Chapter 5

Chapter V

Conclusions and Recommendations

Algebra anxiety exists, and represents an impairment to advancement in technical skills. When viewed in the context of what is known about the mechanisms of the human brain, it is logical to assume that the individuals who have algebra anxiety may not realize why they find algebra to be a more difficult subject for them to learn than the mathematics they may have learned with little or no problem at a younger age. Our study of the Human brain shows us that normal thinking processes are not as "logical" as they were once thought to be, and that our neural network interprets new information based on previous experience.

This means that the previous experience of the student, sets the guidelines for how new knowledge is incorporated into thought patterns. In the case of Algebra, student's previous experience with the use of alphabetical letters has been limited to the construction of words, and the ability of the individual to use letters as variables may be a logical leap beyond the individual's previous experience. It has further been shown that the ability to retain memories is directly related to the chemical activity in the brain. The presence of the chemicals of anxiety may not be conducive to the construction of memories, especially if those memories are inconsistent with the previously incorporated information in the individual's neural network.

Much is yet to be learned about the chemicals produced in the brain when experiencing anxiety. As that information becomes available, Mathematics educators should look at the implications. If educators only educate those individuals that have a predisposition towards abstraction, will our society produce citizens who are capable of filling the need for technological careers in a technological age? Or will we find a way to bridge the gap between individuals with natural powers of grasping abstraction, and those individuals who have sufficient brain capability but because of inconsistencies in their field of experience cannot initially incorporate algebra into their neural network?

This is the rationale behind the lesson, "Algebra without the Letters" in the appendix of this book. The lesson is designed to use information that has previously been incorporated into the neural network at a young age, specifically filling in the box in elementary math problems, and the natural relationships experienced on the playground with a teeter-totter. Once the process of solving in algebra has been given some rational basis in the existing neural network, the brain can then go forward with the process it does best, assimilating information.

The testing of the effectiveness of this type of approach would be one area for further study. The author has experienced success with students on a personal level with this approach, but the effectiveness of the approach is basically unproven. Case studies of students from the five classes studied in this paper, should be continued, to measure the effectiveness of the techniques in their on-going Mathematics education.

As shown by the studies of the human brain, the thinking processes are chemical in nature. As more is learned about the brain chemistry of anxiety, the emotions of students will probably become more of a concern for math educators in the future. Sheila Tobias, the renowned expert on math anxiety also wrote about retention of students in sciences in They're Not Dumb, They're Different (1990):

Freshman science should become again what it once was: the most exciting, mind-expanding course in the curriculum. "Switchers," according to Lipson's reading of the Harvard-Radcliffe protocols, and our second tier stand-ins need to enjoy their science courses. This does not mean those courses should be made easy or watered-down. Eric, Jacki, Vicki, Michele, Stephanie, Tom, and Laura wanted more rather than less challenge, but of a different kind. For them, their courses-particularly their exams-were diminished in scope and value by what they called the tyranny of technique. Baldly stated, they were of insufficient intellectual content to appeal to their wide-ranging minds and interests.(p.88-89)

Similar statements could be made about the education of students in Algebra. If mathematics instructors do not find ways of interesting their students, and building upon their knowledge base in a way that makes sense to them, a great disservice may be done to normal, healthy and intelligent students who currently might not grasp the material placed before them by "the system."

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