Read to succeed -- in math; study shows how reading skill shapes more than just reading
University at Buffalo psychologist identifies a connectivity fingerprint suggesting that the brain's reading network is at work across cognitive domains; 'reading affects everything,' he says
BUFFALO, N.Y. - A University at Buffalo researcher's recent work on dyslexia has unexpectedly produced a startling discovery which clearly demonstrates how the cooperative areas of the brain responsible for reading skill are also at work during apparently unrelated activities, such as multiplication.
Though the division between literacy and math is commonly reflected in the division between the arts and sciences, the findings suggest that reading, writing and arithmetic, the foundational skills informally identified as the three Rs, might actually overlap in ways not previously imagined, let alone experimentally validated.
"These findings floored me," said Christopher McNorgan, PhD, the paper's author and an assistant professor in UB's Department of Psychology. "They elevate the value and importance of literacy by showing how reading proficiency reaches across domains, guiding how we approach other tasks and solve other problems.
"Reading is everything, and saying so is more than an inspirational slogan. It's now a definitive research conclusion."
And it's a conclusion that was not originally part of McNorgan's design. He planned to exclusively explore if it was possible to identify children with dyslexia on the basis of how the brain was wired for reading.
"It seemed plausible given the work I had recently finished, which identified a biomarker for ADHD," said McNorgan, an expert in neuroimaging and computational modeling.
Like that previous study, a novel deep learning approach that makes multiple simultaneous classifications is at the core of McNorgan's current paper, which appears in the journal Frontiers in Computational Neuroscience.
Deep learning networks are ideal for uncovering conditional, non-linear relationships.
Where linear relationships involve one variable directly influencing another, a non-linear relationship can be slippery because changes in one area do not necessarily proportionally influence another area. But what's challenging for traditional methods is easily handled through deep learning.
McNorgan identified dyslexia with 94% accuracy when he finished with his first data set, consisting of functional connectivity from 14 good readers and 14 poor readers engaged in a language task.
But he needed another data set to determine if his findings could be generalized. So McNorgan chose a math study, which relied on a mental multiplication task, and measured functional connectivity from the fMRI information in that second data set.
Functional connectivity, unlike what the name might imply, is a dynamic description of how the brain is virtually wired from moment to moment. Don't think in terms of the physical wires used in a network, but instead of how those wires are used throughout the day. When you're working, your laptop is sending a document to your printer. Later in the day, your laptop might be streaming a movie to your television. How those wires are used depends on whether you're working or relaxing. Functional connectivity changes according to the immediate task.
The brain dynamically rewires itself according to the task all the time. Imagine reading a list of restaurant specials while standing only a few steps away from the menu board nailed to the wall. The visual cortex is working whenever you're looking at something, but because you're reading, the visual cortex works with, or is wired to, at least for the moment, the auditory cortex.
Pointing to one of the items on the board, you accidentally knock it from the wall. When you reach out to catch it, your brain wiring changes. You're no longer reading, but trying to catch a falling object, and your visual cortex now works with the pre-motor cortex to guide your hand.
Different tasks, different wiring; or, as McNorgan explains, different functional networks.
In the two data sets McNorgan used, participants were engaged in different tasks: language and math. Yet in each case, the connectivity fingerprint was the same, and he was able to identify dyslexia with 94% accuracy whether testing against the reading group or the math group.
It was a whim, he said, to see how well his model distinguished good readers from poor readers - or from participants who weren't reading at all. Seeing the accuracy, and the similarity, changed the direction of the paper McNorgan intended.
Yes, he could identify dyslexia. But it became obvious that the brain's wiring for reading was also present for math.
Different task. Same functional networks.
"The brain should be dynamically wiring itself in a way that's specifically relevant to doing math because of the multiplication problem in the second data set, but there's clear evidence of the dynamic configuration of the reading network showing up in the math task," McNorgan says.
He says it's the sort of finding that strengthens the already strong case for supporting literacy.
"These results show that the way our brain is wired for reading is actually influencing how the brain functions for math," he said. "That says your reading skill is going to affect how you tackle problems in other domains, and helps us better understand children with learning difficulties in both reading and math."
As the line between cognitive domains becomes more blurred, McNorgan wonders what other domains the reading network is actually guiding.
"I've looked at two domains which couldn't be farther afield," he said. "If the brain is showing that its wiring for reading is showing up in mental multiplication, what else might it be contributing toward?"
That's an open question, for now, according to McNorgan.
"What I do know because of this research is that an educational emphasis on reading means much more than improving reading skill," he said. "These findings suggest that learning how to read shapes so much more."
What is Godel's Theorem?
January 25, 1999
Melvin Henriksen--Professor of Mathematics Emeritus at Harvey Mudd College--offers this explanation:
KURT GODEL achieved fame in 1931 with the publication of his Incompleteness Theorem.
Giving a mathematically precise statement of Godel's Incompleteness Theorem would only obscure its important intuitive content from almost anyone who is not a specialist in mathematical logic. So instead, I will rephrase and simplify it in the language of computers.
Imagine that we have access to a very powerful computer called Oracle. As do the computers with which we are familiar, Oracle asks that the user "inputs" instructions that follow precise rules and it supplies the "output" or answer in a way that also follows these rules. The same input will always produce the same output. The input and output are written as integers (or whole numbers) and Oracle performs only the usual operations of addition, subtraction, multiplication and division (when possible). Unlike ordinary computers, there are no concerns regarding efficiency or time. Oracle will carry out properly given instructions no matter how long it takes and it will stop only when they are executed--even if it takes more than a million year
Let's consider a simple example. Remember that a positive integer (let's call it N) that is bigger than 1 is called a prime number if it is not divisible by any positive integer besides 1 and N. How would you ask Oracle to decide if N is prime? Tell it to divide N by every integer between 1 and N-1 and to stop when the division comes out evenly or it reaches N-1. (Actually, you can stop if it reaches the square root of N. If there have been no even divisions of N at that point, then N is prime.)
What Godel's theorem says is that there are properly posed questions involving only the arithmetic of integers that Oracle cannot answer. In other words, there are statements that--although inputted properly--Oracle cannot evaluate to decide if they are true or false. Such assertions are called undecidable, and are very complicated. And if you were to bring one to Dr. Godel, he would explain to you that such assertions will always exist.
Even if you were given an "improved" model of Oracle, call it OracleT, in which a particular undecidable statement, UD, is decreed true, another undecidable statement would be generated to take its place. More puzzling yet, you might also be given another "improved" model of Oracle, call it OracleF, in which UD would be decreed false. Regardless, this model too would generate other undecidable statements, and might yield results that differed from OracleT's, but were equally valid.
Do you find this shocking and close to paradoxical? It was even more shocking to the mathematical world in 1931, when Godel unveiled his incompleteness theorem. Godel did not phrase his result in the language of computers. He worked in a definite logical system and mathematicians hoped that his result depended on the peculiarities of that system. But in the next decade or so, a number of mathematicians--including Stephen C. Kleene, Emil Post, J.B. Rosser and Alan Turing--showed that it did not.
Research on the consequences of this great theorem continues to this day. Anyone with Internet access using a search engine like Alta Vista can find several hundred articles of highly varying quality on Godel's Theorem. Among the best things to read, though, is Godel's Proof by Ernest Nagel and James R. Newman, published in 1958 and released in paperback by New York University Press in 1983.
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