THE PHYSIOLOGY OF MATHEMATICAL FUNCTIONINGAccording to Paiget (1949, 1958), children learn primarily by manipulating objects until the age of 12. If children are not taught math with hands-on methods, between years 1 and 12, their ability to acquire math knowledge is disturbed at the point when hands-on explorations were abandoned in favor of abstractions. This clearly sets them up for mathematical disabilities in the next developmental period of formal propositional operations (CTLM 1986, 56).
Brain lateralization, or hemisphere specialization, takes place earlier in girls than in boys. Because of girls' social development away from spatial tasks, the maximum spatial capability of the right hemisphere is fixed (when it stops growing) in a premature stage of development. Research shows that girls are overspecialized in left-hemisphere functioning, and must talk through spatial-visualization tasks, resulting in slow, unnatural performance (Tobias 1978, 113-114).
Psychologist, Julia Sherman, believes that earlier female verbal and reading development leads females to prefer verbal and reading teaching and learning approaches to non-verbal right-hemisphere problem solving approaches. Other researchers see spatial visualization as essential to all levels of math learning. These skills exist on a continuum from low-level, requiring no image transformation, to high-level, involving the visualization and mental manipulation of 3-dimentional figures. Research on athletes suggests that spatial visualization skills can be learned (Tobias 1978, 114-116).
Gerstman Syndrome symptoms include acalculia, right-left disorientation, finger anomia, and agraphia. "The concurrence of these four findings in a right-handed patient strongly predicts pathology in the left parietal lobe, particularly the left supramarginal gyrus." Test calculation by asking the patient to subtract backwards from 100 by sevens (the "serial sevens test"), or, in the less well educated subject, to make change from a dollar. To test right-left orientation, ask the patient to show you his left (or right) hand, to show you your left (or right) hand, and to place his right hand on your left hand. To test for finger anomia, ask the patient to name the thumb, index finger, or little finger. Accept synonyms for the index finger, such as "pointer" (Valenstein and Nadeau, 1997).
Problems in math processing are attributed to anomalies in specific regions of the brain. Gerstmann's syndrome of dysgraphia, dyscalculia, finger agnosia, and right-left disturbance involves the left parietal lobe. Anosognosia involves the right parietal lobe. Right-left disturbance involves the left hemisphere (Pacific Neuropsychiatric Institute 1997).
The right hemisphere of the brain contributes the ability to perceive shapes, remember musical phrases, think holistically, face recognition, and the reproduction of designs. The usually dominant left hemisphere, which controls the right side of the body, specializes in speech, the sequential tasks involved in reading, and numerical tasks. When the right hemisphere is malfunctioning, patients are able to read and write, but have difficulty recognizing faces and remembering geographical locations (Tobias 1978, 109-111). The ladder are common symptoms co-morbid with dyscalculia. Back to the Top
GENETIC AND SOCIAL FACTORS:
As with all abilities, math aptitude can be inherited or an inborn disposition. Studies of identical twins reveal close math scores (Barakat 1951, 154). Research into exceptionally gifted individuals shows high levels of math knowledge in early childhood, unexplained by external influences. Family histories of mathematically "gifted" and "retarded" individuals, revealed common aptitudes in other family members (CTLM 1986, 53).
Even the most "mathematically gifted" individual can be hindered by inadequate math education. Likewise, a "mathematically retarded" individual will not attain competency in math despite intensive systematic training (CTLM 1986, 53).
On the social side, Cohn (1968) explains that having a disability in math is socially acceptable. He asserts that math ability is regarded more as a specialized function than a general indication of intelligence. As long as one can read and write, the stigma and ramifications of math failure can be diminished and sufficiently hidden.
Sharma concurs- explaining that in the West, it is common to find people with high IQ's who shamelessly accept incompetency in math. At the same time, they find similar incompetence- in spelling, reading, or writing- totally unacceptable. Prevailing social attitudes excuse math failure. Parents routinely communicate to their children that they are "no good at math (Sharma 1989)."
Sharma asserts that gender differences in math skills are due more to social forces than to gender-specific brain construction and function. He believes that gender differences can be eliminated by equalizing the activities and experiences of both boys and girls at every level of development. Sharma contends that it is the social forces- that direct a child's experiences and activities- which lead to the differences in the neurological sophistication of boys and girls (Sharma 1989).
For example, most studies show that girls do better than boys in math until the age of 12. Then boys dominate the subject. This difference can be explained by analyzing the gender-specific development of math prerequisite spatial orientation skills. The main reason for this is the methodology of teaching in pre-school and elementary grades, where focus is on fine-motor skill development (Sharma 1989).
Boys and girls are given ample opportunities to play with blocks, Legos, board games, and various materials requiring fine-motor coordination. Naturally, girls have better fine-motor skills early in their development (Sharma 1989). And the learning environment, at this point, exercises these skills.
But as the children age, social biases preclude boys and girls from choosing to play with certain things and in certain ways. At this point of divergence, objects and activities acquire definite gender appropriateness. Blocks, Legos, tree climbing, outdoor activities, and ball sports become "boy" activities. Dolls, playing house, dressing up, talking, cooking, reading, sewing, crafting, and planning social activities become "girl" activities. By avoiding intricate mechanical manipulations and "rough and tumble" physical activities, girls loose ground in spatial organization abilities (Sharma 1989).
Girls' more sedentary activities offer few exercises in space/motion judgement, symmetry, part-to-whole constructions, and development of visualization, muscle memory, and geometric principles. Meanwhile, boys are gaining ground in all of these areas- and their improving spatial organizational abilities better prepare them for mathematics tasks (Sharma 1989). Back to the Top
Cambridge College dean, Mahesh Sharma, asserts that math outcomes are terrible for a number of reasons. Our mathematics curriculums are not reflecting what we know about how children learn mathematics. Typical math curriculums are guided by chronological age. Math is presented in a pile up fashion. Each year, more math concepts are added to the pile of previously presented concepts. This is a tragic approach (Sharma 1989).
Sharma believes that teacher trainers are not bringing all the known aspects of math learning into the teacher preparation curriculum. New math teachers have not been taught the latest developments in learning theory and math conceptualization, and do not know how to use technology as a learning tool (Sharma 1989).
In the end, teachers teach as they were taught. Their teaching style reflects their own learning style. (It is natural to believe that everyone thinks like you do.) Teachers need to realize that if students are experiencing difficulty, they should ask themselves the following questions: Is my teaching style excluding students with certain learning styles? Are the methods and materials I am using appropriate for and compatible with the student's cognitive level and learning style? Has the student mastered requisite skills and concepts (Sharma 1989)?
Recent studies show that student achievement is strongly influenced by teacher levels of expertise. An expert teacher's students perform 40% better than students of a novice teacher. Presently, the average K-8 teacher has taken only 3 or less math or math education classes in college. Not even 50% of 8th grade math teachers have taken a single class on math teaching at this level, and 28% of high school math teachers lack a major or minor in math (USDE 1998). Back to the Top
Center For Teaching/ Learning of Mathematics (CTLM). 1986. III. Progress of Dr. Ladislav Kosc's work on dyscalculia. Focus on Learning Problems in Mathematics. Volume 8: 3&4. (summer & fall).
Sharma, Mahesh 1989. How children learn mathematics: Professor Mahesh Sharma, in interview with Bill Domoney. London, England: Oxford Polytechnic, School of Education. 90 min. Educational Methods Unit. Videocassette.
Tobias, Sheila. 1978. Over-coming math anxiety. Boston, MA: Houghton Mifflin Company.
United States Department of Education (USDE). 1998. The State of Mathematics Education: Building a Strong Foundation for the 21st Century. (January 9). [on-line document] Available at: http://www.ed.gov/inits.html#2. Internet.
Valenstein, E. and S.E. Nadeau. 1997. Gerstmann's Syndrome. [document on-line] Available at: http://www.medinfo.ufl.edu/year2/neuro/v1174.html. Internet.
Dr. Brad B. Hale on the Neuropsychology of Math Disabilities E-mail Dr. Hale
According to Dr. Brad Hale of the University of Victoria, there are a lot of new data to support different types of math disability. Hale's research teams found 5 subtypes of math learning disability caused by brain dysfunction:
(1) visual-spatial [right posterior]
(2) math reasoning [right frontal]
(3) executive/computation [frontal-subcortical]
(4) math facts/knowledge [ left temporal/parietal]
(5) Gerstmann Syndrome subtypes [left parietal dysfunction].
Hale also found two subtypes of math disability showing the visual-spatial and math reasoning pattern in his Specific Learning Disability-psychopathology study; but Hale cautions that there are many neuropsychological processes involved in math and math disability.
Hale invites us to read these selections from his new 2010 book, School Neuropsychology: A Practitioner's Handbook: (Kindle Edition)
Hale, J. B., Wycoff, K. L., & Fiorello, C. A. (2010). RTI and cognitive hypothesis testing for specific learning disabilities identification and intervention: The best of both worlds. In D. P. Flanagan & V. C. Alfonso (Eds.), Essentials of Specific Learning Disability Identification. Hoboken, NJ: John Wiley & Sons.
Hain, L. A., & Hale, J. B. (2010). “Nonverbal” learning disabilities or Asperger Syndrome? Clarification through cognitive hypothesis testing. In N. Mather & L. E. Jaffe (Eds.), Expert Psychological Report Writing. New York, NY: John Wiley & Sons.
Hale, J. B. (2010). Cognitive hypothesis testing for a child with math disability. In C. A. Riccio, J. R. Sullivan, & M. J. Cohen (Eds.), Neuropsychological assessment and intervention for childhood and adolescent disorders (pp. 54-62). New York, NY: John Wiley & Sons.
Hain, L. A., Hale, J. B., & Glass-Kendorski, J. (2009). Comorbidity of psychopathology in cognitive and academic SLD subtypes. In S. G. Pfeifer & G. Rattan (Eds.), Emotional disorders: A neuropsychological, psychopharmacological, and educational perspective (pp. 199-226). Middletown, MD: School Neuropsychology Press.
Hale, J. B., Fiorello, C. A., Dumont, R., Willis, J. O., Rackley, C., & Elliott, C. (2008). Differential Ability Scales–Second Edition (neuro)psychological Predictors of Math Performance for Typical Children and Children with Math Disabilities. Psychology in the Schools, 45, 838-858.
Hale, J. B., Fiorello, C. A., Miller, J. A., Wenrich, K., Teodori, A. M., & Henzel, J. (2008). WISC-IV assessment and intervention strategies for children with specific learning disabilities. In A. Prifitera, D. H. Saklofske, & L. G. Weiss (Eds.), WISC-IV clinical assessment and intervention (2nd ed.) (pp. 109-171). New York, NY: Elsevier Science.
Hale, J. B., Fiorello, C. A., Kavanagh, J. A., Holdnack, J. A., & Aloe, A. M. (2007). Is the demise of IQ interpretation justified? A response to special issue authors. Applied Neuropsychology, 14, 37-51.
Hale, J. B., & Fiorello, C. A. (2004). School neuropsychology: A practitioner’s handbook. New York, NY: Guilford Press.
Hale, J. B., Fiorello, C. A., Bertin, M., & Sherman, R. (2003). Predicting math competency through neuropsychological interpretation of WISC-III variance components. Journal of Psychoeducational Assessment, 21, 358-380.