Learning and Teaching How to Problem Solve

Problem solving is a very important aspect of mathematics but it is a process that I believe is difficult to teach. The first question is what is a problem? A problem can be looked at as when there is no apparent path to a solution, because if there were then it would not be a problem in the first place. In order to students to become good problem solvers, and improve at finding the path to different solutions, I think it is important for teachers to not give them step by step solutions but instead just provide them with the knowledge and basics they need, and guide them. A heuristic method should be used in which they are given guidance but not an instruction manual. This allows students to think in a higher-order about problems, as well we be creative.

            The steps to problem solving include, understanding the problem, devising a plan, carrying out the plan and looking back. I think the first three steps are pretty obvious, but looking back is something I found myself often forgetting to do and often see students do this as well. After every problem is complete, students should ask themselves the question “does this answer make sense?” Reflecting back on the problem is a very important step in completing a problem, one that can often lead to students catching a mistake they have made and again thinking at a higher-order.

            I think another important part about teaching students problem solving skills, is letting them know that making mistakes are perfectly okay in fact they are encouraged. I am a huge believer of learning from your mistakes, especially in mathematics. When a student does not first understand a problem, he/she should at least attempt the question before receiving help or guidance on the problem. I have personally experienced this in high school and continue to see it during my placements. At the beginning of class the teacher will check to see if students finished or at least attempted all of their homework, if they have and have any questions then they will take up the problems as a class. This can also lead to students teaching students, in which when one student got to the solution, they can then show and teach their classmates how. It is also important for the teacher to ask if anyone got to the answer using a different approach or provide him or her with alternate solutions. This can often lead to a class discussion as well, which is another important part of teaching mathematics and problem solving.

            Some say mathematicians are the worst communicators (Fulton, n.a). Discussion is something that is looked at as extremely important in other subjects, but if is often neglected in mathematics. This should not be the case, as many students need to discuss with their classmates out loud in order to organize their thoughts and come to a conclusion. I often find myself at first being confused or not understand a problem, but then when I discuss it with a classmate or instructor, just talking about it out loud allows me to realize how to approach it. Mathematics should be encouraged to communicate. This can be done as a class or in groups, both effective and important.

            Problem solving skills are extremely important in order to be successful mathematics students. Teachers should guide students in becoming good problem solvers through a heuristic approach and by encouraging reflection, mistakes and discussion.

picture one from: http://itsfunny.org/wp-content/uploads/2013/07/How-I-solve-math-problems.jpg

picture two from: http://www.groton.k12.ct.us/Page/6359