# Problem Solving

One recent problem I had to solve that I think exhibits some good problem solving technique was on my last Precalc II exam. It was a simple multiple choice problem that had to do with solving the triangle (finding the length of all of the side and the measure of all of the angles). This sounds easy but I blanked out on the law of cosines equation that was supposed to be used to solve this problem. I felt foolish after the exam but I did not let it stop me from finding the correct answer as opposed to completely guessing. Instead, I looked at the as it was and I ignored the fact that the intention was that students would use the law of cosines to solve it. I looked at it with the goal of solving the triangle with the information given. I do not remember the exact values given in the problem but I remember that the length of two of the sides of the triangle were given and used that fact that the angle corresponding to the longer side would have to be larger which allowed me to eliminate 2 of the four choices. This made it a 50/50 chance as opposed to ΒΌ. Then I looked at the fact that the angle given was larger than the two in left over solutions and therefore the missing side must be larger than the other two and then the choices for the right answer were brought down to one without even using the law of cosines. I feel my approach to that problem attacked the idea of functional fixedness and mental sets ( I was able to ignore the fact that the law of cosines was the equation--algorithm--that would yield the right answer 100% of the time and I was still able to work my way to the right answer). In this case a mental set wasn't that bad to have either because I was able to use the law of sines that I used to solve the previous problems on the exam to check my answer to the problem I just discussed.

Nice example! I think this is a good problem solving strategy for multiple choice exams!

I find it kind of funny that students spend so much time learning and practicing methods just so he or she can remember them for a test, but in the end you didn't even need to know the method you studied to solve the problem. I know I have experienced something like this too before. It is actually pretty frustrating though if you think about the time and energy you put into studying and then don't remember it when it comes to the test or turns out you didn't even need to know it. This reminds me of a discussion I've had in my design class about where creativity comes from. Other countries don't make students learn boring, repetitive facts, then memorize them for a test, and forget everything ten minutes later. Knowledge is meant to be applied and learned through discovery and experience. The way you solved your multiple choice problem demonstrated this really well.

I too have ran into something like this, how students spend much time on remembering formulas that form mental fixedness. There are other ways to solve a problem. Sure, the teacher usually wants you to answer the question with the formula to show work (in your case you probably had a multiple choice test with no shown work) but there are usually other ways to form solutions.

I too have encountered problems like this on both math exams, as well as other subject exams too. Sometimes the best option to solve the problem/equation is just using your own process of thinking and reasoning it out. I have found this to be a great way to start each question just to make sure you are analyzing the entire problem.

I love multiple choice problems for this exact reason. It's usually easy taking away two of the options if you at least studied and know the content of the exam and then that brings you down to a 50% chance of being right! I often do this, especially on math tests.