Dr. Cotter on Learning Disabilities

Approximately one in ten students has a learning disability. For most of them, traditional methods of teaching math are a source of frustration and failure. They find rote memorization to be nearly impossible. Memorizing counting words, then facts, algorithms, and vocabulary is way too much for the struggling brain that cannot easily memorize. Even when children with learning disabilities do memorize, the results usually don’t stick very long. Things are easily forgotten. 

It might be tempting to delay teaching math and concentrate on reading. However, recent research shows that young children who are competent in math, excluding counting skills, will be more competent in reading in elementary grades. Math actually provides a foundation for reading.

Reducing the memory load is the first step for helping these children. Instead of expecting a recital of the numbers from 10 to 100, initially use the transparent number names. For example, use 1-ten 4 for fourteen and 2-ten 3 for twenty-three. This naming gives order and clarity to numbers. The temporary number naming also makes place value a natural part of numbers.

For learning the facts, provide visual strategies. A child is considered to know a fact if they can recall it in two or three seconds. This gives them time to think about a strategy to produce the fact. Use games, not worksheets, for practice. Avoid flash cards, which continuously remind students what they don’t know. 

The approach to learning algorithms has changed greatly over the centuries. No longer is there a need to add long columns of numbers, or to multiply large numbers together, or even divide by more than one digit. That drudgery is nicely handled by calculators and computers. Some might argue that they might not have a calculator available when the need for multi-digit dividing arises, but people today are more likely to have a calculator within reach than to have paper and pencil ready. Since even the answers obtained with electronic devices need to be verified, students today need to learn estimating skills and simple mental calculations.

The field of mathematics does have its own specialized vocabulary. Always use terms correctly; children with learning disabilities find it very difficult to unlearn. Use the appropriate word: say “minus” not “take-away,” “equation” not “number sentence,” “ellipse” not “oval,” and “rhombus” not “diamond.” Relate new words to known words or their root meanings. For example, the dia part in diameter and diagonal means across. Sometimes a math word has a meaning different from everyday use. For example, a diagonal in math is a line between two angles; a diagonal in everyday use is a line that is neither horizontal nor vertical.

It is well known that those with learning disabilities learn best with visualizable images. First, we need to distinguish between visual and visualizable. Something visual can be seen with our eyes; something visualizable can be seen in our mind’s eye. In order for quantities to be visualizable, they must be grouped in fives. A row of nine beads or cubes all the same color is not visualizable; they cannot be seen in one’s mind’s eye. If the first five beads of the row have one color and the remaining four have another color, the row becomes visualizable. It is interesting that the Japanese Council of Mathematics Education requires manipulatives to be visualizable.

Mathematics is much more than a hodgepodge of algorithms and formulas. Teach concepts before procedures. Research shows that what is understood is retained much longer and is much more likely to be applied to other situations. Knowing that area is the number of square units that fit inside a figure makes it easier to find all kinds of areas. And knowing that the area of a triangle is half the area of a surrounding rectangle is easier to remember than one half the base times the height. 

Problem solving is often a troublesome area for children with dyslexia. Lower reading ability may cause an additional complication. Yet problem solving is the heart of mathematics. Help the child approach a problem like a puzzle. Struggling is natural and necessary; it’s part of developing the character trait of persistence. Often it helps to take a break and try later. If a solution is instantly obvious, there is no problem to solve. Encourage the child to imagine the story problem in their mind without the numbers, and then to draw a sketch. For younger children, give them part/part/whole circles to use. Avoid teaching the child to look for key words, such as all together or how many left.

Some other factors that will help these children learn include using movement. Children learn better when they are active. They need to physically manipulative objects, not watch someone or something do it for them. Also give them paper with a grid to make organizing their written work easier.

Dyscalculia, the difficulty in learning math, mainly affects learning arithmetic. This is only one of over 200 branches of mathematics. These children often do very well in geometry and other kinds of math.

Following these recommendations will help prevent another group of people who fail to flourish in mathematics and those who develop math anxiety. Sadly, flash cards, timed tests, and poor teaching are often the cause of math phobia. We can help all children understand, apply, and enjoy mathematics. Then they will be able to pursue one of the increasing number of careers that require advanced math.


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