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Advanced Mathematics

The study of algebra, geometry and other advanced mathematics topics by blind individuals presents several challenges. One of the most serious of these is the fact that blind students cannot visualize the graphical representations of complex mathematical concepts which aid sighted students in their understanding of those concepts. An obvious example of this problem is the difficulty in representing three dimensional objects which may be the focus in the study of certain advanced topics such as geometry. However, even basic concepts often taken for granted can present difficulty for a student who is blind as he or she pursues more advanced study. An individual who is blind and who is employed as a programmer-analyst at a major university illustrates this in her comment:

I have been totally blind since birth and have studied algebra, geometry, and calculus. I found geometry especially difficult because I lacked the understanding of many spatial concepts ... I found that I had difficulty understanding such concepts as how four walls meet the ceiling, and I actually stood on a chair to study this (Dick & Kubiak, 1997, p.344).

Specific issues and guidelines related to the facilitation of the student’s use of tactile displays and graphics to aid in such study is described in the section on tactile graphics.

A second problem relates to the fact that a student who is blind cannot visualize complex mathematical expressions in their entireties. He or she must view these expressions in small portions rather than all at once as their sighted peers do. This inability to view mathematical expressions in their entirety requires the student to retain large portions of the expression in his or her memory as it is manipulated. This can make the study of algebra and other advanced topics more difficult for a less capable student who is blind than it is for his or her sighted peer with equal cognitive ability.

Techniques which facilitate students’ abilities to calculate and remember mathematics facts mentally, and to use tools for keeping track of partial sums and products, can be very helpful in this regard, although they will not eliminate the problem.

As with the development of basic concepts, the need for concrete experiences is critical to the development of many advanced mathematical concepts for a student who is blind. Acting out story problems and applying these problems to everyday situations is just as important at the advanced levels of mathematics as it is at basic levels, if students are to become capable of using their mathematics skills in functional situations or as a foundation in their pursuit of even more advanced mathematical and scientific learning.

The use of models, manipulatives, and real life items found in everyday classrooms and living environments also plays an important role in providing support to the development of mathematical skills and concepts at all levels. These items can be used for functional measuring, comparing, deduction and induction, as well as for motivating students to solve relevant problems. The following strategies are intended as illustrative examples of the use of concrete experiences to support higher mathematics concepts. They are included here as representative samples only; teachers are encouraged to develop an array of concrete experiences and problem-solving situations to help students understand the concepts involved in higher mathematics.

Strategies for teaching concepts in higher mathematics

The examples described above and other like activities can be used to good advantage in clarifying fundamental concepts in upper level mathematics.

References

Dick, T., & Kubiak, E. (1997). Issues and aids for teaching mathematics to the blind. Mathematics Teacher, 90, 344-349.