# Student’s Mathematical Development

Math disabilities can arise at nearly any stage of a child’s scholastic development. While very little is known about the neurological or environmental causes of these problems, many experts attribute them to deficits in one or more of five different skill types. These deficits can exist independently of one another or can occur in combination. All can impact a child’s ability to progress in mathematics.

Incomplete Mastery of Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) students are required to memorize in the earliest grades of elementary school. Recalling these facts efficiently is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations.

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Computational Weakness: Many students, despite a good understanding of mathematical concepts, are inconsistent with computing. They make errors because they misread signs or carry numbers incorrectly, or may not write numerals clearly enough or in the correct column. These students often struggle, especially in primary school, where basic computation and “right answers” are stressed. Often they end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking.

Difficulty Transferring Knowledge: 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. Holding and inspecting an equilateral triangle, for example, will be much more meaningful to a child than simply being told that the triangle is equilateral because it has three equal sides. And yet children with this problem find connections such as these painstaking at best.

Making Connections: Some students have difficulty making meaningful connections within and across mathematical experiences. For instance, a student may not readily comprehend the relation between numbers and the quantities they represent. If this kind of connection is not made, math skills may be not anchored in any meaningful or relevant manner. This makes them harder to recall and apply in new situations.

Incomplete Understanding of the Language of Math
For some students, a math disability is driven by problems with language. These children 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 hear nowhere outside of the math classroom. These students have difficulty understanding written or verbal directions or explanations and find word problems especially difficult to translate.

Difficulty Comprehending the Visual and Spatial Aspects and Perceptual Difficulties.
A far less common problem — and probably the most severe — is the inability to effectively visualize math concepts. Students who have this problem may be unable to judge the relative size among three dissimilar objects. This disorder has obvious disadvantages, as it requires that a student relies almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. Some mathematical problems also require students to combine higher-order cognition with perceptual skills, for instance, to determine what shape will result when a complex 3-D figure is rotated.

### Signs of Math Difficulties

Output Difficulties

• be unable to recall basic math facts, procedures, rules, or formulas
• be very slow to retrieve facts or pursue procedures
• have difficulties maintaining precision during mathematical work
• 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

Organizational Difficulties

• have difficulties sequencing multiple steps become entangled in multiple steps or elements of a problem
• lose appreciation of the final goal and overemphasize individual elements of a problem
• not be able to identify salient aspects of a mathematical situation, particularly in word problems or other problem solving situations where some information is not relevant
• be unable to appreciate the appropriateness or reasonableness of solutions generated

Language Difficulties

• have difficulty with the vocabulary of math
• be confused by language in word problems
• not know when irrelevant information is included or when information is given out of sequence
• have trouble learning or recalling abstract terms
• have difficulty understanding directions
• have difficulty reading texts to direct their own learning
• have difficulty remembering assigned values or definitions in specific problems

Attention Difficulties

• be distracted or fidgety during math tasks
• lose his or her place while working on a math problem
• appear mentally fatigued or overly tired when doing math

Visual-Spatial or Ordering Difficulties: A student with problems in visual, spatial, or sequential aspects of mathematics may

• be confused when learning multi-step procedures
• have trouble ordering the steps used to solve a problem
• feel overloaded when faced with a worksheet full of math exercises
• not be able to copy problems correctly
• may have difficulties reading the hands on an analog clock
• may have difficulties interpreting and manipulating geometric configurations
• may have difficulties appreciating changes in objects as they are moved in space