Over the past week we learnt a lot about problem solving and problem solving strategies. There are so many strategies that you could use to solve a problem, but some of those strategies work best with certain types of problems. Learning how to utilize Polya’s four step process is the first step in becoming great at problem solving. His second step is called “Devise a Plan”, and there are many strategies that fall under this step. Polya’s problem solving strategies are: Guess and Test, Draw a Picture, Use a Variable, Look for a Pattern, Make a List, Solver Simpler Problems, and Draw a Diagram.
The two strategies I rarely use are guess and test, and look for a pattern. To me, these two strategies are a last resort and do not seem as effective to me. The strategies that I would typically use are draw a picture and use a variable. I am more of a visual person, so if I can see the problem it is more likely that I will be able to solve it. Especially in math, it seems that there is always a way to draw a picture, whether it be geometry, solving areas, lengths, and volumes, fractions, or even related rates. Visually seeing the problem helps me identify what I need to solve and which measurements I should use to solve it. Using a variable is also a strategy I use often. This semester, a lot of my classes revolve around proofs, and using a variable is a very important strategy in those classes.
While we were working on some of the problems from Wednesday’s class, I began to get frustrated because I couldn’t figure out the answer right away. At the back of my head I remembered reading the suggestions from successful problem solvers (p. 31) and and I began to calm myself down. I thought about the questions in different ways, and I tried different strategies that I normally would not use. The problems started to become more clear and even though I did not get the answer for a few of the questions, I did gain a deeper understanding of the problem solving strategies.
This week was the first time where I thoroughly looked at the curriculum and it seems easy to understand and follow. Relating the problems we were given to the curriculum helped me gain a deeper understanding of the curriculum and how it is used in problem solving. Choosing a problem, then relating it to the curriculum is efficient, but what I would do is read the curriculum then I would find a problem that relates to it. I’m sure I will use both ways when I start planning my own lessons and finding my own problems since they both work well.
It is important that we tell our students that there are numerous strategies they can use, and that they should become familiar with all of them.