Characteristics of Students with Learning Disabilities in Math

· They have trouble performing computations, doing problem solving, understanding terms and concepts, establishing correct inferences, and connecting prior or new knowledge (Jarrett, 1999, p. 3).

· They have “visual-spatial-motor” or “perceptual-motor” deficiencies. That is, they lack the perceptual skills necessary for number sense and conceptual understanding, including poor spatial and written representational skills (Garrett, 1998). In particular, their motor skills are deficient as evidenced by how they write their numbers and symbols (i.e., they are oftentimes illegible or slow) (Mercer, 1997; Culatta, Tompkins, & Werts, 2003).

· They have weak memory skills related to achieving mastery, recall, and retrieval of facts. They could not follow procedures and processes orally and in written form and deal with problems that have multiple parts (Mercer, 1997; Culatta, Tompkins, & Werts, 2003; Bley & Thornton, 1995).

· They have weak language skills as evidenced by their difficulty in processing terms that have multiple meanings. They are unsuccessful in oral problem solving (Mercer, 1997; Culatta, Tompkins, & Werts, 2003). They especially find it difficult to understand mathematical terms and concepts. For instance, they easily get confused with “spatial and quantitative references such as before, after, between, one more than, and one less than” (Perspectives, 1998, p. 1) and have trouble with terms that have several available interpretations.

· They have weak abstract reasoning skills as indicated by their inability to deal with word problem solving, comparing, and interpreting symbols (Mercer, 1997; Culatta, Tompkins, & Werts, 2003).

· They have weak metacognitive abilities as indicated by their inability to determine a priori strategies that could assist them solve a problem successfully. They experience difficulty recognizing and establishing patterns of actions (or schemes) even if they are or have been presented with a series of similar problems and problem solutions (Mercer, 1997; Culatta, Tompkins, & Werts, 2003; Montague & Applegate, 1993).

· They are usually developmentally delayed (Cawley & Miller, 1989).

· They have weak generalization skills (Woodward, 1991; Rivera & Smith, 1987) that affect the way they perform computations (Kirby & Becker, 1988) and solve applied problems (Montague, 1992).

· They are not entirely deficient in all domains of the mathematics being learned. For instance, some children may have poor skills in one or several areas in arithmetic but have average to better skills in other areas (Geary, 2004).

· They can recall formulas and use them but they do not understand why they work (Perspectives, 1998).

· They have difficulty seeing the forest from the trees, and vice-versa. That is, some could either see the big picture of a process but are unable to successfully perform the corresponding operations in detail or could proceed one step at a time but remain unable to understand what the whole process is all about (Perspectives, 1998; Garnett, 1998). This view is similar to cases with some students with learning disabilities in math who could easily grasp concepts but fail to exhibit computational competence (Garnett, 1998). Further, they have difficulty making a connection and integrating between parts and the corresponding wholes because of their weak memory skills and poor sequencing strategies (Perspectives, 1998).

· They get the ideas and are eager to solve, however, their answers are oftentimes inaccurate (Perspectives, 1998).

According to Geary (2004), students with learning disabilities in math manifest the following behavior in the domains of number, counting, and arithmetic:

· With respect to number concepts such as understanding place-value structures or associating a number with a quantity and its correct symbol and word, it appears that mathematical disability among primary-grades children is not an “authentic disability.” That is, students with and without mathematical disability experience relatively the same difficulty understanding numbers.

· With respect to counting, primary-grades children, both with and without mathematical disability, understand the principles of one-to-one correspondence, stable order, and cardinality which are all necessary in being able to count competently. One area in which the two groups differ is their understanding of order irrelevance. That is, students with learning disabilities in math have difficulty with tasks that require counting objects in their non-adjacent order. For them, counting is a “fixed, mechanical activity” (p. 3). Another area that students with learning disabilities in math have difficulty with is in remembering the correct number counted for a given set of objects.

· With respect to arithmetic and arithmetical strategies, students with learning disabilities in math have weak memory skills. This means that even if they are capable of recalling a basic fact, they still find it difficult to master and recall as many basic facts such as 7 + 2 or 2 x 6 as they could unlike their regular counterparts who could accomplish this in a systematic manner. Further, they tend to “forget facts rather quickly” (p. 3). Having weak memory skills is an indication that students with learning disabilities in math have difficulty storing information in long-term memory. Another source of memory weakness is due to the fact that even if students with learning disabilities in math could recall a fact in long-term memory, they have difficulty suppressing other information that they think is relevant but actually is not which only confuses them. For instance, a child could easily recall how to obtain the sum of 2 and 3. The problem starts when the child thinks that 4 and 6 are also possible answers since 4 follows sequentially after 2 and 3 and that the product of 2 and 3 is 6 (pp. 3-4).

Concerning arithmetical strategies, students with learning disabilities in math employ and get stuck at performing “immature procedures” for combining numbers more often than the unlabeled students. For instance, in finding the sum of 3 + 5, students with learning disabilities in math tend to do a count-all (i.e., raise 5 fingers, raise 3 fingers, then count 1 through 8) instead of a count-on strategy (i.e., raise 5 fingers and then count on through 8) that is more efficient and practical. In the case of more complex additions, say, the sum of two two-digit numbers, while students with learning disabilities in math could perform additions correctly by columns, they have difficulty “putting them all together in the right order” (p. 4).

The summary below provides the cognitive characteristics of SLD in mathematics (Parmar and Cawley, 1997):

1. Their level of mathematical ability is two to four grades lower than the unlabeled students.

2. Their growth rate in mathematical ability is one year of grade equivalent for at least two years of formal schooling.

3. They finish high school with a mathematical proficiency of a 5th or a 6th grader.

4. They could only accomplish one full year of growth in high school for the entire four years of secondary schooling.

5. They manifest limited competence on tests that target minimum skills at the high school level.

6. They produce unusual error patterns.