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Observations On Using Computing Technologies to Help Solve Problems

In the Problem Section for this week, six problems are posed and you are to solve them both with and without using computing technolgies. I posed these problems to a group of experienced math teachers. Some of their commentary on both the success and saisfaction of both solution approaches follow....

  • The most desireable approach...seemed to be to allow the computer to grind out masses of data. Certainly the time saved aided in saving my energies to analyze, observe and conclude. I don't see this method as being better for all cases...I see the computer as a partner who picks up the slack when asked to, but has absolutely no mind of its own.
  • At this time my computer skills probably outpace my math skills and for that reason I found the problem easier to solve on the computer. The beauty of the solution is not seen until the math solution is found. But I probably wouldn't have fully appreciated that solution if I hadn't generated those numbers with the computer while looking for a pattern.
  • Looking back on solving this problem, I wonder if, without the computer, I would have been struck by the same effect as seeing all the consecutive pair patterns appear on the computer screen. That occurance automatically set me to wondering why it was happening, which led to the factoring discovery. But what if I had never learned how to factor? Then that aspect could not have been investigated and the real understanding of the problem would have been lost.
  • The computer approach was more rapid...Somehow, the pen and paper approach felt more satisfying...I got a feeling of "Eureka" from my pen and paper exploration... Actually, the computer solution is more useful because it can be generalized more easily than my sudden realization...
  • This problem seemed to be a simple problem for the computer and a long drawn out problem if done by hand. In the process of working this problem out on the computer I had to work it out by hand on some of the smaller prime numbers. But I could only do that after I saw a pattern...I think there are two advantages to using the computer in this way. One is that students will try problems that they would not otherwise attempt. Two is that the students cannot use memorized steps to solve the problems.
  • I learned through this exercise the importance of thinking through a problem and writing it out before running wildly to the computer...
  • The solution by hand was time-consuming and required a repertoire of mathematical skills and experience. On the other hand, a flip-flop situation existed for the computer-aided solution: the computer program was simple to write and the printout with the solution was obtained quickly, and required fewer mathematical skills or experiences. The question of which solution is more desirable depends on the goals of problem solving and the problem.
What is your reaction...after trying to solve the problems both ways?