Understanding Dyscalculia - the Math Learning Disability

According to the LDA:

Signs and Symptoms of Dyscalculia

- Shows difficulty understanding concepts of place value, and quantity, number lines, positive and negative value, carrying and borrowing
- Has difficulty understanding and doing word problems
- Has difficulty sequencing information or events
- Exhibits difficulty using steps involved in math operations
- Shows difficulty understanding fractions
- Is challenged making change and handling money
- Displays difficulty recognizing patterns when adding, subtracting, multiplying, or dividing
- Has difficulty putting language to math processes
- Has difficulty understanding concepts related to time such as days, weeks, months, seasons, quarters, etc.
- Exhibits difficulty organizing problems on the page, keeping numbers lined up, following through on long division problems

Recent fMRI studies found that dyscalculic school children were significantly disadvantaged in terms of their 'number sense' - estimating the number of objects on a computer screen, for instance. Without a strong sense of quantity, no wonder calculations and estimations are so hard. Although dyscalculia has been suggested to be as common as dyslexia, it is rarely recognized and failing or

From The New Scientist:

"Jill, 19, from Michigan, wants to go to university to read political science. There is just one problem: she keeps failing the mathematics requirement. "I am an exceptional student in all other subjects, so my consistent failure at math made me feel very stupid," she says. In fact, she stopped going to her college mathematics class after a while because, she says, "I couldn't take the daily reminder of what an idiot I was."

Last November, Jill got herself screened for learning disabilities. She found that while her IQ is above average, her numerical ability is equivalent to that of an 11-year-old because she has something called dyscalculia. The diagnosis came partly as a relief, because it explained a lot of difficulties she had in her day-to-day life. She can't easily read a traditional, analogue clock, for example, and always arrives 20 minutes early for fear of being late. When it comes to paying in shops or restaurants, she hands her wallet to a friend and asks them to do the calculation, knowing that she is likely to get it wrong."

Low math scores can prevent admission to highly selective schools, block high school graduations, and close out careers, but isn't this a mistake?

Famous Scientists and Mathematicians with Dyscalculia

"- Thomas Alva Edison belong to bad pupils, he never mastered skills like writing, spelling,
and even arithmetic.
- The physicist George Gamov is described in My World Line by his student, a famous
astronomer, Vera Rubin in the following way: “He could not write or count. It would take him
a while to tell you how much is 7 times 8. However, his mind was able to comprehend the
universe.”
- Mathematician N. N. Luzin belongs to people with a slow reaction. He also developed
slowly, he did not succeed in school, especially in mathematics."

Other dyscalculic mathematicians come to mind, like David Hilbert, one of the greatest mathematicians of the last century who was notoriously bad at arithmetic and an anecdote in which he had to ask whether 7 + 5 was 12 or 13.

From The Mathematical Brain about the overlap between Dyscalculia and Dyslexia:

Dyscalculia seems to be particularly rife among dyslexics, with
around 40% of children with reading difficulties also having
difficulties in learning maths. This is a double whammy for
them. It is also a serious puzzle for science. After all, the other
60% have no more problems than normal. Indeed, dyslexics can
be outstanding mathematicians. What is the difference between
those dyslexics who do suffer from dyscalculia and those who
do not? What is it about dyslexics that puts them at risk of
dyscalculia at all?

Recently, researchers at Stanford published this article on the gray and white matter differences between dyscalculic and typically developing children. The children were matched for IQ and working memory, and significant overlaps with dyslexia were seen (cerebellum and fusiform gyrus / visual word form recognition). The science is helpful for understanding that dyscalculia is a real biological entity, but an enormous gulf still exists in terms of how best to identify students with the LD and better, how to help them.

From The Dyslexic Student and Mathematics in Higher Education (abstract)"

-diagrams and mind maps to represent ideas
- color areas under curves
- label the y-axis on both sides to reduce the chance of losing place
- mnemonics (sine rhymes with line) for definitions and formulae
- Comic Sans font, cream background to reduce glare
- note-keeper, record lectures
- knowing why a method worked (proofs)
- learn each step individually and give each step a label
- custom graph paper
- sticks to cover rows not being used for matrix work
- simple 3D model when doing 2D to 3D transformations
- extra time to read problems, highlight key words

For elementary math:

- work with a solved problem in view
- work 'open-book' with math facts charts, number line, or other reminders
- use personal memory mnemonics for math facts like Memorize in Minutes or Addition the Fun Way
- dictate answers
- color code columns
- label steps

References and Resources:
Dyscalculia, Mathematicians
Dyscalculia Forum
Dyslexic Advantage Network
Thesis on Dyscalculia pdf

Impaired Perception of Fear Gestures in Autism

When people with autism looked at the gestures of others associated with fear, certain areas like the superior temporal sulcus (observation of goal-related gestures) had the same activation patterns as non-autistic controls, but much lover levels of activity were seen in areas such as the amygdala (emotional recognition) and putative sites of mirror neurons like the inferior frontal gyrus and dorsal premotor cortex.Problems recognizing signs of threat or fear in others means that individuals on the spectrum are at increased risk for a wide variety of difficulties, like becoming too friendly with strangers, wandering beyond familiar areas, or not recognizing dangerous situations.

The finding in this study that superior temporal sulcus activation is similar between groups is interesting because it might suggest why cognitive teaching to read gestures helps for many individuals (pathways that support recognizing the intentions of gestures are intact). If a child or adult with autism lacks the more rapid protective quick emotional responses to threat, at least cognitively connecting the dots may take him out of harm's way.

From Liane Willey's wonderful book Pretending to be normal: living with Asperger's syndrome, a description of how her impaired perception of gestures put her at risk from an intruder in her classroom:

"Still, I was not particularly alarmed...I was curious, more intrigued by the effect he had on my quiet room, than I was by the possible effect he could have on my safety. He told me he had been in jail that he had just been released. A tiny bell sounded in my thoughts to alarm my suspicions, but I barely heard it." Fortunately for Professor Willey, she adds, "Ironically, though it was my AS that kept me from understanding this man was oddly misplaced at the best, and harmful at the worst, it was also my AS that helped me to realize I was in trouble." Once he invaded her personal space, her sensory sensitivities triggered an alarm and she immediately backed up. Fortunately too, the man fled after a male student entered the room.

Failure to grasp affective meanings of actions in autism spectrum disorders pdf
Keeping children on the autism spectrum safe
Safety resource for autism spectrum

Eides Lecture on Dyslexia and Giftedness at WA International Dyslexia Assn - This Thursday Jan 14th 7 PM

Drs. Brock and Fernette Eide will be lecturing on Dyslexia and Giftedness at The Shoreline Center, Sheridan Room 18560 First Ave NE Shoreline WA 98155 7 PM

The lecture is free, but donations appreciated on behalf of the Washington Branch of the International Dyslexia Association.

Clock hours are available through 24/7 Educational Services.

For more information, email: info@wabida.org

Finding Success in the Real World - Mentors, Resilience, Up Series

Professor Julie Logan was kind enough to send us her paper on Dyslexic entrepreneurs and we were struck by the figure at right that showed that few entrepreneurs were influenced by education in their pursuit of their current career. Dys4 refers to endorsing at least 4 items on the Adult Dyslexia Checklist.*

By far the strongest influencing factors were a family business or mentor. That's good to know - but are parents or extended family members how important they may be in this regard? ...especially in today's bleak job market.

Finding a mentor is not always an easy task, but a few ideas come to mind:

- Gifts - Think widely about a child's natural gifts, interests, or temperament. If a child doesn't seem to have a particular interest or temperament, could it be that they are just very social and enjoy blending in? Perhaps this is their gift or talent?
- People- Look for teachers, tutors, extended family members who have shared interests or a personality that dovetails well with your child. Get to know them better, how did they choose their career, what do they do outside of work?
- Experience- Look for mini-expertise building activities, or try-outs of different disciplines. Don't overschedule so little free choice is available. Encourage volunteering, but give your child advice or a peptalk before beginning. Students are often unaware of the impressions they make in their first work experiences. The better the experience, the less tolerance for careless work habits, apathy, lack of initiative, etc.
- Make a cold call- Don't be afraid of 'cold-calls', letters, or emails to experts or famous people that your child might admire. When our son was in kindergarten, he became very interested in African art. We were living in Chicago at the time, so we emailed the African art department of the Art Institute of Chicago and asked if we might be able to visit and see off-exhibit items. We were delighted to have a museum intern take us behind the exhibit so that we could see items first hand and hear stories about them (the intern was surprised that he recognized many of the styles). Even if the interests or hobbies change, these experiences broaden their view about what's out there and how they might choose a career based on what they really love.

Over Christmas, we got a Roku and we've been enjoying watching the Up series with our kids. The series interviewed a group of English children through the years from age 7, 14, 21,28, 35, 42, and 49 - looked at their interests, hopes for the future, work, schooling, and families. It's a fascinating program, but interesting on a whole other level when watching with your teen kids. This second time watching it, I was more struck by the sharp contrast between 7 & 14 - 7 year olds seem to have such strong passions and exuberance, but by 14 years old, the children seemed so much more self-conscious and unsure. We talked a lot about Tony, the cabdriver that Michael Apted thought he would see in prison some day - but Tony had gifts of resilience and drive, and the director succumbed to a common bias about physically active and highly independent kids.

For more from Wikipedia on the Up Series.


* The Adult Dyslexia Checklist is an interesting topic, we should tackle another day. Very interesting that it is so different from the checklists that dominate the identification of dyslexia in the early grades.

Cognition Without Control - ADHD, Gifted IQ, and the Learning-Performance Trade-Off

Interesting article from UPenn / Stanford speculating on the benefits of Cognition without Control:

"Late prefrontal development clearly has some negative consequences for childhood
behavior. Yet despite this, there are many examples of learning tasks (e.g., language acquisition)at which children do better than adults...we propose that these differences may reflect the costs and benefits of an immature frontal cortex (hypofrontality) that arise from the inherent tradeoffs between learning and performance. That is, a system optimized for performance may not be optimal for learning, and vice versa."

Reflecting on this research, from the LA Times reporter Melissa Healy:

"In those crucial four years, a toddler's accumulation of knowledge about her world may be unhampered by the discipline imposed by the prefrontal cortex...her prefrontal cortex doesn't stand in the way and try to keep her "on task." And her underdeveloped powers of attention will keep her from getting bogged down by pesky exceptions to rules of grammar or syntax. So, she'll always apply the most general rules she knows -- say, that adding an "s" makes things plural.

The authors call this period of disorderly learning "cognition without control."

This is a theory, not a finding, note the authors, led by the University of Pennsylvania's Sharon L. Thompson-Schill: that evolution may have favored a delay in the maturation of the brain's "braking system" as a means of allowing rough-but-rapid learning of complex matters such as language and social conventions. But it's a theory that might help clinicians and educators begin to identify the best windows for teaching very young children and for helping kids with developmental differences to learn as well."

The researchers go on to speculate that delay in the maturation of the prefrontal cortex is no accident; it may have an important purpose - to foster flexible and broad thinking in our earliest life experiences. Perhaps as brains mature, explosive early childhood learning recedes, giving way to more established pathways and performance more than new learning. If this is so, though - then maybe we should rethink prefrontal coercion strategies in the early years - whether they be educational or pharmacological.

As it turns out, kids with ADHD or kids with superior IQ (see above) have greater delays in the maturation of their prefrontal cortices than non-ADHD or regular IQ age-matched peers. The trend is the opposite in children with autism, though - young autistic children show an early maturation of prefrontal cortices.

So what would an optimal education look like if this is a purposeful pattern of brain development? Is it a mistake to force prefrontal development too early (with stimulants or other means)? What are the ideal times for stimulants for children with ADHD symptoms? Is it jumping the gun to prescribe to preschoolers, kindergarteners, or first graders?

Perhaps Alfred North Whitehead's ideas about the Aims of Education aren't so far off about all this. Whitehead proposed 3 developmental stages of education - the stages of romance (childhood), precision (adolescence), and generalization (young adulthood).

Superior IQ children have delayed prefrontal cortical thickness pdf