Knowledge v Understanding
Why, after several days of modeling and practicing, can my students not solve this problem?
Joe works at Pilgram’s Pride making $8.20 hour. He gets time and half for overtime. What is his total salary for the week?
My math class has been working on problems similar to this one since school began in August. Even the students are asking why I still bring up these problems when we have moved on to yearly wages, commission, budgeting, etc. My answer: “Well, first and foremost, this is a real life problem. Second, life is made up of reading problems. People rarely walk up to you and ask, what is 40 time $8.20. You live your life solving problems.”
Now, what I have discovered as I muddled with the concept of Understanding from Chapter 3 of Backward Design is that I am working with many students whose parents do not work, or only work part time. Most of my students had no concept of what a “normal” work week even meant, much less “overtime”. For years they have seen math reading problems as something difficult and something that had no place in their lives. They do not have the necessary background knowledge necessary to understand the problems.
How did I turn this around? My students, many who are now in Jag, became the characters in the math problems. As students begin to look forward to their first real pay check, suddenly, number of hours took on a new meaning. When they discovered they could only work 15 hours a week, the 40 hour week also took on a new meaning. As one of the students who does work at Townsends and works full time (40 hours) began looking at a new truck, overtime looked really good.
Now, that I had their attention, and they seemed to understand the many problems created in class, I turned the tables. The students had to create the problems, and then introduce their problems to the class. What I discovered in my observation: All but one student proficiently understands how to calculate salary based on hourly pay and time and half for overtime over 40 hours. The students are still not ready to introduce problems involving commission, but we will get there. They now have more than a basic knowledge of the process which can be forgotten; they understand the process and its’ purpose in their own lives.