Thinking more on yesterday's post about exact calculation vs. approximation in problem solving....Because quite different areas of the brain mediate problem solving by exact calculation and approximation, one could also consider them to be alternative learning styles or problem solving strategies.
Often traits of precision (being exact, detail-oriented) vs. big-picture (gestalt) orientaion were thought to be personality-based. But there are advantages and disadvantages of both approaches, so that the ideal way to approach problems would seem to be able to have both tools in your arsenal so that you could choose which approach might be most successful in a particular situation.
The advantages of 'exact' problem solving seem somewhat self-evident. It is precise, allows for greater reproducibility, builds on prior knowledge, and can result in rapid processing with repetition.
Approximate problem solving can also be important though. Because it is representational and approximate, it may more flexible in terms of considering information, it may be more extrapolatable to different situations, and it may provide more accurate information when not all the facts are known or some information is incorrect.
If you teach, it is important to be aware of your orientation (detail vs. gestalt), because it may color how you view your pupil. Detail-oriented teachers may see gestalt students as sloppy and flakey. Whereas as gestalt-oriented teachers may see their precision-orientated students as overly fastidious and rigid. In practical matters as well, there are many situations in which your most obvious way to solve a problem (exact vs. approximate) will obscure your vision from the opposite point-of-view.
How do you do long division? Do you know your facts and perform the stepwise calculations as you learned them? If so, you may not see how your student would prefer to use reverse multiplication and estimate to derive her answer.
How do you figure out where you are when you're lost? Do you retrace your steps, count stop signs or look for landmarks? (exact) Of so, you may have a hard time understanding why your spouse prefers to use geometry, visualize an internal 'aerial' map and head out driving 'over there somewhere'.
The truth is, within every domain their are great men and women on both sides of the this exact-general divide. There are Nobel prize winners or other eminent men and women in science, art, history, economics, engineering, literature who have use either strategy to break new ground using exact or general tools of inquiry.