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

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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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

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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

Don't Bite: In Sum, Dear Reader

Writing this day by day, rather than all at once, this series has taken a number of twists, turns, and quite frankly, unexpected detours, some of which may have made the underlying logic hard to follow.  (Indeed, to the extent that these posts shed light on the inner workings of my mind, you can tell how frightfully coherent my day-to-day has become.  Frightfully, being the operative word…)

In any case, in this, my last ‘science’ post on the subject, I want to revisit some of the topics we’ve discussed, and clarify and expand on others, so that you may leave this series having learnt something – either about me, or self-gratification, or cookies, at the very least.

What was it we learned, after all?

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Don't Bite: Does Self Control Determine Class?

Just to be clear, we'll be talking here about class, folk psychology, and my high school math teacher.  But as ever, I've buried the lead.  Now for some recap, before we get on to the good stuff --

In the last post, we found that the behavior exhibited in the classic cookie task is more strongly linked to vocabulary development than it is to cognitive control. This suggests that what's dictating behavior in the task can't simply be explained by appeal to the child's particular cognitive architecture. Rather, how long children hold out appears to be largely a function of their verbal skills.  One conclusion we might draw from this is that how children perform in the task is related to their ability to verbally strategize.

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Don't Bite: The Defenestration of Cookie

III. Whither the Cookie Task?

WARNING: What you are about to read may contain graphic statistical content.  Side effects may include: contagious yawning, inappropriate arousal, and / or spontaneous combustion, depending on how you like your math cooked... darling.

Psychologists often think about the cookie task as a test of cognitive control, and in keeping with this, tend to assume that it is a measure both of prefrontal maturity, and of executive brain function, more generally.  The idea, then, is that non-delayers are unable to delay gratification – in the same way that three-year olds are unable to switch – because their frontal lobes simply aren’t as serviceable.  Indeed, in the 2006 Psych Science paper that brought this idea to the big screen, the authors suggested that “performance in the delay-of-gratification task may serve as an early marker of individual differences in the functional integrity of [fronto-striatal] circuitry.”

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Don't Bite: A Cognitive Primer

II.  Cognitive Control and Neural Architecture

This is the second in a series of posts on "delay of gratification."
Access #1

In the developmental literature, cognitive control is a technical term that denotes the ability to flexibly choose one response over another, based on goals or context.  This may sound suspiciously like good old-fashioned “self control,” but there’s a hitch:  when psychologists talk about whether or not a child has cognitive control, they're referring to a particular stage of cortical development and a particular type of executive function.  Turns out that the ability to flexibly choose between responses typically doesn't develop in children until around the age four, and it’s related to the developmental trajectory of their frontal lobes – specifically, a bit of brainware called the prefrontal cortex, or PFC [1].
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Don’t Bite: Self Control and the Classic Cookie Task

I.  The Room

Imagine you're four years old.  A tall lady takes you by the hand and leads you into a small white room.  She seats you at a table by yourself, and kneeling down beside you, produces a fresh-baked chocolate chip cookie from her apron pocket.  "We're going to play a little game," she explains kindly.  "You can either eat the one cookie now, or, if you wait, I'll bring a second cookie soon, and you can eat both of them."  But what happens, you ask, if you want to eat the first cookie now?  "Well... then you only get one cookie, sweetie."

At which point you decide: this lady sucks.

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