Characteristics of Students with Learning Disabilities in Mathematics

1
Characteristics of Students with Learning
Disabilities in Mathematics

• F. D. Rivera, Ph.D.
• Department of Mathematics
• San Jose State University, CA
• Module 15, Session 1

2
Characteristics of Students with Learning
Disabilities in Math

• 1.  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).

3
Characteristics of Students with Learning
Disabilities in Math

• 2.  They have visual-spatial-motor or
  perceptual-motor deficiencies.
• They lack the perceptual skills necessary for
  number sense and conceptual understanding,
  including poor spatial and written
  representational skills (Garrett, 1998).
• 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).

4
Characteristics of Students with Learning
Disabilities in Math

• 3.  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).

5
Characteristics of Students with Learning
Disabilities in Math

• 4. 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.

6
Characteristics of students with learning
disabilities in math

• 5. 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).

7
Characteristics of students with learning
disabilities in math

• 6. 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).

8
Characteristics of students with learning
disabilities in math

• 7. They are usually developmentally delayed
  (Cawley Miller, 1989).

9
Characteristics of students with learning
disabilities in math

• 8. 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).

10
Characteristics of Students with Learning
Disabilities in Math

• 9. 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).

11
Characteristics of Students with Learning
Disabilities in Math

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

12
Characteristics of Students with Learning
Disabilities in Math

• 11. 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).

13
Characteristics of Students with Learning
Disabilities in Math

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

14
Characteristics of Students with Learning
Disabilities in Math (Geary, 2004)

• 13. 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.

15
Characteristics of students with learning
disabilities in math (Geary, 2004)

• 14. 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. 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.

16
Characteristics of students with learning
disabilities in math (Geary, 2004)

• 15. 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).

17
Students with Learning Disabilities in Math

• 16. 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).

18
Cognitive Competences of students with learning
disabilities in math (Parmar 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.

19
Cognitive Competences of students with learning
disabilities in math (Parmar Cawley, 1997

• 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.