Volume 4, Issue B ::: September 2000
Accommodating Math Students with Learning Disabilities
by Rochelle Kenyon
There may be more learning-disabled students in your math class than you realize. If you have learners who read numbers backwards, have trouble telling time, confuse partŮ whole relationships, have difficulty keeping score in a game, and have difficulty remembering math facts, concepts, rules, formulas, sequences, and procedures, they may be learning disabled. According to the National Adult Literacy and Learning Disabilities Center, "it is estimated that 50 percent to 80 percent of students in Adult Basic Education and literacy programs are affected by learning disabilities," (1995, p. 1). The implications of such a staggering statistic for the adult basic education (ABE) teacher are worth further investigation. In this article, we will look at some common profiles of learning disabled learners and strategies you can use in your math class to meet their specific learning needs.
The term learning disabilities is often misused and applied to students who learn in different ways. Some people think of learning disabilities as something of short duration that can be cured with help. In fact, a learning disability is a lifelong condition that affects every aspect of one's daily activities. Although many definitions of the term exist, the Interagency Committee on Learning Disabilities' definition, as accepted by the National Adult Literacy and Learning Disabilities Center, will be used as a framework in this article.
"Learning disabilities is a generic term that refers to a heterogeneous group of disorders manifested by significant difficulties in acquisition and use of listening, speaking, reading, writing, reasoning, or mathematical abilities, or of social skills. These disorders are intrinsic to the individual and presumed to be due to central nervous system dysfunction. A learning disability may occur concomitantly with other handicapping conditions such as sensory impairment, mental retardation, social and emotional disturbance. It may occur along with socioenvironmental influences such as cultural differences, insufficient or inappropriate instruction, or psychogenic factors, or with attention deficit disorder, all of which may cause learning problems, but a learning disability is not the direct result of those conditions or influences." (pp. 1-2).
Teaching Strategies and Modifications for the Learning Disabled Math Student
· Avoid memory overload by assigning manageable amounts of practice work as skills are learned.
· Build retention by providing review within a day or two of the initial learning of difficult skills.
· Provide supervised practice to prevent students from practicing misconceptions and "misrules."
· Reduce interference between concepts or applications of rules and strategies by separating practice opportunities until the discriminations between them are learned.
· Make new learning meaningful by relating practice of subskills to the performance of the whole task, and by relating what the student has learned about mathematical relationships to what the student will learn next.
· Reduce processing demands by preteaching component skills of algorithms and strategies.
· Teach easier knowledge and skills before difficult ones.
· Ensure that skills to be practiced can be completed independently with high levels of success.
· Help students to visualize math problems by drawing.
· Give extra time for students to process any visual information in a picture, chart, or graph.
· Use visual and auditory examples.
· Use real-life situations that make problems functional and applicable to everyday life.
· Do math problems on graph paper to keep the numbers in line.
· Use uncluttered worksheets to avoid too much visual information.
· Use rhythm or music to help students memorize.
· Use distributive practice: plenty of practice in small doses.
· Use interactive and intensive practice with age- appropriate games as motivational materials.
· Have students track their progress; which facts they have mastered and which remain to be learned.
· Challenge critical thinking about real problems with problem-solving.
· Use manipulatives and technology such as tape recorders or calculators.
Note: While these strategies are designed with the learning - disabled math student in mind, many of them are applicable to all learners. Source: Garnett et al, 1983.
Dyscalculia-which is defined as a mathematics disability resulting from neurological dysfunction-can be as complex and damaging as a reading disability, which tends to be more routinely diagnosed. According to The Math Page web site, being classified with dyscalculia means having: "intellectual functioning that falls within or above the normal range and a significant discrepancy between his/her age and math skills (usually two years or more). To be diagnosed with dyscalculia, it is important to make sure that math deficits are not related to issues like inadequate instruction, cultural differences, mental retardation, physical illness, or problems with vision and hearing." It is not as commonly diagnosed as dyslexia in school because of the lack of any strict or measurable criteria.
with dyscalculia experience various debilitating problems
in handling daily math functions. According to Garnett (1992), the difficulty is manifested in conceptual understanding, counting sequences, written number symbol systems, the language of math, basic number facts, procedural steps of computation, application of arithmetic skills, and problem-solving. "Mathematics learning disabilities do not often occur with clarity and simplicity. Rather they can be combinations of difficulties which may include language processing problems, visual spatial confusion, memory and sequence difficulties, and or unusually high anxiety" (Bliss, 2000).
Adult education teachers need to individualize instruction for students who have learning disabilities in math. Using diverse approaches, specific emphases, and strategies and modifications that capitalize on students' strengths and minimize their weaknesses will help them to compete successfully in ABE classes. One common approach recommended by many experts in the field is the CSA sequence: from concrete, to semiconcrete, to abstract. The use of manipulatives is also encouraged. Let's take a look at two hypothetical students who are experiencing math learning disabilities and how their teachers might best facilitate their learning.
Timothy is a 28-year-old restaurant worker who dropped out of school in ninth grade. His supervisor referred him to the Adult Center, and is providing him with incentives to improve his math skills. On the Test of Adult Basic Education (TABE), Timothy scored 8.1 in reading and 8.9 in language. In math overall, he scored only a 2.3, indicating a significant discrepancy. In the placement interview, the counselor was able to determine that Timothy "has always struggled to learn math." In math class, he experiences emotional blocks and is unable to think clearly. When his frustration level peaks, he often becomes belligerent and leaves class. In addition to high anxiety, he has difficulty mastering the basic counting sequence and math facts in the four basic operations. He also experiences difficulty in placing basic facts into long-term memory, and remembering and accessing information. He depends on the "counting all" procedure using his fingers, circles, pencil marks, or other visible reminders rather than more mature counting strategies.
Timothy's instructor might decide to capitalize on his intrinsic learning style: Is he a tactile, visual learner? She should try to try to provide a stress-free environment where learning is not tied to credits or grades. Using the CSA sequence will help him to understand math concepts and therefore alleviate some of his anxiety. After he understands the concepts, the instructor can develop some pocket-sized math fact charts that Timothy can rely on when needed. She should use intensive practice with motivational games and reading material, not forgetting that manipulatives are always useful. If he can learn to use drawing to express math, he may grasp concepts more easily. Exercises that include memory aids and thinking strategies might also be useful. Timothy's progress will be slow but steady, and his fear of math should gradually diminish.
Bernadette is 43 years old with nine children and five grandchildren. Her husband just passed away after a long illness. Bernadette dropped out of high school at 16 when she became pregnant with her first child. She has never been employed outside the home. Her husband was substantially older than she and convinced Bernadette that she was not capable of handling money. She has never paid a bill, used a checkbook or credit card, or made a transaction at a bank. According to Bernadette, "math was her least favorite subject." Bernadette was brought to the Adult Center by one of her children who is employed at the school. Bernadette had always envisioned returning to school, but life's responsibilities never allowed her the time to do so.
During her first meeting with the counselor, Bernadette admitted to having always been in a special class where she was "stupid in math." The results of the TABE revealed a discrepancy between her math and reading/language scores. Previous school records were located and confirmed a diagnosed learning disability. Her inability to do math caused lowered self-esteem, withdrawal of effort, and avoidance behaviors to anything involving numbers. She generally lacks persistence in math. She has a limited ability to estimate, cannot retain math facts, and forgets the order of procedures. She has trouble understanding mathematical concepts. She has a limited ability to solve problems in one particular way, but gets confused when the same problem is presented in several different ways. Her visual/perceptual/spatial problems make it difficult to express answers to a problem with paper and pencil.
Bernadette's math teacher can capitalize on Bernadette's strength in listening and following sequential directions. Bernadette needs to work with manipulatives so she can use her tactile senses rather than depending upon reading, by breaking down problems into step-by-step sequences. She might pair her with a volunteer tutor and use math videotapes and drill and practice activities. If tutoring can take place in a private room, Bernadette can learn without interruption and without the stigma of feeling that she is being judged. Once she has developed some confidence, Bernadette may benefit from working with other students who also enjoy using manipulatives. The math problems they work on should all be designed to have meaning to Bernadette, related to functional needs such as shopping expenses, checking accounts, and recipe calculations. Bernadette may become a regular in class as she sees the relevance of math in her life and learns that she is capable of successfully handling money and other math-related household tasks.
Common Problems of Learners
Accommodations is a long word to describe a different way of doing something. The term is defined by the University of Kansas in its handbook Accommodating Adults with Disabilities in Adult Education as "÷any change to a classroom environment or task that permits a qualified individual with a disability to participate in the classroom process, to perform the essential tasks of the class, or to enjoy benefits and privileges of classroom participation equal to those enjoyed by adult learners without disabilities. An accommodation is a legally mandated change that creates an equitable opportunity for task completion or environmental access. Further, an accommodation is an individually determined adjustment to a functional need" (1998, p. 54).
They can be strategies and modifications that are used by the classroom teacher; there are also accommodations such as specialized equipment, assistive technology, and variations in the methods and materials of testing for adults with learning disabilities.
Accommodations are required by law. They help persons with disabilities to have a fair and equal chance to work, learn, and have access to physical facilities such as buildings and parks. They are based on individualized, documented needs and may include any or all of the following: (1) using special equipment, (2) changing how others think and feel about disabilities, (3) learning and working in a different place or in a different way, and (4) changing procedures. The following suggestions for accommodations were compiled from the Math Remediation and Learning Strategies web site.
Learners whose visual processing speed poses problems in classroom learning might use a note taker or a tape recorder so they can concentrate on the lesson rather than on taking notes. They might receive large print handouts including important textbook pages or take notes in different colored pens to help differentiate concepts. Trained tutors can be useful to these learners. Those who have trouble with short-term memory and auditory processing also may find useful a note taker or a tape recorder with a counter. It might help them to sit close to the teacher, or to use math videotapes to reinforce class work. Meeting with a trained tutor and tape recording important tutor explanations can also help.
Tactile learners benefit from the use of calculators, manipulatives such as blocks, Cuisinaire rods, beans, or any other hands-on materials with which they can solve problems using their hands. The scratchy surface of sandpaper, which can be cut into numbers or other shapes, provides a stimulus to tactile learners. Fluid reasoning and long-term retrieval problems can be alleviated by use of a note taker, a tape recorder with tape counter, handouts, math video tapes, fact sheets or flash cards, calculators, strategy cards, color-coded problem steps and trained tutors.
All learning-disabled students should have the benefit of accommodations in testing situations. These adjustments might include extended time; private, quiet test areas; or enlarged-type test questions. Test readers or listening to the test on audiotape can help those who have difficulty reading. Responding on the chalkboard; having the test printed on specially lined paper; color-coded math equations for those who have trouble discerning visual symbols but respond to color; using calculators; or doing the test orally are other accommodations that may be appropriate.
Working with learning disabled students is both rewarding and challenging. Numerous resources are available to assist you in developing instructional modifications and accommodations and finding appropriate materials and resources. Keep in mind that techniques that work well with learning disabled students can be equally effective with their nondisabled classmates.
The special needs of a student with learning disabilities make that student unique. Meeting those needs so that the student will best learn, by enhancing strengths and minimizing deficits, will increase his or her ability to learn. With some additional planning, the rewards of such accommodations will be shared by the student and the teacher.
Cooper, R. (1994). Alternative Math Techniques Instructional Guide. Harrisburg, PA: Pennsylvania Department of Education, Bureau of Adult Basic and Literacy.
Garnett, K., Frank, B., & Fleischner, J.X. (1983). A strategies generalization approach to basic fact learning (addition and subtraction lessons, manual #3; multiplication lessons, manual #5). Research Institute for the Study of Learning Disabilities. New York, NY: Teacher's College, Columbia University.
LDinfo Web Site: http://www.ldinfo.com/dyscalculia.htm#top
Math Remediation and Learning Strategies web site: http://www.conknet.com/~p_bliss/Math.html
Miller, S.P., & Mercer, C. D. (1997). "Educational aspects of mathematical disabilities." Journal of Learning Disabilities, 30 (1), 47-56.
National Adult Literacy and Learning Disabilities Center (Summer, 1995) Adults with Learning Disabilities: Definitions and Issues.
North Dakota State University's web site: http://www.cc.ndsu.nodak.edu/at/guide/sec09.html no longer includes the references it had when the first draft of this article was written.
Web Site: http://www.dyscalculia.org/teacher.html
About the Author
Rochelle Kenyon received her doctorate in Educational Leadership from Florida Atlantic University. She has been in adult education for the past 29 years as a teacher, educational specialist, curriculum supervisor, and school administrator and is retired from an administrative position in the Broward County public schools. She is an adjunct professor at several South Florida universities.