Archive for January 28th, 2006

A Research Paper for Paraeducator II Class

Saturday, January 28th, 2006

MATH LEARNING DISABILITIES

Among students who are classified as learning disabled, arithmetic difficulties are as common as reading problems. Some studies suggest that 6% of school age children have significant math deficits. Such students may respond to repeated failure by not trying to learn anymore and by lowered self-esteem. As such students reach adulthood, their math illiteracy will handicap them in daily living, and will limit their job prospects. What are some of these math disabilities?

One disability involves mastering basic number facts in all four operations (addition, subtraction, multiplication, and division). Such students need help with thinking strategies, not just fact practice. Mathematical reasoning is the goal, not mindless computation. The use of a pocket facts chart can be helpful. Eventually, students will hopefully note a pattern to these facts. Much practice in small doses is helpful. A small number of facts should be presented for mastery at a time, and practice should be interactive, with active engagement by the student. It can be helpful for the student to chart his/her own progress. Another helpful strategy is to ask the student, “How do you remember (math fact)?” Have him drill himself using his own strategy.

The brain tends to remember material that:
• It is ready for.
• Has meaning.
• Can be arranged in patterns.
• Can be linked to previously learned information.

Another math disability involves the student being reliably unreliable in paying attention to operational signs, borrowing/carrying appropriately, and in sequencing steps in complex operations. Such a student may not be very disabled, in reality. He may have a good grasp of math concepts, but have weak lower level skills. Graph paper or lined paper turned sideways can help the student organize written work on a page. This is an aid in properly aligning columns of numbers for addition/subtraction, and for division problems. The teacher and Para educator can partner with the student to help him develop his/her own compensations for this disability.

Other students do have good informal math understanding, but have difficulty with the formal procedures, language and symbols of math. This informal/formal gap is a factor in the majority of math learning problems. Such students need many experiences with concrete materials, or manipulatives, which they can physically hold, move, and group to make strong connections between informal and formal math. Such children are not really helped by the practice of using workbooks. Students must become demonstrators of math ideas, not just problem answerers. To truly succeed in math, understanding must be connected with the symbolic representations of math. If students do not see the connection between real things and more abstract mathematical principles, they will not look for patterns or meaning. They will view math as a collection of unconnected facts to be memorized, but not understood. To establish the connection between math and meaning, the practice of estimation can be used. The student can then note whether his final answer really makes sense.

Math disability may arise from a misunderstanding of the language of math. Some students with language deficits may react to math problems as signals to do something, rather than as mathematical sentences to be read for understanding. For such students, the teacher should slow down the pace of delivery in presenting concepts, offering explanations, giving directions and asking questions. Information should be given in small chunks. Students should be encouraged to read and say problems before and after computing them, and to ask themselves, “Does this answer make sense?” It can be helpful for students to play teacher and explain their understanding of the math problem to others. Also, students who work on math in small groups are more likely to ask necessary questions.

A rare math learning disability is associated with visual-spatial-motor organization. Such students have tell-tale accompanying weaknesses: a poor sense of their body in space(clumsiness), disorganization, and difficulty understanding non-verbal social signals of gesture and facial expressions. These students need repeated experiences with real materials that can be felt, seen and moved around. They also learn well verbally.

Some students have developed emotional blocks which keep them from really thinking about math. Such students need many opportunities to see themselves as successful thinkers. If the student can be helped to see that math is not so much computation as it is problem solving, or thinking, he or she can be helped to overcome anxiety. The teacher and Para educator should work with the student to define his strengths, and then use those strengths to teach the student those concepts he/she finds to be difficult.

In Your Child’s Growing Mind, author Jane Healy, states:

Most people think of math as arithmetic, the study of numbers, and the rules or operations such as addition and multiplication that we use to manipulate them. Guess again! Mathematics is a much greater science of relationships, which uses numerical symbols to describe fundamental truths about our universe. The numbers or symbols on a page represent powerful abstract concepts – but they are rooted in concrete experience. (page 322)

This quote emphasizes what has already been stated. To help a student who is experiencing difficulties with math, math must be tied to real life, to concrete experience. The student must also be helped to see that math makes sense. It is not a grab-bag of facts to be memorized. According to Jane Healy, the child must develop two separate abilities to experience success in math:
1. The ability to comprehend relationships, to reason abstractly and to solve problems.
2. The ability to follow rules, to analyze, to compute accurately, to observe carefully, to form educated guesses, and to maintain an orderly line of thinking in problem solving.

Younger students can engage in play activities which help to build mathematical brains. Some of these activities involve:
• Small objects to count and arrange.
• Board games and dice, to learn the following of rules.
• Sorting and classifying hobbies.
• Unit blocks, patterns, and toy clocks to manipulate.

The child’s active, physical involvement in these real activities is essential, since most people learn by doing (active), not from watching it happen (passive). This is a way to teach children from the bottom up, rather than by presenting abstract rule systems too early. The more varied the experiences, and the more first-hand meaning the experiences have to the student, the more likely they will form a basis for advanced reasoning necessary for math.

Students can also be helped to overcome math difficulties by working with them to develop problem-solving skills:
• Encourage questions.
• Ask open-ended questions and welcome creative responses.
• Provide toys and games that encourage play the child creates himself.
• Show the child how to estimate.
• Practice “guess and test”, the forming of hypotheses.
• Take time to listen to the child’s ideas.
• Model adult problem-solving.
• Help the child to tolerate some uncertainty as he finds the best solution to a problem, or tests a hypothesis.

Certain facts and skills need to become automatic for a student to succeed in math. To build automaticity, the following are important:
• Motivation and involvement by the learner.
• Repetition.
• Novelty.
• Presentation through looking, saying, hearing, touching, and body movement. The more senses that can be involved in the learning process, the better.

Finally, families can help children overcome math learning disabilities and build a strong mathematical foundation by involving them in some of the following activities:
• Family games.
• Cooking.
• Shopping.
• Money-managing (allowance).
• Music lessons.
• Hobbies involving collecting and exploring nature.
• Measuring and weighing.
• Using maps and following directions.
• Calculator games.

BIBLIOGRAPHY

“Wright, C. Christina. “Learning Disabilities in Mathematics.” LDOnLine. October, 1996. WETA, Washington, D.C. January 28, 2006.

Rosner, Jerome. Helping Children Overcome Learning Difficulties. New York: Walker Publishing Company, Inc., 1993.

Healy, Jane. Your Child’s Growing Mind. 3rd ed. New York: Broadway Books, a division of Random House, Inc., 2004.