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.
Case-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