Why We All Should Study Higher Level Math

Happy Pi Day! March 14 is 3-14, the first 3 digits of the math term, pi (π). Our family, with my husband being a mathematician, celebrates Pi Day with PIE! In the year 2015, it will REALLY be Pi Day.... 3-14-15, the only one in our lifetime! You can find Pi on my car's license plate, 3PT1415 (3 point 1415), my gift to my husband on his birthday. Only one of the people in the car tag office got it when they asked me why I wanted that plate number, and I said, "My husband's a mathematician." In fact, the lady typing the application tried to spell "mathematician" several times, then gave up and wrote "husband is math guy." The one who got the concept immediately just laughed and told me how great it was.

As a school principal, working with homeschoolers, one of the most frequently asked questions I hear is "My son/daughter keeps asking me why he has to learn algebra anyway, and I really don't have a good answer. After all, he doesn't plan to be an engineer or a scientist."

I am often surprised by the people who make this statement. It shows me that people really do not understand mathematics as a body of study and how such study contributes to our overall quality of life, even - if not especially - if one is not an engineer or a scientist.

If you go on the internet and google "why study math" you will get many articles where trite examples of math being used in other subjects are shown. You might see a explanation that art involves mathematical shapes, such as triangles. You might see that sports involves percentages. You might see something about a housewife going grocery shopping and using her calculator to make sure she has enough money to cover the cart of goods.

The problem is, all these examples, which we hope will satisfy our students, will only satisfy them if they do not study higher mathematics. That is, many people think that mathematicians add and subtract and divide really big numbers, maybe 14 columns wide!!! Being told the above examples should prove to your child that higher mathematics is needed only works if you do not realize that all the above examples are mathematics that one should have learned by the end of fifth grade at most; indeed, some are examples of kindergarten mathematics. So only one who has not studied higher levels of math would believe that those examples are FROM higher level mathematics and that, therefore. the truth has been proved.

The one thing you never really hear explained to students is what mathematics does to your brain, and what mathematics does to your brain is why you study higher level mathematics. Did you know that one of the two biggest single predictors of whether your student will complete college in four years is whether your student has studied trigonometry? It's a fact. {The other predictor is no less politically incorrect, and it is how high your SAT scores are. The higher the SAT score, the vastly greater your rate of success in college. It's the truth;. Live with it. Your exception is noted.}

Why would a single subject - trigonometry - be such an indicator of success in college? It is not that students who would take trigonometry are just better students with which to begin. It is that, in the learning of trigonometry, one trains the brain in a level of abstract thinking as well as a level of connectiveness in ideas that is not found in most other branches of knowledge. Reading difficult, college-level articles in any subject is not so hard if you have studied trig. After trig, you will be able to leap 3 or 4 ideas away in milliseconds to get to the needed concept. After talking with a person for a short amount of time and trying a few ideas on them, one can often tell who has taken trig and who hasn't, whether they have ever used it again in later life or not. If you can master trig, you can pretty much master any subject, any day, any why. Four months of study brings a lifetime of benefits.

Higher levels of mathematics allow us to learn to see how the dominoes will fall in highly complex situations. Many of our national and local and church problems come with a large number of variables that need to be considered. If we want to fix Problem A, we can change a factor, some factors, or all the factors. Being able to comprehend the effects of those changes cannot be done with simplistic thinking.

When studying trig, one of the first things you find out is that most trig problems cannot be solved in 3 lines. A number of the problems cannot be solved on one page or even two pages. Learning how to keep a problem in your head as well as explain that problem's solution cogently on paper so that others can also understand it is one of the benefits of studying trig. Perhaps an industry wished to move into our town and wants some sort of concessions from the town. How can we learn to solve problems involving an industry's effects on a region's environment, ecology, politics, health care, education, superstructure, economy, social structure, arts programs, etc. --- each one of which carries many variables to consider as well as the intricacies of their multiple interactions --- if we can only handle problems with one variable, and that one variable is the simple X of 4 × 5 = X ? We cannot.

Studying higher levels of mathematics will allow a person to see consequences of actions further down the time line than someone who does not study those same math courses. Lack of study in higher mathematics will make us dependent upon the next glitzy politician or speaker who will smooze us with his unrealistic ideas. We become easier to swindle, easier to confuse, easier to manipulate. It's that "deception in the end times thing," rearing its ugly head again in yet another way.

Not studying higher mathematics will lock you out of ever changing fields in the future. The average adult now has 5 to 7 major career changes (not job changes) in his or her lifetime. The skills that you think you will need as you plan your life from your tenth grade perspective will be different from the skill sets actually required in each of those new areas - some of which haven't even been invented yet - that you will want to enter in the future. Emerging careers rarely involve being less skilled than previous generations' careers. Keep the doors open. Study higher levels of mathematics when you are young, when your mind is more nimble, when your time commitments do not involve your own spouse and children, and when your energy to devote to a difficult task is at its peak level. It doesn't get easier to learn math as you get past age 30, though a determined person can make their way.

One thought comes to me from my experience. I have never met a person older than thirty who sincerely wishes they had learned less mathematics. Every single one wishes they had more mathematics. My husband frequently encounters adults who, due to changes in their job, have to go back to college to up their degree level. The single biggest factor that stands in the way of them doing so is the thought of encountering mathematics again after having neglected it in school. We have frequently heard, "My company wants me to get my master's degree, but I have to take a statistics class. They have two, one based on trigonometry and one based on calculus. What should I do since I stopped math after algebra I?" There are only two choices, go back and study math from Algebra I onward (and try to do 4 years of high school math in one or two semesters so you can get into the program) or not get the degree and thereby risk losing your job.

One other thought on why one should take mathematics courses all the way through the calculus is so that you don't miss all the fun. All the math done before calculus is really not mathematics. It is arithmetic. Most mathematicians will tell you that the calculus is the first real math course. Not taking the calculus would be like learning your letters, letter sounds, and basic phonics, but never reading a single sentence, much less picking up a single book to read. The calculus is easy compared to what comes before it.

So, this explanation should assist you when your child asks, "Why do I have to study algebra and all those higher maths?" If, however, you want a quick answer that will appeal to most teens, just say, "So you can outthink me when you're done."

Finally, when you ARE asked this question, do NOT - under any circumstances - stop math class to answer it. Tell your student, "Finish your math now, and we'll discuss this issue later over dinner." If they don't ask again at dinner, they really didn't want to know the answer. They were just trying to get some time to jog a rabbit trail in order to avoid math. Keep them focused on the work first. Educational philosophy can come later. This little technique works for almost every topic in any subject. Do the work first; discuss the need for it later.

I hope this helps you get a better view of what is actually going on in mathematics education. If it makes you yourself wish to go back through some mathematics, I highly recommend the Demystified series. Amazon carries all of them, such as Algebra Demystified. They are designed for the adult who realizes they left some gaps in their math and science education, and they are now encountering situations where those gaps should be filled quickly. I carry a set of the most used ones in my office. Come by and see them sometime. And now, go eat some pie for National Pie Day! I'm hoping for coconut cream myself.