Two Column Problem Solving Reflection

What an interesting idea. Often, our focus on problem solving is to create the most elegant and concise (and correct, of course) solution that we can; there is very little emphasis on the process of problem solving itself. We might discuss it minimally in describing how we came to such and such conclusion but one would not expect to hear about the attempted avenues that failed. In two column problem solving, however, every vein of thought can be presented on the page and every error is shown (depending on the level of detail that the solver decides to write down). The benefit of teaching problem solving in this way is that it assures students who are not yet familiar with 'the art of problem solving' that every thought and every consideration is valuable and can help them develop confidence in their ideas. Having them write down even wrong ideas shows that as teachers, we value the process and hard work of the individual student.

In actually working the problem through using the method, I found that when I had an idea, the necessity of writing it down dampened my thoughts somewhat as I felt an obligation to crystallize into coherent words rather than just jotting down and trying out my idea. Also, I felt slightly restricted by the columns and wound up writing everything everywhere and anywhere. That being said, I see the value in using this method if I found a problem particularly difficult and was unable to complete a problem in one go - having my lead-in thoughts on paper would help to remind myself where to go when I revisit the problem at a later date.