Quandaries
and Queries 

Subject: increasing accuracy Name: Mahdi Who is asking: Student Level: All Question: 

Hi Mahdi, I do not have 'techniques' to improve those kinds of algorithmic processes. What I do have is some words of encouragement and some sources you might look at for futher encouragement. The ability to do such calculations is NOT essential to doing mathematics (or physics). There are a couple of ways to come to terms with the connections. One is current studies of the brain, how even young children do mathamtics, etc. There are very many multiiple pathways used in the brain for doing mathematics. Those connected to numerical algorithms are only one small part. A couple of books that talk about this are Brian Butterworth, The Mathematical Brain, Macmillan, 1999. Stanislaw Dehaeme, The Number Sense, Oxford University Press, 2000. Some people really do have major differences, and difficulties with this. The word used for extreme cases is 'dyscalcula'  (the analog of Dyslexia). Try a web search on this term and you find some pages, including suggestions for teachers (and learners). The second word of encouragement would be to read about some very successfull people in the past, such as Michel Faraday, who had serious problems of this sort  but were very effective thinkers, reasoners etc. using other ways of mathematical work. A general book on this is: Thomas West, In the Mind's Eye, Prometheus Books, Amherst, New York, 1998 Faraday did NOT use formulas, but did reason with diagrams and images, developing laws of electricity and inventing the electric motor. There are more exhaustive studies of his work in other books. So I would also work at strengthening other ways of doing mathematics and mathematical reasoning in areas such as physics. If you hang in, there will be a point (often around the middle of second year university) where the public face of the problems and work changes, where such calculations are an increasingly minor part of what you need to do, and where other abilities (working with visual patterns, even connections made at a kinesthetic level) become the critical issues. I have seen students who stuggled through precalculus and the first couple of courses in calculus, suddently become the top students in the class, and others who depended too much on calculation hit a wall. So do not be fooled into believing that you cannot do math because you have difficulty with simple arithmetic calculations! To return to your original question. I think it is perfectly appropriate to use calculators and computers to do 'routine' calculations. These are 'things that make us smart'. I hope your teachers will show some broader sense of mathematics and find appropriate ways to develop and assess the more important features of doing mathematics, and leave the issues of computation to their proper (very limited) place. In a good system of education, dyscalcula would have good diagnosis and support, as would dyslexia. Neither is a sign of stupidity, or lack of effort. Nor need they be barriers to success. (There are university faculty with each of these 'learning disabilities'.) Walter Whiteley 

