Archive for the 'Blogging on Peer-Reviewed Research' category

Let's stop mistaking 'thought experiments' for science

Trends in Cognitive Sciences recently published a provocative letter by a pair of MIT researchers, Ted Gibson and Ev Fedorenko, which has been causing a bit of a stir in the language camps.  The letter - "Weak Quantitative Standards in Linguistic Research" and its companion article - have incited controversy for asserting that much of linguistic research into syntax is little more than - to borrow Dan Jurafsky's unmistakable phrase - a bit of "bathtub theorizing."  (You know, you soak in your bathtub for a couple of hours, reinventing the wheel).  It's a (gently) defiant piece of work: Gibson and Fedorenko are asserting that the methods typically employed in much of linguistic research are not scientific, and that if certain camps of linguists want to be taken seriously, they need to adopt more rigorous methods.

I found the response, by Ray Jackendoff  and Peter Culicover, a little underwhelming, to say the least.  One of the more amusing lines cites William James:

"Subjective judgments," they claim, "are often sufficient for theory development. The great psychologist William James offered few experimental results."

Yes, but so did "the great psychologist" Sigmund Freud, and it's not clear whether he was doing literary theory or "science"...  More trivially, James was one of the pioneers of the fields and didn't have access to the methods we now have at our disposal.  That was his handicap - not ours.

We can contrast that (rather lame) response with what computational linguist Mark Liberman said about corpus research last week in the New York Times:

"The vast and growing archives of digital text and speech, along with new analysis techniques and inexpensive computation, are a modern equivalent of the 17th-century invention of the telescope and microscope."

Here, here, Mr. Liberman.  I couldn't agree more.

Last month, Michael Ramscar and I published a seven-experiment Cognitive Psychology article, which uses careful experimentation and extensive corpus research to make something of a mockery of one piece of "intuitive" linguistic theorizing that has frequently been cited as evidence for innate constraints.  Near the end of the piece, we take up a famous Steve Pinker quote and show how a simple Google search contradicts him.  After roundly (and amusingly) trouncing him, Michael writes - in what must be my favorite line in the whole paper -

"Thought-experiments, by their very nature, run into serious problems when it comes to making hypothesis blind observations, and because of this, their results should be afforded less credence in considering [linguistic] phenomena.”

No doubt, this one-liner owes some credit to a brilliant P.M.S Hacker quote (actually a footnote to one of his papers!):

"Philosophers sometimes engage in what they misleadingly call 'thought-experiments.'  But a thought experiment is no more an experiment than monopoly money is money."

Let's stop mistaking 'thought experiments' for science.

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Bad Metaphors Make for Bad Theories

Imagine for a moment, that you have been thrown back into the Ellisonesque world of the 1980’s, with a delightful perm and even better trousers.  One fragile Monday morning, you are sitting innocently enough at your cubicle, when your boss comes to you with the summary of a report you have never read, on a topic you know nothing about.  “I’ve read the précis and I’d love to take a peek at the report," he intones, leaning in.  "Apparently, they reference some fairly intriguing numbers on page 76.”  You stare blankly at him, wondering where this is going.  “Yess—so I’d love if you could generate the report for me.”  He smirks at you expectantly.  You blink, twice, then begin to stutter a reply.  But your boss is already out the door.  “On my desk by five, Susie!” he whistles (as bosses are wont to do) and scampers off to terrorize another underling.

You would be forgiven if, at that moment, you decided it was time to knock a swig or two off the old bourbon bottle and line up some Rick Astley on the tapedeck.

Because the task is, in a word, impossible.

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Language doesn't feature much at the top

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

There is currently a debate raging over at The Economist over whether language shapes thought.  In the latest rebuttal, posted by the whimsical L.B., she makes the claim that:

"These days, scientists do not just make claims, they make measurements. The scientific study of how language shapes thinking comprises decades' worth of empirical discoveries, published in premier academic journals like Science and Nature..."

L.B. makes it sound like the two 'premier' journals regularly devote their pages to the sundry and subtle workings of the Whorfian question.  --Which is a misleading way to make it sound, I assure you.  (If by "like Science and Nature" she means PNAS, there may be slightly more credibility to the claim, but I'll take her at face value for the moment).

In the past year, I've had a number of manuscripts peer-reviewed at these journals, and in the interim, I've spent the time to actually dig through the archives of both journals to find out what work on language they've published over the last decade.  While L.B.'s claim is technically correct, it's also misleading.  The only Whorfian topics that have been published in either journal are to do with numerical cognition in the Pirahã.  'Decades worth' of discoveries have been published in other journals, no doubt, but Nature and Science have devoted relatively few pages to the question of how language shapes thought, or any other topic in language, period.

To give you a flavor: this year, Nature published 0 original research articles on language.  The best they did was a news brief on the genetic basis for stuttering and a feature on speed reading.  Science published 1.  On average, Nature publishes less than 2 a year on language; Science publishes a little over 3.  For Nature, that's 2 out of over 800+ articles published a year.  Clearly a hot topic.

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Bayesian Fundamentalism or Enlightenment?

Dec 05 2010 Published by under Blogging on Peer-Reviewed Research

"Whatever society at large views as its most powerful device tends to become our means for thinking about the brain, even in formal scientific settings. Despite the recurring tendency to take the current metaphor literally, it is important to recognize that any metaphor will eventually be supplanted. Thus, researchers should be aware of what the current metaphor contributes to their theories, as well as what the theories’ logical content is once the metaphor is stripped away."

Jones & Love, 2011

While surfing the web for preprints, I found an upcoming Brain and Behavioral Sciences (BBS) release by Matt Jones and Brad Love which I would highly recommend as thought-provoking, lucid and approachable reading material.  It's entitled : "Bayesian Fundamentalism or Enlightenment?  On the Explanatory Status and Theoretical Contributions of Bayesian Models of Cognition" and it's part intellectual history, part rigorous scientific critique.  I should preface this by saying that I am not a Bayesian modeler, and while I'm acquainted with Bayes' laws and have read some Bayesian papers on language acquisition -- which mostly led to yawning and quiet grumbling about how they'd set up the problem wrong -- I am not in the best position to assess the merits of the arguments in this paper.  So I won't.  I just really liked reading it.  I'm eagerly anticipating the full BBS article, which, I'm assuming, will include responses from Tenenbaum, Griffiths, Chater and the rest of the Bayes high court.  If their replies are anything like their conference demeanor, it's going to be fun..

If you've read this far, and you're not familiar with Bayes' law, the Internet is chalk full of Bayesian fanatics, so a little Googling should find you a decent tutorial, like this one.  I do suggest reading it too : there have been dozens of articles lately in the popular science press about the application of this kind of probability modeling to, for example, medical statistics.

Now, if you're not familiar with the journal, that's something else entirely -- and must be remedied!  BBS is a excellent resource for getting your head around a problem, because it allows researchers to meticulously advance a new claim, or set of claims, and then invites scholars in their discipline to submit a one-page reply.  For scholars and the lay public alike, this is a brilliant means of both highlighting the issue and clarifying the positions at stake.

To get an idea of how this works, it's worth taking a look at this classic Boroditsky & Ramscar (2001) reply to an early Bayesian BBS article.  B&R somehow manage to make the entire contents of the abstract a joke.  (You'll see what I mean).

Excerpts, after the jump:

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The Knobe Effect

As an avid reader of Language Log, my interest was recently piqued by a commenter asking for a linguist's eye-view on the "Knobe Effect":

"Speaking of Joshua Knobe, has any linguist looked into the Knobe Effect? The questionnaire findings are always passed off as evidence for some special philosophical character inherent in certain concepts like intentionality or happiness. I'd be interested in a linguist's take. If I had to guess, I'd say the experimenters have merely found some (elegant and) subtle polysemic distinctions that some words have. As in, 'intend' could mean different things depending on whether the questionnaire-taker believes blameworthiness or praiseworthiness to be the salient question. Or 'happy' could mean 'glad' in one context but 'wholesome' in another, etc…"

Asking for an opinion, eh?  When do I not have an opinion?  (To be fair, it happens more than you might expect).

But of course, I do have an opinion on this, and it's not quite the same as the one articulated by Edge.  This post is a long one, so let me offer a teaser by saying that the questions at stake in this are : What is experimental philosophy and is it new?  How does the language we speak both encode and subsequently shape our moral understanding?  How can manipulating someone's linguistic expectations change their reasoning?  And what can we learn about all these questions by productively plumbing the archives of everyday speech?

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The question is : are you dumber than a rat?

Many developmental psychologists buy into an argument that suggests that children are dumber than rats.  Should you?


Human cognition is geared towards the central task of predicting the world around it.  As you may remember from an earlier post I did on the A-not-B task in infants, children aren't born understanding causal relationships right off the bat -- as a kid, you need to learn that when batter goes into the oven, it comes out as cake; when a dog jumps in water, it comes out wet; and when a shaggy-dog runs dripping through the house, mommy gets mad. As an adult, prediction operates in just about everything you do, from how much you drink at a party (who do you really want to be going home with?) to how hard you push down on the breaks (how fast do you need the car to stop?) to what you think I'm going to say next (yep, there's lots of evidence that you're predicting my words in a manner not wholly unlike Google auto-complete).

One thing that matters immensely in all of this is informativity.  There are many illusory correlations in the world that you might forge -- how do you establish the causal links that matter and are meaningful?

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Why are Zipfian distributions found in language?

This post is a scholarly addendum to today's main post, aimed to satisfy the curiosity of my academic readers.  I'm going to leave you with an excerpt from an excellent book chapter, "Repetition and Reuse in Child Language Learning," by Colin Bannard and Elena Lieven.  The two take up the question of why Zipfian distributions are found in language.  A short suggested reading list with annotations follows.  Please feel free to leave links to other suggested reading in the comments..

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Mollies, PokeBalls, and Naked Ladies : A Topsy-Turvy Lesson in Learning Words from Context

This morning, I scrawled a letter to a friend that began with the following:

Spent the weekend at the FyeahFest with a starry-eyed lot of starving hipsters, in vintage hops and wingtips. Had not realized how obvious the effects of doing molly are on the pupils… the droves wandering past had eyes like shining saucers.

Unlike my trusted ami de plume, you may not know what on the lord's green earth I just said.  In particular,  if you’re not into psychedelics or don’t know anyone who is, you may be wondering just what ‘molly’ is, anyway.  The extraordinary thing is that -- odds are -- even if you’ve never heard the word used before, you can probably wager a pretty good guess as to what it means.

Take a moment.  What’s your bet?

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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

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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

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