A question that I have heard many times from my own students and others is this: "When am I ever going to use this?" In this post and future posts, I'm going to address possible answers to this question, and I'm going to also take a look at what mathematics educators could learn from the question itself.
Let's look at the answer first. When I was in school myself, the most common response given by teachers was a list of careers that might apply the principles being studied. This is the same response that I tend to hear today.
There is some value in this response for a few of the students, but the overwhelming majority of students just won't be solving for x, taking the arcsine of a number, or integrating a function as part of their jobs. Even as a total math geek, I seldom use these skills in practical ways outside my tutoring relationships.
Can we come up with something better, that will apply to every student? I say that we can. Let's start with algebra.
Algebra is the point in the study of mathematics where students discover that problems can be solved even when information is missing. In fact, it is possible to create formulas where all the information is missing. These formulas can be applied when the information arrives. In life, this is something that is done all the time. We have a task to do, and we need a process for that task. In practice, we often find a similar task that we have done previously, and modify its process for the new task. The process is analogous to the formulas used in algebra.
The real skill that is learned in algebra is one that is widely applicable. Solutions to specific problems can be generalized, and if necessary, adapted to work for new problems. Troubleshooting, investigation, and efficiency are all issues that are touched by the back-and-forth process of abstraction and application.
Here is an illustration that may be helpful to you or your students: Let's say there is a student in gym class who asks why they need to do pushups and sit-ups. "When will I ever use this in my career"? The answer is that they probably won't, unless they go into one of a small number of careers. The answer to this student is very clear: "You probably won't use this." Why do it? It's exercise. Having strong muscles and a healthy body is of benefit to anyone, regardless of chosen career.
In a similar way, the study of algebra strengthens one's ability to apply existing processes in new situations.
Rather than rambling on for a long time in one post, I'm going to write about other math disciplines and their universal applications in other posts. Also, I'll address what I have learned from the existence of this common question.