Dyscalculia (difficulty in learning or comprehending mathematics) was originally identified in case studies of patients who suffered specific arithmetic disabilities as a result of damage to specific regions of the brain. Recent research suggests that dyscalculia can also occur developmentally, as a genetically-linked learning disability which affects a person's ability to understand, remember, and/or manipulate numbers and/or number facts (e.g. the multiplication tables). The term is often used to refer specifically to the inability to perform arithmetic operations, but is defined by some educational professionals and cognitive psychologists as a more fundamental inability to conceptualize numbers as abstract concepts of comparative quantities (a deficit in "number sense"). Those who argue for this more constrained definition of dyscalculia sometimes prefer to use the technical term Arithmetic Difficulties (AD) to refer to calculation and number memory deficits.
Dyscalculia is a lesser known disability, similar and potentially related to dyslexia and Developmental Dyspraxia. Dyscalculia occurs in people across the whole IQ range, and sufferers often, but not always, also have difficulties with time, measurement, and spatial reasoning. Current estimates suggest it may affect about 5% of the population. Although some researchers believe that dyscalculia necessarily implies mathematical reasoning difficulties as well as difficulties with arithmetic operations, there is evidence (especially from brain damaged patients) that arithmetic (e.g. calculation and number fact memory) and mathematical (abstract reasoning with numbers) abilities can be dissociated. That is (some researchers argue), an individual might suffer arithmetic difficulties (or dyscalculia), with no impairment of, or even giftedness in, abstract mathematical reasoning abilities.
The word dyscalculia comes from Greek and Latin which means: "counting badly". The prefix "dys" comes from Greek and means "badly". "Calculia" comes from the Latin "calculare", which means "to count". That word "calculare" again comes from "calculus", which means "pebble" or one of the counters on an abacus.
Dyscalculia can be detected at a young age and measures can be taken to ease the problems faced by younger students. The main problem is understanding the way mathematics is taught to children. In the way that dyslexia can be dealt with by using a slightly different approach to teaching, so can dyscalculia. However, dyscalculia is the lesser known of these learning disorders and so is often not recognized.
Another common manifestation of the condition emerges when the individual is faced with equation type of problems which contain both integers and letters (3A + 4C). It can be difficult for the person to differentiate between the integers and the letters. Confusion such as reading a '5' for an 'S' or not being able to distinguish between a zero '0' for the letter 'O' can keep algebra from being mastered. This particular form of dyscalculia is often not diagnosed until middle or high school is entered. Contents [hide]
* 1 Potential symptoms * 2 Potential causes * 3 See also * 4 External links * 5 Further reading * 6 References
* Frequent difficulties with arithmetic, confusing the signs: +, −, ÷ and ×. * Inability to tell which of two numbers is the larger. * Reliance on 'counting-on' strategies, e.g., using fingers, rather than any more efficient mental arithmetic strategies. * Difficulty with everyday tasks like checking change and reading analog clocks. * Inability to comprehend financial planning or budgeting, sometimes even at a basic level; for example, estimating the cost of the items in a shopping basket or balancing a checkbook. * In some severe cases, the sufferer may have very bad co-ordination, causing them to fall or trip often * Difficulty with times-tables, mental arithmetic, etc. * May do fairly well in subjects such as science and geometry, which require logic rather than formulas, until a higher level requiring calculations is obtained. * Difficulty with conceptualizing time and judging the passing of time. * Problems differentiating between left and right. * Having a poor sense of direction (i.e., north, south, east, and west), potentially even with a compass. * Difficulty navigating or mentally "turning" the map to face the current direction rather than the common North=Top usage. * Having difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 10 or 20 feet away). * Inability to grasp and remember mathematical concepts, rules, formulae, and sequences. * An inability to read a sequence of numbers, or rotating them when repeated such turning 56 into 65. * Difficulty keeping score during games. * Difficulty with games such as poker with more flexible rules for scoring. * Difficulty in activities requiring sequential processing, from the physical (such as dance steps) to the abstract (reading, writing and signaling things in the right order). May have trouble even with a calculator due to difficulties in the process of feeding in variables. * The condition may lead in extreme cases to a phobia of mathematics and mathematical devices.
Scientists have yet to understand the causes of dyscalculia. They have been investigating in several domains.
* Neurological: Dyscalculia has been associated with lesions to the supramarginal and angular gyri at the junction between the temporal and parietal lobes of the cerebral cortex. * Deficits in working memory: Adams and Hitch argue that working memory is a major factor in mental addition. From this base, Geary conducted a study that suggested there was a working memory deficit for those who suffered from dyscalculia. However, working memory problems are confounded with general learning difficulties, thus Geary's findings may not be specific to dyscalculia but rather may reflect a greater learning deficit.
Studies of mathematically gifted students have shown increased EEG activity in the right hemisphere during algorithmic computational processing. There is some evidence of right hemisphere deficits in dyscalculia.
Other causes may be:
* Short term memory being disturbed or reduced, making it difficult to remember calculations. * Congenital or hereditary disorders. Studies show indications of this, but the evidence is not yet concrete. * A combination of these factors.
Although dyscalculia may be difficult to diagnose, there are strategies that teachers and parents should know about to aid students in learning mathematics.
1. Encourage students to work extra hard to "visualize" mathematics problems. Draw them or have them draw a picture to help understand the problem, and make sure that they take the time to look at any visual information that is provided (picture, chart, graph, etc.)
2. Have the student read problems out loud and listen very carefully. This allows them to use their auditory skills (which may be strength).
3. Provide examples and try to relate problems to real-life situations.
4. Provide younger students with graph paper and encourage them to use it in order to keep the numbers in line.
5. Provide uncluttered worksheets so that the student is not overwhelmed by too much visual information (visual pollution). Especially on tests, allow scrap paper with lines and ample room for uncluttered computation.
6. Discalculia students must spend extra time memorizing mathematics facts. Repetition is very important. Use rhythm or music to help memorize.
7. Many students need one-on-one attention to fully grasp certain concepts. Have students work with a tutor, a parent, or a teacher after school hours in a one-on-one environment.
8. If possible, allow the student to take the exam on a one-to-one basis in the teacher's presence.
9. The student might like instant answers and a chance to do the problem over once s/he is wrong. Often their mistakes are the result of "seeing" the problem wrong.
10. In early stages, design the test problems "pure," testing only the required skills. In their early learning, they must be free of large numbers and unnecessary destructive calculations.
11. Allow more than the "common" time to complete problems and check to see that student is not panicking (tears in eyes, mind frozen).
12. Most importantly, be PATIENT! Never forget that the student WANTS to learn and retain. Realize that mathematics can be a traumatic experience and is highly emotional because of past failures. The slightest misunderstanding or break in logic can overwhelm the student and cause emotional distress. Pity will not help, but patience and individual attention will. It is typical for students to work with until they know the material well and then get every problem wrong on the test. Then 5 minutes later, they can perform the test with just the teacher, on the chalkboard, and many times get all problems correct. Remember that this is very frustrating for the teacher/parent as well as the student. Patience is essential.
13. Assign extra problems for practice and maybe a special TA (teaching assistant) or special education is assigned to assist the affected student.
14. When presenting new material, make sure the student with discalculia is able to write each step down and talk it through until they understand it well enough to teach it back to you.
15. Go over the upcoming lesson with so that the lecture is more of a review.
TECHNOLOGY AND REOURCES
The technology for remediating and accommodating persons with mathematics disabilities has not developed as readily as the technology for reading and writing. However, the technology, which is available now, can provide beneficial assistance for some problems.
The limited technology can be of help, especially to those who have problems writing numbers down in the correct order. The most common currently available tools include the following:
* hand-held calculators that can help a learner who has problems writing numbers in the correct order; * talking calculators that vocalize data and resulting calculations through speech synthesis; * special-feature calculators that enable the user to select options to speak and simultaneously display numbers, functions, entire equations, and results; * on screen computer calculator programs with speech synthesis; * large display screens for calculators and adding machines; * color coding for maintaining columns; * big number buttons and large keypads; * textbooks on CD-ROM and video-taped mathematics lessons
Computer-assisted instruction (CAI) mathematics courses (instruction targeted to special students) are being developed. These are particularly helpful to the user with learning disabilities if the learning is reinforced with voice output. Here are some computer programs that may be helpful for mathematical learning.