myself after a desperately bespectacled Grace Kelly?

(More on that later…)

In any case : in today’s posting, I take up a rather curious property of human languages that you may have never properly been introduced to.  And that property is Zipfian.

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5 responses so far

Why dictionaries don't supply meaning : Miller on communication

Aug 26 2010 Published by under Forget What You've Read!

At the moment, I am taking a (temporary) break from my furious critiquing of peer review, and have begun working busily on a new series about the workings of human languages.  Writing about this is for a general audience is hard, particularly because I suspect that many people have unexamined intuitive views about language that might be very different from the view I am trying to put forth. Additionally, if you're a linguist, an analytic philosopher, or a psychologist studying language, you will likely have a long-held world view that my writings may challenge.  (It's all rather intimidating, really...)

But in any case, one of the serious puzzles that I'll be piecing together in upcoming posts is how on earth we are able to communicate about the wonderful complexity of the world through a noisy, lo-fi channel (speech).  Some of the most important questions I'll be asking are : How do we understand what someone means through words?  How do we communicate meaningfully through words when we speak?  What is the relationship between words and the world?

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15 responses so far

Eyes Wide Shut : A Field in Search of a Science

Aug 25 2010 Published by under Forget What You've Read!

Today's post is the third in a series on the politics of ideas, and examines the current political climate of psychology and cognitive science.  In earlier posts, I discussed how certain crooked editorial practices can effectively subvert the review process, and how lack of transparency in review breeds precisely the kind of culture that anonymous-review was designed to undermine.  Today, I address the question of why these problems exist in the first place, and explore how changing the culture of review may also change the culture of the field -- for the better.  Enclosed are tales of incest, money laundering, and epicycles.  Count yourself forewarned.  If you would like to skip straight to my practical suggestions, these can be found in the second-to-last section: "Changing the Culture through the Journals."

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19 responses so far

Eyes Wide Shut : The Anonymous Workings of Peer Review

Aug 24 2010 Published by under Forget What You've Read!, Links Best Served Cold

Anonymous

Since my writings on the Hauser controversy several weeks ago, I have watched the scandal unfold with some interest.  This is not least because the post I wrote was subjected to some fairly vicious attacks, both in the comments section and in comments on other blogs.  I was accused of ‘gossip-mongering’ and ‘idle speculation,’ among other, less savory activities.  On one blog, it was even suggested that I had anonymously commented on my own post as a supposed ‘insider’ to lend credence to my story.  (For the record : come on!)

Given the potential fall-out for researchers associated with Hauser, I can understand why tempers might be running hot.  However, one of the things that has interested me throughout the process, is that all of the nastiest comments I’ve received have been anonymous.  Certainly, there have been self-identified researchers who politely disagreed with me or pressed me to justify or clarify certain statements.  Yet, for the most part, hostility arose from the nameless.  Anonymity, it would seem, empowered commentors to lash out against me in a way that I expect they never would in ‘real life’ [1, 2].

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47 responses so far

What You Missed: A Mathy Roundup

Aug 22 2010 Published by under Links Best Served Cold

While Melody was enjoying Portland following the Cognitive Science conference, Jason took you on a mathematical tour of the mind and brain. This week we did a series on numerical cognition and developmental dyscalculia.

If you're just getting started now, might we suggest checking them out in order:

1. The Developmental Origins of Numerical Cognition

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.

2. What is Dyscalculia? How Does It Develop?

A more recent definition according to the DSM-IV-R is offered as well, which defines developmental dyscalculia as a learning disability in mathematics, the diagnosis of which is established when arithmetic performance is substantially below that expected for age, intelligence, and education.

3. Developmental Dyscalculia Explained: Strategy, Memory, Attention

Experimental studies of developmental dyscalculia and math disability in children have focused primarily on skill development in arithmetic, which can be divided into two sections: counting knowledge, and strategy and memory development.

4. Numbers on the Brain: Neurobiology of Mathematics

Depending on task demands, we speculate that this core quantity system, analogous to an internal “number line,” can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

For an evolutionary perspective, there were two companion pieces this week at The Thoughtful Animal:

5. What Are The Origins of Large Number Representation?

Surely, humans have something unique that allows us to do things like multivariate regression and construct geometric proofs, however, but let's start at the beginning. I will hopefully convince you that there is an evolutionarily-ancient non-verbal representational system that computes the number of individuals in a set. That knowledge system is available to human adults and infants (even in cultures that don't have a count list), as well as to monkeys, rats, pigeons, and so forth.

6. The Origins of Small Number Representation

Small numbers do not need to be counted or estimated; instead, they are subitized. Upon seeing a scene with a small number of objects you have a sudden, immediate sense of how many objects there are. This happens in parallel rather than serial- you do not need to count the items individually. Therefore, judgments made about displays of 1, 2, 3, or 4 items are rapid, accurate, and confident. As the number of items in the scene increases, judgments are increasingly less accurate and made with less confidence.

And if you haven't had quite enough child development this week, here are a few more links to whet your appetite:

From the Washington Post: Working Mothers Not Necessarily Harmful to Child Development

Should kids be walking to school instead of driving?

Childhood memories of dad might help men effectively cope with stress later in life.

Does Parenting Rewire Dads? A fascinating article in Scientific American by Brian Mossop

Parents' mental health suffers when children struggle. No surprise there, really.

Are today's superheroes sending the wrong message to boys?

For today's dose of kids are cruel: Kids who squint are less likely to be invited to peers' birthday parties.

From the New York Times: What Is It About 20-Somethings? Is "emerging adulthood" a new developmental stage? And a response in Slate.

Signing off from the city of angels,

Melody & Jason

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Numbers on the Brain: Neurobiology of Mathematics

Aug 19 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. Here is part 4 in a week-long series on this lesser-known learning disorder.


ResearchBlogging.orgCase-studies of patients with various brain lesions have demonstrated the dissociation of different calculation elements, thereby supporting the assumption that numerical ability represents a multifactor skill, requiring the participation of different abilities across diverse brain areas. Mathematical and arithmetic abilities can be impaired as a result of language, spatial, or executive deficits:

  • Anarithmetia could be interpreted as a defect in understanding how the numerical system works, and is associated with damage to the left angular gyrus. Damage to the left angular gyrus is also associated with Gerstmann’s syndrome, which combines dyscalculia with finger agnosia (and results in an inability to count on one’s fingers), as well as dysgraphia and right-left disorientation. When electrical stimulation is applied to the angular gyrus in otherwise normal individuals, they present with signs of Gerstmann’s syndrome.
  • Patients with acalculia in Broca’s aphasia present with errors in the syntax of calculation. That is, they present “stack errors” (e.g. 14 is read as 4). While counting forward is not affected, counting backward, which relies more on verbal sequencing is impaired. Errors in converting numbers from verbal code to numerical code are present (e.g. “three hundred and seven” to 307), as are hierarchical errors (e.g. patients do not understand the difference between the two instances the word “hundred” appears in “three hundred thousand, two hundred fifty seven”). As this is associated with Broca’s aphasia, it is associated with the left inferior frontal gyrus.
  • Patients with acalculia in Wernicke’s aphasia present semantic and lexical errors in saying, reading, and writing numbers. However, simple mental arithmetic operations are errorless. Like in Broca’s aphasia, most of the errors that present in this case are language related. As these symptoms are associated with Wernicke’s aphasia, the left posterior superior temporal gyrus is implicated.
  • Patients with spatial acalculia have no difficulties in counting or in performing successive operations. However, some fragmentation appears in reading numbers (e.g. 523 becomes 23), resulting from left hemi-spatial neglect. Reading complex numbers is also prone to errors, as the spatial position of each digit relative to the other digits becomes important: 1003 becomes 103, 32 becomes 23, or 734 becomes 43. When writing, patients can't line up numbers in columns, creating difficulty in arithmetic calculation. Moreover, digit iterations are frequent (e.g. 27 becomes 22277), as are feature iterations (e.g. 3 is written with extra loops). The patient might have a full understanding of “carrying over” in subtraction, but be unable to find the proper location to write the number.
  • Patients with frontal (executive function) acalculia have damage in the pre-frontal cortex. These patients typically present with serious difficulties in mental arithmetic operations, successive operations (particularly subtraction), and solving multi-step numerical problems. They generally also have serious disturbances in applying mathematical knowledge to time (e.g. they could not tell you if America was founded closer to 10 years ago or to 200 years ago). When aided by pencil and paper, however, most of these patients do not commit errors.

Dehaene and colleagues carried out a series of fMRI investigations, in which they found a set of parietal, prefrontal, and cingulate areas which were reliably activated by patients undergoing mental calculation. They’ve also implicated the left and right fusiform gyri and occipito-temporal regions in recognizing visual number forms. The angular gyrus was activated by digit naming tasks as well as mental multiplication. This was demonstrated by a study in which a normal patient’s angular gyrus was electrically stimulated, which disrupted multiplication.

A brain region that has received lots of attention in dyscalculia research is the horizontal segment of the intraparietal sulcus (HIPS), in both hemispheres. Activation of the right and left HIPS has been seen during basic calculation tasks as well as digit detection tasks. Further, is it multi-modal, responding equally to spoken words and written words, as well as Arabic numerals. Right HIPS activation has also been seen in tasks where subjects estimate the numerosity of a set of concrete visual objects. Electrical stimulation of the anterior left HIPS disrupted subtraction. One study found a left IPS reduction in grey matter in children with developmental dyscalculia at the precise coordinates where activation is observed in normal children during arithmetic tasks.

One study conducted by Molko and colleagues studied individuals with Turner Syndrome, a genetic condition associated with the X-chromosome, which is associated with abnormal development of numerical representation. In the right IPS, a decrease in depth as well as a trend toward reduced length was observed for Turners patients when compared with control subjects.

Despite the relative inter-subject irregularity of cortical geometry, there are general consistencies found in normal individuals. For example, the anterior-posterior orientation of the IPS, its downward convexity, as well as its segmentation into three parts, was observed in all non-impaired individuals. In contrast, the right intraparietal sulcal pattern of most subjects with Turner Syndrome did not conform to those patterns, due to aberrant branches, abnormal interruption, or unusual orientation. For example, the three segments were only observed in 7 of 14 Turner Syndrome subjects, while the downward convexity was only seen in 3 of 14.

In agreement with the fMRI findings of the Dehaene study, during exact and approximate calculation tasks, Molko found reduced activation in the right IPS as a function of number size. Similar fMRI under-activations were found in a broader parieto-prefrontal network in two other genetic conditions associated with developmental dyscalculia: fragile X syndrome and velocardiofacial syndrome.

Taking all this fMRI data together, Dehaene offered a tripartite organization for number processing in the brain:

The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal “number line,” can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

Get Your Literature On
Ardila A, & Rosselli M (2002). Acalculia and dyscalculia. Neuropsychology review, 12 (4), 179-231 PMID: 12539968

Dehaene, S. (2004). Arithmetic and the brain Current Opinion in Neurobiology, 14 (2), 218-224 DOI: 10.1016/j.conb.2004.03.008

Isaacs EB, Edmonds CJ, Lucas A, & Gadian DG (2001). Calculation difficulties in children of very low birthweight: a neural correlate. Brain : a journal of neurology, 124 (Pt 9), 1701-7 PMID: 11522573

Molko N, Cachia A, Rivière D, Mangin JF, Bruandet M, Le Bihan D, Cohen L, & Dehaene S (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40 (4), 847-58 PMID: 14622587

Dehaene, S, Piazza, M, Pinel, P, & Cohen, L (2003). Three Parietal Circuits for Number Processing Cognitive Neuropsychology, 20, 487-506

3 responses so far

Blind Item: The (magical?) verbal behavior of children

Aug 18 2010 Published by under Blind Item

In 1951, a renowned American psychologist wrote the following:

"What factors in a child's background and environment are associated with the rapid development of speech? Girls have a slight advantage over boys in their speed of development in nearly all the aspects of language that have been studied. ...Children in families with low incomes tend to be neglected, and their linguistic retardation is the most noticeable aspect of their generally retarded development. Children in more favored homes develop speech much faster. Children who are associated primarily with adults develop rapidly, and thus single children outstrip children with many brothers and sisters. Children from multiple births and children from polylingual homes are often retarded."


Who is he?

Hint: The title of the paper he's famous for contains the word "magical." (Dead giveaway, yes?)

Brownie points if you can identify which of these views have withstood the test of time and which have not.

5 responses so far

Developmental Dyscalculia Explained: Strategy, Memory, Attention

Aug 18 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. Here is part 3 in a week-long series on this lesser-known learning disorder. (See parts one, and two, and a companion post at The Thoughtful Animal)

Cognitive Explanations for Developmental Dyscalculia: Strategy, Memory, Attention

Strategy
ResearchBlogging.orgExperimental studies of developmental dyscalculia and math disability in children have focused primarily on skill development in arithmetic, which can be divided into two sections: counting knowledge, and strategy and memory development.

Counting is governed by five principles:

  • the one-to-one correspondence rule, where one word is assigned to each counted object;
  • the stable order rule, where the order of counting words must be stable across different sets of counted objects;
  • the cardinality rule, which states that final counting word assigned represents the total number of objects in a set;
  • the abstraction rule, which states that objects of any kind can be counted;
  • the order irrelevance rule, which states that items in a set can be counted in any order.

A mastery of counting is essential to the discovery of the most efficient strategies for basic arithmetic procedures such as addition and subtraction, and later, multiplication and division.

In many models of cognitive development, it is thought that children think or behave a certain way under certain rules for an extended period of time. Then, they undergo a brief and sometimes mysterious transition and begin to act and think in a new way. Robert Siegler, however, prefers to conceptualize developmental change as variable and gradual, with multiple different strategies available to a child as the child’s brain matures. There are, naturally, some problems where there is really only one logical or efficient strategy. Indeed, after some time experimenting with different strategies, both in progressive and regressive directions, most children will focus on the best, most logical strategy, and lock onto it for much of the remainder of their lives.

It makes sense that the normally developing child will use a variety of different strategies when faced with the same or similar problems. For example, there are at least three common strategies that children can use for addition. The most efficient is direct fact retrieval: 3 + 3 always equals 6. Another is the min strategy, where kids count up from the larger number: 9 + 2 = (9 + 1) + 1 = 10 + 1 = 11. A third is decomposition into easily manipulated numbers: 19 + 22 = 19 + 20 + 2 = 39 + 2 = 41. Typically-developing children will ultimately lock into one of these or another strategy when faced with a random addition problem.

Artist's Rendition of Siegler's Strategy Choice Model

Given Siegler's model, we might hypothesize that children who have been diagnosed with dyscalculia may be unable - for any of a number of reasons - to settle on the optimal problem-solving strategy. While this does not preclude children from gaining efficiency over a long period of time, it is likely to leave them lagging behind the rest of their peers, significantly slowed down by the wide variety of problem-solving strategies available to them. Indeed, empirical evidence shows that children with developmental dyscalculia are generally two grade levels below their peers in arithmetic and mathematics.

Memory
After the period of exploration in which the child eventually uncovers the best problem-solving strategies, the mastery of elementary arithmetic is achieved when all basic facts can be retrieved from long-term memory without error. Mastery of basic arithmetic is crucial to later competence in more complex mathematical operations such as long division, fractions, geometry, calculus, and so on. Therefore, even if a child has successfully discovered the most efficient strategy, deficits in memory could lead to disabilities in arithmetic and mathematics.

When a computation is executed, the probability of direct retrieval increases for each subsequent solution to the same problem. However, in order for the execution of a computational strategy to lead to the construction of a long-term memory representation between a problem and its solution, both the equation’s augend (i.e. the first number) and addend (i.e. the second number), as well as the answer, must all be simultaneously active in working memory. Thus, arithmetic and mathematical ability is directly related to the function (or dysfunction) of the working and long-term memory stores.

In order to create a long-term memory for an arithmetic fact, such as 13 + 7 = 20, an individual must be both proficient (i.e. accurate) and efficient (i.e. speedy). Proficiency is important because if the child commits many computational errors, then the child is more likely to retrieve incorrect answers from long-term memory when later presented with the same problem. Efficiency is likewise important because with slow counting speed, the working memory representation of the augend is more likely to decay before the addend and solution have been fully represented. Under these circumstances, even if the child reaches the correct answer, its association with the rest of the equation in long-term memory will be weak.

Each of these possibilities have been found observationally as well as experimentally:

Cognitive studies indicate that when solving arithmetic problems, in relation to their normal peers, [mathematically disabled] children tend to use immature problem-solving strategies, have rather long solution times, and frequently commit computational and memory-retrieval errors. (Geary, 1993)

Brian Butterworth further refines the role of working and long-term memory in the storage of arithmetic facts by presenting evidence that retrieval times show a very strong problem-size effect for single-digit problems: the larger the sum or product, the longer it takes to solve. Further, adults without any mathematical disability are quicker to solve an equation in the form of “larger addend” + “smaller addend” than they are to solve the same equation where the addends are reversed. Similarly, non-impaired Italian children age 6-10 took longer to solve a “smaller” x “larger” multiplication problem than a “larger” x “smaller” equation, despite the fact that the Italian education system teaches “smaller” x “larger” first (e.g. the 2x multiplication table is learned before the 6x multiplication table). Both of these findings reflect the limitations of counting speed on arithmetic problem-solving. This seems contradictory to the earlier theory, which suggests that equations with which you have more experiences are more strongly stored in long-term memory – since the 2x arithmetic facts were presumably encoded into long-term memory well before the 6x arithmetic facts. This finding suggests more complex numerical organization to the storage and representation of arithmetic facts in long-term memory, beyond rote association.

Information processing theory offers yet another model for the role that the function or dysfunction of working and long-term memory has in the pathology of developmental dyscalculia and other mathematical impairments. Central to information processing theory is the idea of limited capacity: the human mind has only a finite capacity for information processing at any one time. A fundamental assumption to this theory is that each type of mental process takes up some amount of the “space” or “energy”. At one extreme are automatic processes, which require virtually no space or energy. These processes work without intention or conscious awareness, don’t interfere with other processes, don’t improve with practice, and are not influenced by intelligence, education, motivation, or anything else. Examples include breathing and sweating. On the other end of the continuum are effortful processes, which use up the resources available in working memory, and have the opposite properties of automatic processes.

When confronted with an arithmetic task, a nonimpaired student can complete the task with fairly efficiently – even if the solution isn’t accessed via direct fact retrieval. For a student with math disabilities, however, the process is laborious and takes a significant amount of energy. When a nonimpaired student is confronted with a straightforward arithmetic problem such as 5 + 11 + 37, the student can quickly identify the steps needed to solve the equation and move on to the next item on the worksheet. When a mathematically disabled student is confronted with the same problem, even after having learned and understood the fundamentals of counting and addition, each of the steps necessary to compute the answer takes up significantly more effort to complete. By the time the student moves on to the next item on the assignment, he has already expended a considerable amount of mental energy - significantly more than the first student has - and has likely taken more time to complete each problem. After the first three or four items, his or her energy store is perhaps depleted, and the rest of the worksheet is riddled with errors because the student has no mental energy left to tackle the subsequent calculations.

Attention
Also associated with information processing theory is inhibition, which is the active suppression of irrelevant sensory input. Related to this is the idea of resistance to interference, or attention, which is the ability of an individual to concentrate on “central” information and ignore “peripheral” information. Normally-achieving students can complete an arithmetic worksheet in a noisy classroom with minimal distraction, and accuracy is usually quite high. Students with developmental dyscalculia, however, may have issues with processing due to a deficit in inhibition.

Peter Rosenberger found evidence that low achievement in math is related to attentional deficits. He tested 102 children in one study of paper-and-pencil tests and questionnaires; those children for whom the math achievement quotient was below 100, the reading achievement quotient above 100, and the difference between the two was 20 points or greater were designated “dyscalculic.” Children who met the opposite criteria were designated “dyslexic.” Seventy-two children qualified as dyscalculic, and thirty qualified as dyslexic. The groups were highly comparable in overall scholastic aptitude; in fact, only the arithmetic score could distinguish the two groups**.

He found that the “freedom from distractibility” quotient of the Weschler scale was lower for the dyscalculics, although this was confounded with the score of the arithmetic subtest. Of four factors calculated from the DSM-III questionnaire that each participant received, only the factor of inattention was statistically different between the groups, and was higher for dyscalculics. Rosenberger thus suggests that specific math underachievement is, in at least some cases, the result of failure of children with attention deficits to automatize number facts in the early grades. If true, he writes,

this finding would suggest that [an attentional deficit] is not merely an additive or aggravating factor in problems with math performance, but in fact interferes with the development of aptitude for this skill [in the first place].

**Which makes me wonder why he chose to discuss dyslexia in the first place.

Get Your Literature On
Gallistel CR, & Gelman R (1992). Preverbal and verbal counting and computation. Cognition, 44 (1-2), 43-74 PMID: 1511586

Siegler, R. (1994). Cognitive Variability: A Key to Understanding Cognitive Development. Current Directions in Psychological Science, 3 (1), 1-5 DOI: 10.1111/1467-8721.ep10769817

Geary, D. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114 (2), 345-362 DOI: 10.1037/0033-2909.114.2.345

Butterworth, B. (2005). The development of arithmetical abilities Journal of Child Psychology and Psychiatry, 46 (1), 3-18 DOI: 10.1111/j.1469-7610.2004.00374.x

Rosenberg PB (1989). Perceptual-motor and attentional correlates of developmental dyscalculia. Annals of neurology, 26 (2), 216-20 PMID: 2774508

7 responses so far

What is Dyscalculia? How Does it Develop?

Aug 17 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. Here is part 2 in a week-long series on this lesser-known learning disorder. (See part one, and a companion post on comparative numerical cognition in humans and animals at The Thoughtful Animal)

Developmental Dyscalculia: Definition, Prevalence, and Prognosis

ResearchBlogging.orgIf we're going to seriously discuss a developmental learning disorder, the first thing that might be done is to define it. Ruth Shalev and colleagues, from the Shaare Tzedek Medical Center in Jerusalem, have provided two different definitions for developmental dyscalculia. First, they offer that developmental dyscalculia is a specific, genetically determined learning disability in a child with normal intelligence. The usefulness of this definition, however, is limited when it comes to differentiating students with dyscalculia and students who are simply weak in arithmetic. A more recent definition according to the DSM-IV-R is offered as well, which defines developmental dyscalculia as a learning disability in mathematics, the diagnosis of which is established when arithmetic performance is substantially below that expected for age, intelligence, and education.

Prevalence studies have been carried out in various parts of the world, all with (surprise!) different definitions for developmental dyscalculia. Despite the definitional inconsistency, the prevalence of developmental dyscalculia across countries is fairly uniform, at about 3-6% of the school population. That percentage is similar to the the prevalence of other developmental learning disorders, such as developmental dyslexia and attention deficit/hyperactivity disorder (ADHD).

The manifestation of developmental dyscalculia generally changes with age and grade. First graders (age 5-6) typically present with problems in the retrieval of basic arithmetic facts and in basic computational exercises. By the time children reach age 9-10, they've finally mastered counting skills, are able to match written Arabic numerals to quantities of objects, understand concepts of equivalence or inequivalence, and understand the ordinal value of numbers. They also are generally proficient with handling money and understanding the calendar, two skills which require basic arithmetic proficiency. Instead, children diagnosed with developmental dyscalculia at this age present with deficits in the retrieval of overlearned information such as multiplication tables. In an attempt to bypass their difficulty in solving basic arithmetic problems, these children will use inefficient strategies in calculation. Errors typically include inattention to the mathematical operator, use of the wrong sign, forgetting to “carry over,” or misplacement of digits.

The best kind of study of a developmental learning disorder is one in which the same groups of individuals are studied over the course of months or years, in what is called a longitudinal study. Choose your favorite overused analogy: longitudinal studies are the gold standard, the holy grail, the raison d'être of developmental scientists. Longitudinal studies of dyscalculia, however, are few and far between, so not much is known about the prognosis of those individuals who are diagnosed with developmental dyscalculia. In one short longitudinal study, Shalev and her colleagues examined a group of 140 ten and eleven year old children who had developmental dyscalculia, and reexamined them at age thirteen and fourteen. Their performance, after three years, was still poor, with 95% of the group scoring in the lowest quartile of their school class. Fifty percent continued to meet the research criteria for developmental dyscalculia. The group did a second follow-up in 2005, when the group was finishing high school, at age sixteen and seventeen:

  • 51% of the group could not solve 7x8 (versus 17% of controls);
  • 71% could not solve 37x24 (versus 27%);
  • 49% could not solve 45x3 (versus 15%); and
  • 63% could not solve 5/9 + 2/9 (versus 17%).

Forty percent of the group scored in the lowest fifth centile for their grade; ninety-one percent in the lowest quartile. Children whose diagnosis of developmental dyscalculia had persisted also presented with more behavioral and emotional problems than those who no longer qualified for the diagnosis. These problems included anxiety/depression, somatic problems, withdrawal, aggression, and delinquent behavior. Cognitive factors associated with persistent developmental dyscalculia were lower IQ, inattention, and writing problems.

Unlike dyslexia, ADHD, and other learning disorders, which affect more males than females, developmental dyscalculia shows a more equal distribution between the sexes. To date, no convincing answer has been offered for why the usual predominance of boys is not observed for developmental dyscalculia. Many researchers have attributed other non-neurological factors to the etiology of developmental dyscalculia*, some of which may preferentially impact girls more than boys, including lower socioeconomic status, mathematics-induced anxiety, overcrowded classrooms, and more mainstreaming in schools. Differential treatment towards girls by math teachers is also a potential confound.

*This brings up an important point for any psychopathology, which is the notion of equifinality. When a pathology (such as dyscalculia, but also e.g. depression, social anxiety, schizophrenia, any of the personality disorders, etc), is defined based on presentation of symptoms, there are often multiple biological and experiential trajectories that can result in such an outcome. One subset of individuals who are diagnosed with dyscalculia may possess some genetic variant that impairs their numerical abilities, while another set of individuals may show the same set of symptoms due to environmental factors such as SES or gender. This is why it is so hard to study psychopathology, and why any one variable only accounts for a small amount of the variance in a disorder.

Image source.

Get Your Literature On
Shalev, R., Manor, O., Kerem, B., Ayali, M., Badichi, N., Friedlander, Y., & Gross-Tsur, V. (2001). Developmental Dyscalculia Is a Familial Learning Disability Journal of Learning Disabilities, 34 (1), 59-65 DOI: 10.1177/002221940103400105

Shalev, R., & Gross-Tzur, V. (2001). Developmental dyscalculia Pediatric Neurology, 24 (5), 337-342 DOI: 10.1016/S0887-8994(00)00258-7

Shalev, R., Auerbach, J., Manor, O., & Gross-Tsur, V. (2000). Developmental dyscalculia: prevalence and prognosis European Child & Adolescent Psychiatry, 9 (S2) DOI: 10.1007/s007870070009

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