Struggling With Science Courses - Need Advice

BCEagle91
Thu, 17 Sep 2009 22:40:58 +0000

An exercise is a question that tests the student’s mastery of a narrowly focused technique, usually one that was recently “covered.” Exercises may be hard or easy, but they are never puzzling, for it is always immediately clear how to proceed. Getting the solution may involve hairy technical work, but the path towards solution is always apparent. In contrast, a problem is a question that cannot be answered immediately. Problems are often open-ended, paradoxical, and sometimes unsolvable, and require investigation before one can come close to a solution. Problems and problem solving are at the heart of mathematics. Research mathematicians do nothing but open-ended problem solving. In industry, being able to solve a poorly-defined problem is much more important to an employer than being able to, say, invert a matrix. A computer can do the latter, but not the former.

– The Art and Craft of Problem Solving, Paul Zeitz.

You can build up problem-solving abilities reading puzzle-books, belonging to a math team and working on problems, going through old math contests and talking about math problems with your peers. Of course this was stuff that would have been done at a younger age.

Zeitz talks about methodology and lore in math. The methodologies involve learning the material, processes and procedures and approaches for tackling problems without an obvious approach. The lore is about reading a ton of past problems, tricks and techniques. You might get a problem that is impossible to solve without some bit of math lore that you came across somewhere.

College professors, especially in science courses, like to give you problems that require a little bit more of a stretch. Sometimes the problem isn’t possible to do in a reasonable amount of time without knowing more than the prerequisites in the course. Sometimes the professor includes something in the news that he’s hoping that some in the class will be paying attention to.

It sounds like you are trying to do a lot of the right things but there is something missing. You indicated that it might be a language or logic problem - perhaps you haven’t had practice at trying to think out of the box. I’m sure that there are many others in the same position. I don’t know if there is a quick fix for this. It’s a kind of mentality in solving puzzles, playing with riddles, telling jokes and puns, learning theory and trying to answer the question of why?