Can you help me solve this problem?

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I'm sure many of you, even today, have run into a problem or were assigned a problem in which you had to find a solution. Last semester I took Calculus I, where I ran into numerous math problems where I got stuck and didn't know how to solve it. Sometimes I spent hours on one problem, repeatedly trying to solve it in different ways. I would try using different algorithms to help lead me to the correct solution. Once in awhile, I would find myself in a mental set, where I come across a math problem and assume to incorporate the most recently learned formula, when really I can solve the problem without it. Fully understanding the idea of the problem before solving it would have helped me avoid this barrier.

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In an article I read, there was a study done on algebra students to see if there was a correlation between writing about a problem while solving it and the students overall performance in solving the problem. In the study, the students were asked to solve a difficult problem that required much more than a simple use of equations and formulas. The experimental group was told to write down the steps they took during the process of solving the problem. On the other hand, the control group was just simply told to solve the problem. The results in fact showed the scores of the experimental group to be significantly higher than the control group.

In the article, Kenneth Williams concludes that "writing about a mathematical concept helps students to organize their thought processes about that concept, focus on difficult points and more clearly understand the concept." The writing procedure helped the students' organization, as well as giving them guidance through more difficult problems. Overall, this research suggests students to write down the steps taken in the process of problem solving, as it has been evidenced to be advantageous to their learning.

Link:

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CDsQFjAC&url=http%3A%2F%2Fuserwww.sfsu.edu%2F~jcooks%2Fold_projects%2Fmathguides%2Fmath15.doc&ei=ZfZvT9rWIMXdgQfWka1r&usg=AFQjCNHFI8k-3XeUs8w-pogqTtrnSs1L-g

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That's interesting, I had no idea there has been studies done on the whole math equation conundrum. I've found that through personal experience if I get stuck, many times just stepping back and taking a break will help me figure it out. Seems similar to what you found in Calculus.

It's really interesting that this study was conducted, and I definitely think there is truth in the findings. I know that when I study for a math exam, it helps me to write down the steps on how to figure out a certain type of problem, and also to think about what a problem is really asking and what it means.

I remember in some math classes in high school students would have to right down the steps to everything they did in a problem. Students hated doing it and found it pointless. Maybe it was helpful after all.

I have had numerous problems that I've spent hours of time repeatedly doing until finally, I had come to the correct answer. The steps I usually took were relevant to the chapter, they were from the chapter actually, and I would wonder how I wasn't coming to the correct answer. In the end, my steps of problem solving were a little too complex for the problem, and the correct answer was found from a concept as simple as 6 or 7 chapters from before. If I had wrote down the steps that I should have taken, I would have better comprehended when and where, when given a problem that pertained to it, I needed to use that easier type of problem solving. Basically, math sucks because it makes you do complicated levels of thinking that you stick with and when you run across a problem that takes little to no brainpower, you put ALOT of thinking into it.

I also took Calc I last semester and found myself using algorithms which were incorrect for the situation and getting frustrated. Although I had been told about several problem solving steps which would help me, I always thought I was too "smart" for those, and could get along. Looking back, I should have tried some of the problem solving tips you outlined, as well as others.

It is interesting to relate this to the theory that there are many ways to approach problem solving. A number of people would probably more efficiently solve this problem without writing about it.. perhaps these people are more "mathematical" thinkers. More "creative" thinkers, however, would undoubtedly benefit from taking the approach of writing.

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This page contains a single entry by satoh009 published on March 25, 2012 11:49 PM.

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