What I'm trying to say is that there is more to advanced subjects such as mathematics or physics than just speed alone. It isn't the primary factor in determining the success level of a student. I would rather rate level of understanding and knowledge, and the interest that the student has in such topics, as a primary determinant of a student's ability to succeed.
True, I'm not trying to debate the usefulness of the small error percentage when going at a faster pace. I'm simply trying to determine whether methodical thinking can be disadvantageous from an educational viewpoint. It is clear that methodical thinking is a great advantage
for working professionals who cannot afford, either on behalf of themselves, or the company/government/organizations they are working for, to mess up with their calculations. Even a 1% error percentage may be enough to destroy months of painstaking work. So if caution is required in the professional field, why is it left to wild abandon in (most) testing situations? (Disregarding the few tests that need a methodical approach to finish problems
I understand where you are coming from, obviously it may be necessary for engineers if they are working on a fixed time schedule and have a lot of work to do. Concentration, however, parallels the thought processes that I originally mentioned in the first post. While concentration and the actual thought process closely follow together, even the most ably concentrated person, who is totally fixated on getting his/her task done, can still accomplish tasks slower or faster than his/her peers. Perhaps thinks just "click" faster for those faster-minded individuals?
Alas, I have seen this as well. People who would make excellent scientists end up going into other fields that don't utilize their strengths. I'm not saying that it is a "waste" per se, but it is a little disappointing.
I still wonder why swift calculations seem to be more desired in the educational community than a methodical, accurate approach. I mean, shouldn't scientists be given the time to think things through? Modern computers can swiftly crunch algorithms at several billion operations per second...