Thursday, August 9, 2012
On a daily basis, I get the question about why we study math. The truth of the matter is that most of us will never have to write the equation of a circle or use the quadratic formula once we get through high school. So why do we have to do it during high school? Mathematics is about problem solving methods. Every math problem that gets discussed and assigned forces us to use many, if not all, of the detailed methods of problem solving. Each individual problem becomes a small but important lesson for solving problems in general. Math is traditionally learned by first doing many simple problems. Then the simple problem solving methods are put together to solve complex problems. For instance, in order to solve algebraic equations, being knowledgeable about addition, subtraction, multiplication, and division is a must. Ordering the steps to be carried out, evaluating expressions, and learning how and when equations are used must be mastered as well. Knowing this, we then ask the question. What do all problems, mathematical or not, have in common? Successful problem solvers understand what is expected in the problems they face. In other words, they know all of the details surrounding the problem at hand, which is the most important step to solving problems. It requires attention to detail and therefore, patience. After examining the details, intelligent choices need to be made regarding the beginning steps of developing a strategy. The plan must be carried out in an order that makes sense. Careful planning, possibly using justifiable experimentation, must take place. Once an actual solution is obtained, it must be tested to determine whether or not it is reasonable. These components of problem solving are basic to everyday situations. In my math courses, the goal is to learn to be problem solvers and independent thinkers. I often allow students to arrive at an incorrect solution. This allows us to discuss their solution and the process the student used to arrive at the solution. We can discuss ways to improve the solution and many times students can see where they went wrong as they explain their reasoning. It is also a goal to help students understand the usefulness of their solution. I often relate math problems to buying a car. In the process of buying a car, we study what it is we want/need, what we can afford, and what cars are available. We narrow down our choices and make a final decision. After the final decision, it is a good idea to take a look at our choice and run through the process again to make sure the car makes sense and suits our needs. For most of us, mathematics is basic training in problem solving. For those who learn to enjoy math and it’s specific brand of mental stimulation, there are plenty of careers that make a lot of money involving mathematics. As a math teacher, I encourage students to work hard in mathematics and try to be positive about math. Who knows where they may go with it?