Killer Math Problems

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Many times, calculus problems take a lot of brain juice to find the right answer. They require me to counter the problems with using heuristics while reaping the benefits. The problems include salience of surface similarities (Wait! I saw a "volume" problem yesterday and I just can't do this question the same way.), mental sets (All of the other questions used this formula but now I can't seem to figure out how to use it in this question!), and functional fixedness (Perhaps the equation can be used only if it is slightly tweaked but I don't see it.)
I learn many examples in class and in my homework to give my brain a wider range of options to liken a new problem to. In this way, I can fly through test problems because I know how I did similar homework problems.

I researched several problem solving barriers at and found some interesting mental blocks: emotional (impatience, frustration, or fear of standing out),perceptual (stereotypes or confusing the problem's perspective), intellectual (lacking knowledge or the ability to use it), and environmental (stress, lack of support and communication, or distractions.
The ways to combat these blocks are logical but yet difficult to carry out consistently. The most basic suggestion is to be methodical in problem solving. This will help eliminate blocks like impatience, stereotypes, and distractions. Also, I have to realize that problems often include obstacles and that these obstacles are not my fault. The final bit of advice is that I should practice using analytical and creative approaches while solving problems so that I can use the full range of my knowledge.

Barriers to finding the best solution
Overcoming the Blocks to Problem Solving


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I have a similar experience in the calculus courses I have taken. There are many specific ways of solving different types of problems. I found that sometimes this was helpful, especially when there were two ways to solve a single problem. Other times, I found this very frustrating, like when I just couldn't think of how to do just one problem. I sometimes felt like there were just too many ways to solve problems stored in my head that once in a while I would just blank. I think that sometimes having more options can be helpful and eliminate mental sets but can sometimes make it harder to solve a specific problem.
I hadn't thought of these other problem solving barriers before, but I think that knowing about them and how to fight against them can help all areas of problem solving and critical thinking!

I think I always encounter similar problems when I am trying to solve problems of my calc2 class this semester. I have particular difficulty in generating alternatives. Also, I become anxious when problems always need to be solved with another formula or theorem. I thought mathematical thinking was very intuitive. I like the analysis you found about problem solving barriers. I think emotional and perceptual factors prevent me most of times. I am easy to get nervous and frustrated.

I experienced similar problems during Calculus I last semester. While the homework problems were fairly easy to solve, when it came to the test I could not find any similarities between the exam problems and problems from our book. What I didn't realize is that I was experiencing surface similarities. That is, the test questions focused on the same topics, but I could not figure them out because they appeared differently. Fortunately, after a few tests I became aware of this issue and studied in a new way to help me understand the exam concepts better.

I always have that feeling that the homework questions don't match up with the actual test. I can do the homework without much problem at all and then the test comes along and I struggle. It is hard to overcome the idea that the test questions are the same as the homework just in a different setting and different situation. I know personally that is hard for me to deal with. Probably why I do worse on the test than the homework assignments.

This is a very interesting post and it seems like a lot of people can relate to it, including me. I'm not exactly sure if these kind of learning barriers such as salience of surface similarities are just things that we need to be more aware of in order to over come. Maybe there is a different teaching method that can be used so that there is less of an issue when it comes to applying methods on tests. I have always classified myself as being bad at math but I think that these barriers might actually just be my problem.

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This page contains a single entry by redi0069 published on March 19, 2012 8:49 AM.

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