Fred Worth, Ph. D.
“I hate math!” I often hear this statement from people. Often the implication is that the person should not have to learn mathematics or cannot learn mathematics. Sometimes it is that the person sees no value because “I’m never going to use it.” Let me give a short response to these issues.
Should people learn mathematics?
Obviously, as a mathematician, I think the answer is “Yes.” But the reason may surprise you. It is not solely because of the usefulness of the subject. Let us be honest. Many of the skills one learns in algebra will never be used in real life. It is unlikely that most people will ever have the need to factor a quadratic. The most important reason for learning mathematics is that it helps develop the ability to think.
Being able to think logically is vitally important in life. If I cannot think logically then I cannot make intelligent decisions on many issues that will be of importance in my personal life. I will not be able to vote wisely. I will not be able to make good financial decisions. Parenting decisions can be hindered in many ways by poor logical-thinking skills.
I know of nothing that aids in logical thinking better than mathematics. Mathematics involves problem-solving techniques, such as breaking a large problem down into smaller parts that are more easily solved. That will help in problems with which we deal in areas that have nothing to do with mathematics.
The key ingredient in developing logical thinking is avoiding the temptation of looking at mathematics as a collection of algorithms. Yes, there are many algorithms in mathematics, and they are important; but in addition to knowing how to use them, I need to understand when to use them and why. I need to understand why they work.
What about attitude?
A lot of people are greatly hindered in mathematics because of attitude. The attitude problem can be that of teacher or student. Parents need to be careful that they do not poison their children’s attitudes toward mathematics. Otherwise they will spend much time fighting through an attitude they helped create.
“But what do I do if I don’t like it?” The short answer is, “Get over it.” There are many things in life that we do not like but have to do anyway. Going to the dentist is not fun, but I do it. Paying my taxes is not fun, but I do it. We need to realize the benefits we get from these activities. As mentioned above, learning how to do mathematics can help us learn how to think.
I am not so naïve as to think that a simple decision will make everyone love mathematics. We can, however, decide that we will have a good attitude about doing things we do not want to do. We can start looking at the value of the activity to help us get past the attitude.
“But I’m not good at it!”
Such a statement is an assessment of past experience. It should not be allowed to become a predictor of future achievement. When a child is struggling with mathematical concepts, it is easy to assume that the concepts under consideration are the problem. I would guess that in at least 90% of the cases that is not the problem. Normally, if a child begins struggling with 6th grade mathematics, the problem is probably with an incomplete understanding of 4th grade mathematics. Go back to the previous material and test for understanding—not just for correct answers, but for why things are done. Not understanding that is often the problem with later struggles.
“Will I ever use it?”
Some mathematical concepts are not likely to be used by people who do not get involved in technical fields. Some will not even likely be used by those folks. Nevertheless, there are many places where algebra, geometry, trigonometry and other mathematics can be used. However, there is one important thing to remember here. You cannot use what you do not know. If I never learn something, then I certainly cannot ever apply it.
There are some obvious areas of mathematics that will indeed be used.
Suppose a recipe calls for 2-3/4 cups of jalapeños, and the recipe is designed to feed 4 people. What do you do if you want to make it for 7 people?
One of the requirements for the athlete pin in Cub Scouts is running 600 yards in 2 minutes and 45 seconds. We have an oval track that is a quarter mile, which is 440 yards. How do I choose where to have the Scouts end if I want them to run 600 yards? Suppose I make it easier by making them run one and a half laps, which would be easier to mark off. What would be an appropriate time to give them in which to run the longer distance?
Other uses for mathematics in daily life include the following:
Prices per unit at the grocery store
Discounts on merchandise
Figuring a tip at a restaurant
Figuring how much paint is needed to buy to paint my living room
These are things that all of us are reasonably likely to encounter in life. There are many others. Mathematics is important for far more than just providing me with an income, although that is obviously VERY important, at least to me and my family.
I do not use calculus very often in my daily life outside of my teaching. Trigonometry I use occasionally; geometry often, especially when I am building something; algebra quite a lot, although it is not always obvious. A lot of times, people would use those things if they knew how to do them. If they do not, they just make a guess or skip it. Often the guess is good enough. Other times they have to go out to the garage and cut another piece of wood for that project.
Can one conclude that these ideas will make everyone a mathematical genius who likes nothing better than to solve mathematical problems? Obviously not; however, I hope it will help people appreciate the usefulness of mathematics a little bit more.