Is High School Math “Useless Nonsense”?
You’re in the merge lanes exiting from Route 28 onto 7 West on your way back to Ashburn. Progress toward home is being measured in fits and starts of inches and sighs; engines and tempers verge on overheating. You’ve already merged left toward Route 7’s lanes when a car zooms by you on your right, shooting up the empty lane to nose into the long line of waiting cars at the last possible moment. Another goes by. Then another. You reconsider your decision to be considerate. The exhaust enclouded line suddenly seems endless, and you ask yourself, “Should I ‘cheat’ too and get home sooner?”
Well, should you? Is it worth the dirty looks and gestures from the “considerate” drivers to be one of the line budgers? Or do you become one of the “vigilantes” who punish the “sidezoomers” by blocking them? So many options to choose from, so many decisions to make! What’s a “non-math” person to do?
The World is Divided Between “Math People” and “Non-Math People,” Right?
The student newspaper at my high school published last month a point-counterpoint type article debating the value of high school math. “So even if you dislike math in high school, you might end up needing it [in college],” one author states in “The Glories of Math! Or Not …” The piece’s co-author concludes – after surveying his parents at the dinner table and teachers in school – that high school math is “useless nonsense,” and that no one ever uses “complex formulas and problem solving methods … in real life situations.”
But do the writer’s parents never, ever, really never use the problem-solving skills they were exposed to in their algebra, geometry, and calculus classes a quarter-century ago? Maybe they use them in their everyday activities and aren’t even aware of their secret powers. Is there a possibility that his mom does indeed get into a situation – maybe just once a day, mind you – where she weighs the merits of two options and chooses between them? It might be something as mundane as choosing a cell phone plan, or it could be something that affects the whole family, like deciding which job offer to accept. Maybe sometimes there are more than two options involved, like four or five, in various combinations (or permutations, as we call them in algebra). Maybe sometimes these situations come up more than once a day. Just maybe.
If we stop to really think about it, we encounter numerous and myriad circumstances daily that are easier to survive if the observation, pattern recognition, skepticism, and perseverance skills we hope high school math sharpened in us are up and running. Some are more obvious to us if they involve numbers, like when we’re in Best Buy trying to figure out which combination of discount coupons gives us the best deal on the latest and greatest electronics. Or recalling the rules and ramifications of probability and odds when buying a lottery ticket, investing in the stock market, or deciding which health or life insurance plans to spend your money on (yes, insurance plans are just as much gambling as going to Vegas is).
And some are not so obvious. Is it possible that the writer’s dad forgets that the doodles he created the night before while scheduling planning committee meetings for his high school reunion look suspiciously like vertex-coloring graphs from Discrete Math? It’s certainly likely he doesn’t realize that airlines use this same high school math method to ensure all of his classmates get to that 25th Reunion on time next October.
Maybe It’s Not Just About the Numbers
Crazy Thought: Consider that high school math may not really be just about numbers. Let’s go out on a limb here and say that the numbers are not necessarily the most important part of our math classroom experiences. What if numbers (even the dreaded fractions!) are nothing more than the “alphabet” or “language” we use to develop our problem-solving abilities while in the sheltered worlds we call middle and high school? And what if they are actually the easiest language we’ll ever use? Once we exit the school-world, the Universe does this crazy thing to us and swaps out all those even-numbered math problems on p. 546 for WORD PROBLEMS! More accurately, they’re not just word problems anymore, they are LIFE PROBLEMS. Really.
Instead of having those nicely numbered and formatted textbook and worksheet problems to solve, you soon find yourself in a cubicle reading the latest email from the boss tasking you with recommending the best way to increase sales by 3% next quarter. Even if you recall how linear programming works (that would be from Algebra 2), you need those observation and pattern recognition skills to figure out just what “best” means (because your boss didn’t bother to tell you what she meant by “best”), what are all the factors that affect and drive sales, where can you get the needed information, what information is relevant and what is not (and everything in-between). Even though some of these pieces of the puzzle may be represented by numbers, they are not numbers in themselves; they are company policies, government regulations, economic conditions, the season of the year, the demographic makeup of the customers, product inventory levels, and the availability, training, and performance of the company workforce. This is where you truly start appreciating those skepticism (did I consider everything? is this the answer she was looking for?) and perseverance (do I need to model just 11 possible situations or is a twelfth necessary?) skills.
And if you find yourself in a profession completely devoid of numbers, you still don’t escape problems/puzzles and the tools necessary to unravel and understand them. Even that kid who majored in English and became a film critic depends on the same observation and pattern recognition skills she developed in factoring polynomials to identify and put movie themes in context for her readers.
Sometimes the “real world” jumps into our lives sooner than we expect. In class the other day, a discussion of our county’s school budget issues got a bit heated. Students expressed concerns about the potential for new athletic and parking fees, the reduction of staffing for athletic and guidance programs, as well as the elimination of summer school. One student was impressive in her ability to apprehend the complexity of a seemingly simple issue. Upset that freshmen sports may be eliminated, she concisely discussed not only the immediate impact on incoming freshmen athletes, but identified the not-so-obvious effects this change would have on JV and varsity sports years down the road. Her ability to recognize and analyze these connections – and make predictions based on them – is the same ability we use when solving those multi-step geometry problems that contain a mix of parallel-line, interior-angle-sum, supplementary/complementary-angle, similar-right-triangle mini-problems. Just no numbers this time.
The author’s argument is persuasive, but only if we think high school math is only about numbers. But what if it isn’t just about numbers? Just maybe his parents (and the rest of us) use high school math more often than we recognize. Maybe we actually use it a lot. Just maybe.
Wondering what the traffic jam at the beginning of this piece is about? Good, because math guys actually have put a lot of effort into figuring out who’s right in that situation. The considerate-mergers? The sidezoomers? The vigilantes? Admittedly, this is not an “everyday” use of math in the sense that you or we have the resources to figure it out, but it is an “everyday” situation in which math can help us. (For the solution, either Google “queuing theory merging traffic” or think about zippers while sitting in your car.)
On the other hand, the next time you go into McDonalds, consider whether you’ll get your burger and fries sooner if you form three lines while waiting for someone to take your order, or is a single line feeding into the three registers better? High school math just might help — and there’s no numbers involved, just a big ol’ juicy Big Mac!