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Unfortunately, the effects of math disabilities can also be cumulative. Computational weakness can keep a student from reaching higher-level math, regardless of that student's potential for abstract mathematical thinking. Because of this, children with math disabilities stand the best chance of reaching their potential when developmental differences are dealt with promptly — before students lose confidence or develop a fear of the subject.
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The following is a list of math skills and warning signs that may indicate a math disability:
Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) that students are required to memorize in the earliest grades of elementary school. Recalling these facts automatically is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations. A student with a deficiency in this skill may:
* be unable to recall basic math facts, procedures, rules, or formulas
* be very slow to retrieve facts or pursue procedures
* have difficulties with precision during mathematical work
Computation
Many students, despite a good understanding of mathematical concepts, are inconsistent at computing. They make errors because they may misread signs, carry numbers incorrectly, or not write numerals clearly enough or in the correct column. These students often struggle — especially in primary school, where basic computation and correct answers are stressed — they often end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking. A student with a deficiency in this skill may:
* have difficulties with handwriting that slow down written work or make it hard to read later
* have difficulty remembering previously encountered patterns
* forget what he or she is doing in the middle of a math problem (this may also indicate an attention problem)
* have difficulties sequencing multiple steps
* lose appreciation of the final goal and overemphasize individual elements of a problem
* feel overloaded when faced with a worksheet full of math exercises
* not be able to copy problems correctly
Knowledge Transfer
One fairly common difficulty experienced by people with math problems is the inability to easily connect the abstract or conceptual aspects of math with reality. Understanding what symbols represent in the physical world is important to how well and how easily a child will remember a concept. Given a description of an equilateral triangle, for example, a student with this problem may find it impossible to visualize, or draw, such a triangle. A student with a deficiency in this skill may:
* not be able to distinguish between what is important in a math problem and what is not, particularly in word problems that include irrelevant information
* be unable to appreciate the appropriateness or reasonableness of solutions generated
* find it difficult to switch between multiple demands in a complex math problem
* have difficulty interpreting and manipulating geometric configurations
* find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
The Language of Math
For some students, a math disability is driven by problems with language. These students may also experience difficulty with reading, writing, and speaking. In math, however, their language problem is confounded by the inherently difficult terminology, some of which they never hear outside of the math classroom. These students find word problems especially difficult to translate, as they have difficulty understanding written or verbal directions or explanations. A student with a deficiency in this skill may:
* be confused by language in word problems
* have trouble learning or recalling specialized terms
* have difficulty understanding directions
* be unable to explain their confusion about math concepts and procedures
* have difficulty reading texts to direct their own learning
* have difficulty remembering assigned values or definitions in specific problems
Spatial Organization
This problem is similar to, but more severe than, knowledge-transfer problems. In general, it is an inability to effectively visualize math concepts. Students who have this problem may, for example, be unable to judge the relative size among three dissimilar objects. This disorder requires that a student rely almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. A student with a deficiency in this skill may:
* have difficulty laying out problems in a neat and organized manner
* be unable to describe what a three-dimensional object would look like if the object is rotated and viewed from a different angle
* be unable to comprehend what quantities and mathematical formulas represent in the real world
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