Researchers were able to temporarily and reversibly impair the ability of ordinary people to perform arithmetic operations. Dyscalculia is an impairment "in its own right", which is not necessarily related to a general impairment in other cognitive skills
Zvi Atzmon, "Galileo" magazine
The British Ministry of Education - one of the first to officially recognize dyscalculia - defines it as follows: a deficiency in the ability to acquire arithmetical skills. Dyscalculic students may have difficulty understanding simple numerical concepts, lack an intuitive understanding of numbers, and have difficulty learning facts and procedures related to numbers.
Even when a dyscalculic student arrives at a correct answer or solves in an appropriate way, he may do so mechanically and without feeling confident in his answer or the way he took. It should be noted that this definition, which considers a deficiency in the ability to acquire arithmetic skills, refers specifically to developmental dyscalculia, DD, the initials of Developmental Dyscalculia.
As an introduction to a review article they published in 2001 in the journal Pediatric Neurology, the physician-researchers Ruth Shelo and Varda Gross-Zur, from the Shaarei Zedek Medical Center in Jerusalem, write as follows: Developmental dyscalculia is a specific learning disability that impairs the acquisition of arithmetic skills in children who are otherwise normal children ( and see: for further reading).
Acquired vs. developmentalWe will clarify that developmental dyscalculia means difficulty and delay in acquiring arithmetic skills in children, while acquired dyscalculia is an impairment - usually following a stroke - in the ability to handle numbers and perform arithmetic tasks in people who had a good command of these abilities before the brain injury (and see: Anat Barnea, "Mathematical Brain: On Abilities and weaknesses", "Galileo" 40). In this examination, the terms developmental dyscalculia (DD) and acquired dyscalculia are equivalent to the terms that describe deficits in the ability to read: developmental dyslexia and acquired dyslexia.
Amazing cases and deficiency "due to" itselfTo demonstrate and refine the concept of dyscalculia (acquired, in this case) as an impairment in itself, and not as another facet of a general cognitive impairment, the well-known dyscalculia researcher Brian Butterworth tells about the case of Signora Gadi (pseudonym), who was the account manager of a hotel in Italy Until she had a stroke. The incident did not impair her linguistic skills (lips) at all, but her number manipulation skills were fatally damaged.
So, for example, she can no longer count past the number four! If five objects are presented to her, she counts - in Italian she plays - like this: "One, two, three, four. That's it, this is where my math ends." When the researchers tested her arithmetic abilities, such as addition and subtraction, these were completely cut off when the number was greater than 4. The former talented accountant is once again unable to even say which is greater than, 5 or 10. Every number greater than 4 has been completely erased from her mind, including the day of the week, her age and the number of her shoes. To make a phone call she needs a special dial.
Butterworth also tells about 30-year-old Charles (pseudonym), suffering from severe developmental dyscalculia, one that is certainly justified in being called ocalculia (that is, a complete impairment of arithmetic ability). Charles holds - and with great pride - a degree in psychology; The reason for his special pride is the great difficulties he overcame on his way to receiving the degree. The most difficult obstacle was his admission to the university, since despite all efforts he could not pass a test in mathematics.
Charles is diligent and intelligent - this is what Butterworth testifies to him, but his deficiency when it comes to numbers and arithmetic is a huge obstacle. When he buys in a store he has no idea what the prices mean, and he has no estimate of how much his purchase will cost. He is unable to perform two-digit calculations, such as calculating how many are 37 minus 19. And if that is not enough, to answer the question "Which is greater, 3 or 9?" He had to use his fingers.
When did the dinosaurs become extinct?In his book "Illusions of the Brain" (translation: Jenny Navot-Prives; and see: for further reading), the renowned neurologist Villianor Ramachandran describes Bill Marshall, an outstanding retired pilot, whom he met a week after Hela suffered a stroke. "He was in high spirits," reports Ramachandran, "spoke fluently, intelligently and clearly."
In the conversation, Bill accurately described details about his past, his children and grandchildren. After a heartfelt, meaningful and fluent conversation, the neurologist asks: "Bill, can you subtract seven from a hundred? How much is one hundred minus seven?". Bill Mahamham, clearing his throat, went back and repeated the question several times, making sure that it was indeed the question, and finally answered hesitantly, "Ninety-six?"
The neurologist makes another attempt: "How much is seventeen minus three?". Bill repeats the question, hesitates and finally tries "twelve?" At this point the neurologist asks: "Bill, is the result greater or less than 17?" Now Bill answers without hesitation: "Smaller". The neurologist points out to himself that the former pilot is not able to do the simplest math, but certainly knows what the subtraction process means.
Now Ramachandran asks: "Which number is bigger: one hundred and one or ninety-seven?", and receives an immediate answer: "101 is bigger", and even a correct mathematical explanation: "it has more digits".
So the neurologist tells him a story about a man who visited a museum where dinosaur skeletons are displayed, and was interested in knowing how old the fossilized skeletons were. He approached the guard and asked to find out: "What is the age of the bones of this dinosaur?" "Sixty million and three years," answered the guard. The critic wondered: "Sixty million and three years? I didn't know it was possible to be so precise in determining the age of dinosaur bones." Upon hearing his question, the guard hastened to explain: "I took office here three years ago, and then they told me that the bones are sixty million years old."
"Bill laughed out loud at the story," Ramachandran reports, noting that it takes a sophisticated mind to understand the joke, which is based on what is known as "the misplaced mistake." Ramachandran concludes: Bill understood what subtraction meant, knew that a 3-digit number was greater than a 3-digit number, and took a sophisticated joke based on misplaced precision - yet he could not subtract 17 from XNUMX. He has damaged a brain mechanism necessary to perform arithmetic operations, even the most basic ones. He suffers from severe (acquired) dyscalculia.
A defect in its own rightAnother way that may indicate that dyscalculia is an impairment "in its own right", which is not necessarily related to a general impairment of other cognitive skills, is the examination of people with severe mental impairments, but impressively, and even amazingly, preserve their calculation abilities (that is, who do not have dyscalculia) .
Butterworth reports on a 64-year-old man who suffered from a degenerative disease that manifested itself in worsening and progressive damage to the language areas of his brain, damage that was discovered - and in a startling way - on an MRI: large areas of his brain had completely degenerated. His language ability deteriorated the most - he hardly understood what was said to him.
This patient was able to name only 2 body parts out of 8 organs that he was asked to name, he was not able to name a single one out of 7 that were presented to him, and the score he received in the speech fluency test was zero. But when it comes to math: he won a score of 100 (!) in the test of subtracting two two-digit numbers, and with exactly the same score in tests of multiplication of two-digit numbers.
Researchers Lauren Cohen (Cohen) and Stanisla Dehaene (Dehaene) reported (1999) on a patient who, in reading aloud math exercises that were presented to her, made a sweeping mistake (about 90 percent of the reading aloud was wrong), and yet, her answers to the exercises were accurate. For example, when she was presented with exercises 6-8, she read: "Five minus four", but her answer was correct: 2. She was accurate in giving answers to addition, subtraction and division exercises; In comparisons, which of two numbers is greater; and determining whether a number is even or odd. And all this, as mentioned, when she made a mistake in reading aloud the vast majority of the exercises she solved.
Javier Seron (Seron) and a group of fellow neuropsychologists from Belgium reported on an 86-year-old Alzheimer's patient who failed the inference and logic tests used to diagnose toddlers, and which four-year-olds usually pass, including the number retention tests (does the number of lead soldiers in a row increase when the spaces between them are increased). Nevertheless, this Alzheimer's patient quickly and accurately performed calculations with numbers, and also did very well in tests of extracting the square root of four-digit numbers!
As for developmental dyscalculia, which is not due to a degenerative disease, we can mention the report by Beata Hermelin and Neil O'Connor from the University of London about a young man with severe autism, who does not speak and does not understand speech, and whose communication ability is extremely limited and based on movements. This young man was able to identify prime numbers, and factor odd numbers, with greater speed and accuracy than trained mathematicians (Psychological Medicine, 1990).
From all these examples it becomes clear that there is indeed such an "animal", dyscalculia (and in its extreme form - acalculia), as a distinct impairment, and that it is possible to point to a double separation (dissociation) between the ability to handle numbers and make calculations with them and linguistic-semantic ability.
That is, there may be severe damage to arithmetic ability that is not accompanied by language damage, and there may also be damage to language ability that is not accompanied by dyscalculia. Therefore, it can be assumed that certain structures in the brain, circuits or specific brain pathways, are what give us the ability to handle numbers and make calculations.
Severe damage to the functioning of these areas will be manifested in dyscalculia, while if these areas are functioning, arithmetic abilities are preserved, even when other cognitive skills deteriorate severely. If there is indeed no overlap between the brain areas whose dysfunction is manifested in dyscalculia (or at least in certain types of dyscalculia) and areas in which some dysfunction is manifested in dyslexia (or at least in certain types of it), we should not be surprised that in a certain person arithmetic skills can be extremely impaired, while the ability His reading is correct. The same applies to general linguistic abilities, logical thinking and other cognitive functions.
What causes dyscalculia?
Acquired dyscalculia usually occurs in people who have had a stroke in the left parietal lobe. And in more detail: for years there has been evidence indicating that the angular gyrus, which is part of the parietal lobe, is essential for performing arithmetic tasks.
About a decade ago, Marcus Kiefer and Stanisla Dehaene (Kiefer & Dehaene. Math Cognition, 1997) found, using electrical potential recordings, that solving difficult arithmetic exercises evokes activity in the central region of the two parietal lobes, the left and the right (the left is more active), but simple multiplication operations evoke Activity only in the left parietal lobe.
In this context we will mention Gerstmann's syndrome, which manifests itself in dyscalculia (acquired), agnosia of the fingers (inability to grasp and identify the correct fingers), disorientation between left and right and dysgraphia (difficulties in writing).
It turns out that Gerstmann's syndrome is found in people whose brains have suffered damage to the left angular ridge. In connection with the two deficiencies - finger agnosia and dyscalculia - we recall that children (and sometimes adults as well, and we have already seen this) count and calculate with the help of their fingers, that the decimal system originates from the ten fingers of the hands, and that the word digit - the literal source of our digital world - indicates both a finger and a number .
However, in later studies, researchers came to know that the intraparietal sulcus is even more important in performing certain specific arithmetic operations.
In 2001, Elizabeth Isaacs (Isaccs) and her colleagues from the Great Ormond Street Children's Hospital (GOSH) in London compared the brains of two groups of teenagers who were born prematurely. The subjects of both groups had normal intelligence, except that one of the two groups included teenagers whose math achievements were very low. For the purpose of comparing the brains, the researchers used a sophisticated analysis method of MRI findings.
In terms of the structure of the brain, the researchers discovered one distinct difference between the two groups: in those with difficulty with math, the thickness of the "gray matter", that is, the layer of the cortex, in part of the left parietal lobe, was lower. This is an area known as the intraparietal sulcus (IPS). Indeed, there was already evidence that indicated the involvement of this area in performing numerical calculations, both according to fMRI tests of brain activity when performing arithmetic tasks in healthy subjects, and according to the location of brain lesions in cases of acquired dyscalculia.
Boys, girls and family-genetic relationship
Ruth Shalu and Warda Gross-Zur point out in their review that developmental dyscalculia originates from brain defects that genetic factors have an effect on the degree of susceptibility to them. They point out that in various studies, including their own, a "family connection" has been found for developmental dyscalculia.
For example, if one of two identical twins is diagnosed with dyscalculia, the chance that the other twin will also be diagnosed as such is 10 times greater than the prevalence in the general population. And what's more, if one of the children in the family has been diagnosed with dyscalculia, the chance of each of the other children in the family being diagnosed with dyscalculia is 5 to 10 times higher than the general prevalence in the population (a prevalence whose value is determined by different methods and by different researchers, to 1% in the population and up to about 6%).
In this context, it is interesting to note that the percentage of girls suffering from dyscalculia slightly exceeds the percentage of boys suffering from it (in the study of Shalu and Gross-Zur, a ratio of 1.1:1 was found). This figure stands out against the background of the fact that other learning disabilities, such as dyslexia and ADHD, appear in boys up to 3 times more often than in girls.
Although we realized that arithmetic ability is not just an echo of general cognitive ability, but a specific ability in itself, still in many cases dyscalculia is accompanied by other learning disabilities - dyslexia or hyperactivity, for example - or neurological diseases, such as epilepsy.
Dyscalculia is relatively common among dyslexics - about 40% of children who have problems with reading also experience difficulties in learning arithmetic. However, it must be remembered that this means that 60% of dyslexics have no problems in mathematics; Moreover - notes Butterworth - there are well-known mathematicians who are dyslexic. It is important to reiterate: in many cases, dyscalculia is the only abnormal expression in a child, who is otherwise completely normal.
Genetic evidence and Turner syndrome
Nicolas Molko (Molko) and his colleagues from France reported (2003Neuron, ) on their efforts to find a connection between dyscalculia and brain structures, as well as to locate the genetic basis for the impairment. For this purpose, account performance was checked at the same time; Brain areas are active when performing arithmetic tasks, using fMRI; Cerebral structures, especially the intraparietal gyrus, using MRI; And all this in a group with a common genetic abnormality - girls with Turner's syndrome, for example - who lack an X chromosome (45:X, which means they obviously do not have a Y chromosome and have only one X chromosome).
Girls and women with Turner syndrome have normal language ability, and they are not mentally retarded, but their visual-spatial abilities are impaired and so is their math ability; They especially have difficulty calculating with large numbers. Molko and his colleagues chose a group of people affected by Turner syndrome thinking that this is a group whose genetic common denominator is clear - as mentioned, the missing X chromosome (in some cases only part of the X chromosome is missing).
Indeed, according to the researchers, a defect in the size and structure of the right intraparietal gully in the ternary was discovered in structural tests done using MRI. The researchers also examined the brain activity in the subjects during the performance of various arithmetical tasks, including accurate calculations and approximate estimation tasks.
It turned out that in both types of tasks, the activity of the intraparietal gully in blocks in the syndrome is different from the corresponding activity in the control group, and especially so when treatment of larger numbers is required. In normal subjects, when making precise calculations, as the size of the numbers increases, more and more activity of the intra-apical gyri is added. It can be assumed that these brain areas serve as a kind of computational reserve power, which is mobilized when the calculation becomes more difficult. And here, in Turner's subjects, there was no such increase in the activity of the intraparietal gyrus when the numbers in the calculation increased.
The fact that in Turner syndrome blocks deficits in arithmetic tasks are detected - developmental dyscalculia, alongside an abnormal pattern of brain activity when performing arithmetic tasks, as well as an abnormal structure of the right intraparietal gyrus - can testify to the involvement of this brain structure in arithmetic tasks and dyscalculia. The fact that in ternaries the intraparietal gyruses do not mobilize for help when it is required as the numbers increase can explain, according to Molko and his colleagues, the difficulties in performing arithmetic operations typical of Turner syndrome defects - difficulties that are significantly exacerbated (compared to normal subjects) when the numbers increase.
Monkeys, Cells and Computations
In this context, of the involvement of the intraparietal gyrus in numerical calculation processes, two reports given at the Society for Cognitive Neuroscience conference held in May 2007 in California are particularly interesting. Andreas Nieder (Nieder) and his colleagues from the University of Tübingen used microelectrodes to examine the responses of neurons located deep in the intraparietal gyrus of rhesus monkeys, who had previously been trained to distinguish the number of objects presented in front of them.
It turned out that some cells respond to the number of objects when they are presented all at once in the visual field, while other cells respond to the number of objects following their serial presentation, one after the other. Cells that responded to the cumulative number serially did not respond to the presentation of the same number of objects at the same time, while cells that responded to multiple objects presented together did not respond to the serially cumulative number of objects. However, after the number of objects was encoded in one of the two types of cells, the numerical information was drained to the cells that responded to the number of objects regardless of how they were presented.
The finding is particularly interesting not only because it turns out that neurons know how to count, but because it directly demonstrates the involvement of the neurons in the intraparietal gyrus in processing numbers, albeit in our relatively distant relatives, rhesus monkeys.
Elizabeth Brannon from Duke University in the United States reported cells in this area in macaque monkeys. These are cells whose response depends as a monotonic function on the number of objects displayed in the cell's receptive field, from 2 objects to 32. In some of these cells, the rate of neural activity increases as the number of items in the receptive field increases, while in other cells there is an inverse relationship between the number of objects and the rate of activity the nervous
Draining the information from the different cells and comparing the activity of cells belonging to these two groups of cells can form the input to those "counter" cells that Nider and his colleagues identified.
From the mouths of infants and mammals
While reading and writing are processes that require learning, the experts point out that babies are born with certain mathematical skills, innate skills that do not need to be learned. Counting, adding numbers, comparing numbers and estimating sizes - all these are abilities that develop independently, without study.
Babies a few weeks old, long before they can speak or understand words, are gifted with simple but impressive numerical skills. If, for example, a soft baby is presented with a group of objects several times, each time with a different number, he will spend more time looking at them than if each time the group of objects is presented, their number remains the same. In an entertainment movie we would see such a baby hiding a big yawn and saying in a ducky voice "How boring, always the same number?!".
Furthermore, babies know how to add and subtract, and these are not children who will become mathematicians or accountants. If, for example, a baby is shown one doll that is moved behind a curtain, and then another doll is shown that is moved there, the baby expects that there will be two dolls behind the curtain (and for those of us who have forgotten their Talmud: 2 = 1+1...). This can be proven, because if the curtain is pulled back and one or three dolls are discovered, the baby looks longer than if, as expected, two dolls are discovered. As if he is saying to himself (without words, which he has not yet acquired): what happened?? One and one is not two anymore?!
A 3-4 year old toddler, Shalev and Gross-Zur note, can count four objects, and at the age of 6 - up to 15, while understanding the meaning of these numbers.
"Produce" dyscalculia for a moment
Dr. Cohen Kadosh from Ben-Gurion University in Beer-Sheva and University College London and his colleagues decided to test whether it is possible to artificially induce temporary dyscalculia in a normal person, and which area of the brain must be affected to bring about this result.
If it were possible to "freeze" for a short time small, well-defined parts of the brain, it would be possible to prove which region whose "freezing" would manifest itself in the symptoms of dyscalculia, and thus deduce - at least seemingly - the function of which brain region is impaired in dyscalculia.
The principle idea may seem correct, but - it is impossible to cool a small and defined brain area for a short time, in a completely reversible way that does not involve any risk. However, although it is not possible to freeze, it is certainly possible to disrupt, for example by means of an anesthetic that is eliminated quickly. Indeed, this method is used for temporary, quickly passing paralysis of one half of the brain (hemisphere) - a procedure known as the "Wada test".
The Wada test is used, for example, to identify the "speaking" hemisphere (in the vast majority of humans - it is the left hemisphere), or to verify that one of the hippocampus (right or left) is normal, before surgery on one of the two hemispheres of the brain. The paralysis is done using a short-lived anesthetic, but it involves an invasive operation - an injection into an artery carrying blood to one of the hemispheres. This procedure paralyzes, for a short time, an entire half of the brain, so that in this way it is not possible to detect the function of reduced brain areas.
A possible way to disrupt the operation of a limited brain area is to inject electricity - meaning a low current intensity, which does not cause any damage beyond a momentary operation disruption - using a suitable electrode that directly touches the brain tissue. This method was used by Wilder Penfield (Penfield, see: "Galileo" 100, milestones in psychology and neuroscience) to stimulate brain areas, and it is used for momentary disruption of function, for example to precisely locate the center of speech, in order to avoid damaging it. However, this method requires opening the skull and exposing the brain, and hence it is possible only in those difficult cases where opening the skull and brain surgery is required, for example for the purpose of removing a tumor.
But for several years it has been possible to infuse a weak electric current into defined brain tissue in a completely non-invasive manner. This refers to the method known as TMS - magnetic stimulation through the skull (Transcranial Magnetic Stimulation). With the help of a suitable device that is activated from the outside - it can not touch the scalp at all - a strong magnetic field can be infused in a targeted brain area.
The magnetic field creates electric currents, and these can briefly disrupt the operation of the area where the magnetic field is focused. The specific characteristics of the induced current determine what its effect will be on the brain tissue - whether it will stimulate neural activity (as indicated by the term stimulation), or disrupt activity. Indeed, TMS is the means used by Cohen Kadosh and his colleagues to briefly disrupt the activity of targeted brain areas.
It became clear to the researchers that when they disrupt - for only fractions of a second - the neural activity in the right intraparietal gyrus of non-dyscalculic people, their processing of numerical-quantitative information becomes one that is characteristic of dyscalculics. Disruption in the corresponding area, the intraparietal gully in the left hemisphere, did not cause momentary dyscalculia.
Despite its name, in this case the device does not stimulate activity but disrupts it, and the method of identifying "dyscalculic behavior" that the researchers used was also somewhat "upside down". The subjects were presented with pairs of numbers (for example: 2 and 4) and they were required to determine which of the two numbers was larger.
This, when the two numbers were presented in a different physical size, for example when the 2 is presented as a large number while the 4 is a small number. The instruction to the subject was to indicate which number had the larger physical size, ignoring the value of the numbers. And here, in normal subjects who are asked to indicate which of the two numbers is physically larger, the immediate, automatic processing of the number values tends to interfere with the decision regarding the physical size and slow it down. On the other hand, for dyscalculia, who are to some extent "blind" to the meaning of the value of the number, the collision of the numerical value with the physical size is less disturbing.
And here, in those fractions of a second in which the action of the right intraparietal gyrus was disrupted in non-dyscalculic subjects, their responses were very similar to those of dyscalculics. On the other hand, the TMS disruption of the left intraparietal gyrus did not produce "momentary dyscalculia". The conclusion of Cohen Kadosh and his colleagues: damage to the function of the right intraparietal gyrus is the cause of dyscalculia. And if you want to investigate its causes and focus on providing solutions - this is the target center towards which, according to the results of this study, the research and possibly the treatment methods should be directed.
An interesting, even very, question is: what is the relationship between mastery of numbers and success in math (or on the contrary, dyscalculia) and success in areas of mathematics that are not largely based on numbers, such as algebra and geometry?
Brian Butterworth deals with this question, which is usually quite limited, by saying that if the claim is true that at the root of developmental dyscalculia is a deficiency in the basic, innate perception of the meaning of numbers, following a defect in a "brain unit (module)" specific to numbers ( number module), so there is no reason why dyscalculia cannot successfully learn mathematical aspects that are much less dependent on "number sense" - for example geometry, or algebra. And maybe this is what underlies those jokes about a math professor who always mistakes the excess at the grocery store.
Zvi Atzmon is the scientific editor of the magazine "Galileo"