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Introduction

Barriers to Achievement in Mathematics

With the notable exception of the article reprinted from the New Beacon, (included for its interesting historical perspective), a thorough review of the literature reveals that achievement in mathematics among blind and severely visually disabled persons is, and always has been, extraordinarily low. There are several reasons for this unfortunate situation. The first and perhaps most important reason is that mathematics is very visual in nature. Visual reference is the basis for much of the language of mathematics, with the description of such things as direction, quantity, and shape as fundamental elements. The development of spatial and directional concepts, as well as understanding of the concepts of object permanence and conservation of mass and volume is often delayed in children who are congenitally blind; and the student who is blind must piece together information which is perceived as a whole, in its entirety, by the sighted student.

For a person who has no sight or very little useful sight, the study of mathematics is difficult. It requires considerably more effort on the part of the student who is visually disabled than does the study of fields which are more verbal in nature. Generally, in order to achieve at reasonably high levels in mathematics, blind students must possess greater aptitude for the subject than their sighted counterparts. Since mathematics is difficult for blind persons to learn, students are unlikely to demand more emphasis on the subject. Younger students, of course, have no knowledge of the fact that they are not receiving sufficient training.

A second major reason for poor achievement in mathematics among blind students is that teachers of visually impaired students and rehabilitation specialists often lack skill and knowledge in the area of mathematics instruction. Many have had inadequate preparation in the Nemeth Code. While it is logical for personnel preparation programs to concentrate on the literary braille code, instruction in the Nemeth Code is often relegated to a subordinate position in the array of skills and knowledge. Consequently, many teachers lack confidence in their ability to teach the reading and writing of braille symbols in mathematics; this becomes a neglected area of instruction.

A third reason for inadequate mathematics instruction is that only a small minority of individuals who join the field of special education and rehabilitation have technical backgrounds in which mathematics was a major portion of their study. Many teachers and rehabilitation specialists have concerns about their personal level of mastery of the field. There is a natural tendency in the art and practice of teaching to place emphasis on areas which are of interest to the instructor, areas in which the instructor has expertise. Mathematics, therefore, usually is not the focus of instruction.

All of these factors taken together combine to result generally in poor achievement among students who are blind. That lack of expertise in mathematics results in a lasting deleterious effect on the students' further education and training, and thus, it has a deleterious effect on the individual's entire life including, in many cases, the choice of career paths. In the worst cases, the absence of well-developed skill in mathematics can result in no career path at all!