Even after being identified as learning disabled LD , few children are provided substantive assessment and remediation of their arithmetic difficulties. This relative neglect might lead parents and teachers to believe that arithmetic learning problems are not very common, or perhaps not very serious.
This does not mean that all reading disabilities are accompanied by arithmetic learning problems, but it does mean that math deficits are widespread and in need of equivalent attention and concern.
Evidence from learning disabled adults belies the social myth that it is okay to be rotten at math. The effects of math failure throughout years of schooling, coupled with math illiteracy in adult life, can seriously handicap both daily living and vocational prospects. In today's world, mathematical knowledge, reasoning, and skills are no less important than reading ability.
As with students' reading disabilities, when math difficulties are present, they range from mild to severe. There is also evidence that children manifest different types of disabilities in math. Unfortunately, research attempting to classify these has yet to be validated or widely accepted, so caution is required when considering descriptions of differing degrees of math disability.
Still, it seems evident that students do experience not only differing intensities of math dilemmas, but also different types, which require diverse classroom emphases, adaptations and sometimes even divergent methods.
Many learning disabled students have persistent trouble "memorizing" basic number facts in all four operations, despite adequate understanding and great effort expended trying to do so. For some, this represents their only notable math learning difficulty and, in such cases, it is crucial not to hold them back "until they know their facts.
As the students demonstrate speed and reliability in knowing a number fact, it can be removed from a personal chart. Addition and multiplication charts also can be used for subtraction and division respectively. For specific use as a basic fact reference, a portable chart back-pocket-size, for older students is preferable to an electronic calculator.
Having the full set of answers in view is valuable, as is finding the same answer in the same location each time since where something is can help in recalling what it is. Also, by blackening over each fact that has been mastered, overreliance on the chart is discouraged and motivation to learn another one is increased. Several curriculum materials offer specific methods to help teach mastering of basic arithmetic facts. The important assumption behind these materials is that the concepts of quantities and operations are already firmly established in the student's understanding.
This means that the student can readily show and explain what a problem means using objects, pencil marks, etc. Suggestions from these teaching approaches include:.
Some learning disabled students have an excellent grasp of math concepts, but are inconsistent in calculating. They are reliably unreliable at paying attention to the operational sign, at borrowing or carrying appropriately, and at sequencing the steps in complex operations. These same students also may experience difficulty mastering basic number facts.
Interestingly, some of the students with these difficulties may be remedial math students during the elementary years when computational accuracy is heavily stressed, but can go on to join honors classes in higher math where their conceptual prowess is called for. Clearly, these students should not be tracked into low level secondary math classes where they will only continue to demonstrate these careless errors and inconsistent computational skills while being denied access to higher-level math of which they are capable.
Because there is much more to mathematics than right-answer reliable calculating, it is important to access the broad scope of math abilities and not judge intelligence or understanding by observing only weak lower level skills. Often a delicate balance must be struck in working with learning disabled math students which include:.
Many younger children who have difficulty with elementary math actually bring to school a strong foundation of informal math understanding.
They encounter trouble in connecting this knowledge base to the more formal procedures, language, and symbolic notation system of school math.
In fact, it is quite a complex feat to map the new world of written -math symbols onto the known world of quantities, actions and, at the same time to learn the peculiar language we use to talk about arithmetic. Students need many repeated experiences and many varieties of concrete materials to make these connections strong and stable.
Teachers often compound difficulties at this stage of learning by asking students to match pictured groups with number sentences before they have had sufficient experience relating varieties of physical representations with the various ways we string together math symbols, and the different ways we refer to these things in words. The fact that concrete materials can be moved, held, and physically grouped and separated makes them much more vivid teaching tools than pictorial representations.
Because pictures are semiabstract symbols, if introduced too early, they easily confuse the delicate connections being formed between existing concepts, the new language of math, and the formal world of written number problems. In this same regard, it is important to remember that structured concrete materials are beneficial at the concept development stage for math topics at all grade levels.
There is research evidence that students who use concrete materials actually develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, may better understand mathematical ideas, and may better apply these to life situations.
Structured, concrete materials have been profitably used to develop concepts and to clarify early number relations, place value, computation, fractions, decimals, measurement, geometry, money, percentage, number bases story problems, probability and statistics , and even algebra.
Of course, different kinds of concrete materials are suited to different teaching purposes see appendix for selected listing of materials and distributors. Materials do not teach by themselves; they work together with teacher guidance and student interactions, as well as with repeated demonstrations and explanations by both teachers and students.
Often students' confusion about the conventions of written math notation are sustained by the practice of using workbooks and ditto pages filled with problems to be solved.
In these formats, students learn to act as problem answerers rather than demonstrators of math ideas. Students who show particular difficulty ordering math symbols in the conventional vertical, horizontal, and multi-step algorithms need much experience translating from one form to another.
For example, teachers can provide answered addition problems with a double box next to each for translating these into the two related subtraction problems. Teachers can also dictate problems with or without answers for students to translate into pictorial form, then vertical notation, then horizontal notation.
It can be helpful to structure pages with boxes for each of these different forms. Students also can work in pairs translating answered problems into two or more different ways to read them e. I just wish i had used your service earlier.
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