EVALUATING EFFICIENCY

•  You have probably noticed that there can be several different ways to solve the same math problem. The way in which you choose to solve a problem often depends on how familiar you are with math, and how comfortable you are using certain operations or applying specific math properties. Although there may ultimately only be one correct answer to an individual math problem, there may be as many as ten different ways to solve it.

• Any method that allows a student to access a math problem is a valid method. If you have to use repeated addition, for example, due to poor skills in working with multiplication facts, you can still reach the correct answer using your method. Sometimes students rely on one method because it is the only one they have ever seen, and they do not consider that there may be a different   way to approach the same problem. The way in which most people in the same culture would choose to solve a certain problem is called the standard algorithm for that kind of problem. However, the standard algorithm for one kind of problem is often different from one culture to the next. That alone proves that there can be many valid ways to problem-solve in math.
• A math congress or math meeting of some kind can be very valuable for students. In such a meeting, students are invited to share their method of solving a certain math problem with the rest of the class. Every different method that someone has used is shared so that all the methods can be discussed.  There are several purposes to this kind of meeting. First, each student’s thinking is presented and honored. Second, students learn to talk about and explain their thinking process. Third, new ways of solving problems are introduced to  students (and sometimes the teacher). Finally, methods of solving problems can be evaluated to see which method is the most efficient.
• An inefficient method may provide a correct answer, but require so much time to reach it that it is not practical to use. It can also be inefficient if it leads to an inaccurate result. An efficient method is one that allows students to reach a correct answer with the minimal amount of effort. The method has to be repeatable with the numbers of any similar problem, and the student needs to understand why the method works. Learning to evaluate different methods of solving math problems is an important step in developing maturity as mathematician.

 Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers.

1.   Have you ever considered trying to solve a math problem in more than one way? Why, or why not?
2. Have you ever thought you were “doing it wrong” because you were doing something different than other students, but then you got the correct answer? Explain.
3. Would you be willing to share an unusual method of solving a problem if you were given the opportunity? Why, or why not?
4. What makes a method of solving a problem inefficient?
5. How do you know if a method is efficient?