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is critical to students with learning deficiencies in mathematical skills and/or concepts. Many learning deficiencies might not occur in the first place if this instructional triad were the universal basis for all instruction in mathematical concepts. It is true that children can learn 8 x 7 = 56 by other procedures such as excessive repetition, but the question becomes, "Is this learning or training?" If one believes in the training premise, can it then be assumed that all hope for teaching exceptional children to reason or think is to be abandoned? For some students training may be adequate, but for most students learning is desired. All citizens, regardless of exceptionality, are entitled to reason to the best of their ability. Manipulative materials and experiences are an integral part of teaching such reasoning ability to students. Ultimately, mathematical skills and concepts must be applied in daily living. This requires judgment, reasoning, decision making and logic. Unfortunately, too many teachers of, and materials for, the mathematically handicapped rely on instruction that is abstract in nature and depends almost exclusively on repetition. In discussing diagnosis, prescription, and instruction for the mathematically handicapped, the three major considerations are: (1) the content to be learned, (2) the learner, and (3) the materials of instruction.

MATHEMATICAL CONCEPTS AND SKILLS Diagnosis, Prescription and Correction of Deficiencies