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.
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.