Why Study Algebra

Many of the students in my algebra class wonder why they should study algebra since, for the most part, they will never use the algebra concepts after taking the class. I will tell you why you should take it and why you should try to do really well at it.

You will not find a better environment than algebra for learning and developing problem solving skills. The rules of algebra do not change and therefore algebra gives you a solid framework to practice in. You do not need to worry about uncertainties in the problem environment. When you work on an algebra problem, you examine what you do and do not know about the problem and you note similarites between the problem at hand and others you have done or have seen done in the book or in class. You make a guess at how to solve it, you try it, and you have ways to check your answer when you come to your solution. Nothing magical or unpredictable happens. You take a path, you get a solution, you verify your solution, and you try again if you get an incorrect solution.

We can define algebra as the study of the relationship between sets of numbers. The relationship produced by a given function remains the same no matter what we do. If we try to develop problem solving skills in the relm of human relationships, then we have the added complexity of uncertainty between individuals. We cannot always know if we really solved the problem and therefore our practice may allow us to develop poor problem solving skills. In algebra we know that we can get the right answer if we use the right solution method. We learn to not trust an answer until we have verified the results. We may have made incorrect assumptions about the data or the solution method, or we may have made an arithmetic error somewhere along the way. Practicing problem solving in algebra helps us work more carefully when we examine problems in sociology, psychology, biology, chemistry, or physics*.

To conclude: have no fear of that algebra class. Take it knowing you will struggle, but that you will also learn very valuable lessons in problem solving that you can take with you to other disciplines. Sure, you will probably forget the formula for compounding interest right after the final exam, but you will work more carefully in the rest of the classes. You will also know that such a formula exists for computing interest when you get that credit card bill — you will not think your banker does magic tricks with numbers to steal money from you.

Have a Methodology

I think of problems as obstacles that get in the way of accomplishing something you want to do. Most creatures deal with problems by instinct and trial and error. Successful trials get stored away and get used when the same problem comes up again. Rational creatures, have the added ability to incorporate things learned from others. You may disagree with me on this point when you see children insist on learning from their own experience when parents try to convince them not to engage in some activities. We can also extrapolate from one problem to another through analogy to help us deal with problems that seem similar.
Polya developed a useful method that formalizes the process of human problem solving. Although he worked on mathematical problems, one can apply this method to any type of problem. You can find many sources that describe his method in detail, including his book , How to Solve It. I will summarize his method here in the following way:

  1. Understand the problem, including what you do and do not know about the problem.
  2. Create a plan of how you will try to solve the problem. Here you will make “educated guesses” about how to go after the problem.
  3. Execute your plan. If it does not work, go back to step 2.
  4. Review your progress, what did and did not work, and develop a strategy for solving similar problems in the future.

As you think through our strategy before actually doing it, you can sometimes very accurately predict your outcome. For example, when picturing how to get from your house to a city you’ve never gone to before, you can picture the path you will have to take, all the left and right turns, the distances, and the types of roads. With tools, such as Google maps, you can even get a satellite and street views to give you more accurate predictions of what you will see on the route. Although you can think about and make complicated plans and strategies to solve a problem, you still must do what all creatures do and try out your strategy. You have not solved the problem until after you have gone through your plan.

Having a structured methodology, such has the one presented by Polya, maximizes your ability to find a solution to your problem. Solving your problem will let you get on your way to accomplishing what you want to do.