Living Mathematics: A Story to be Told
(Warning: The following article contains some math. Proceed with excitement to begin to reclaim the true story you may never have been told.)
“I’m just not a math person.” “I don’t get math.” “When will we ever use this stuff?”
Throughout my 25+ years of math instruction, I have occasionally caught wind of these student phrases. You may have heard them too, or even uttered them yourselves. Understandably, the mental acrobatics of math learning can at times be overwhelmingly stretching, resulting in such exclamations of pain and frustration. Many times, these are declarations of giving up or decisions to close the chapter on math learning. Unfortunately, these are the wrong exclamations and choices to make at such times; they reveal a misunderstanding of the true nature and value of math education- for everyone.
At Chapel Field, we strive to present and teach math classically- stripping away modern-day constructs surrounding math; the “new math” inculcated starting in the 1980’s and other similar reinventions of math unnecessarily obscure the beauty and goodness of pure math by ladening it with utilitarian and even progressive agendas. In addition, may I say there is a growing culture that goes against truth-telling, against logical thinking, against law and order, and against the very heart of God? This does not help our students rise above or correct the aforementioned misjudgments. What is pure mathematics, and how is it a beautiful story to be told?
Let’s start with the fact that math is living. Our English department presents to students living books- real, live, great, whole works- original sources- as opposed to textbooks about books with excerpts already digested and filtered by “professionals.” Who would care to feed on that? We want to feast on the real original works of Shakespeare. Likewise, math classically presented is the real thing- students interact with it firsthand. It is alive, and students come alive (e.g. The entire class cheering as a problem comes to resolution!) Math is also living because math is not an object you get, it’s an action you do. It is a sport that requires training, discipline, hard work, and lots of practice and drills for refinement of muscle memory. For personalsuccess, soccer players cannot remain on the bench merely observing how dribbling and head shots are to be done; mathletes and athletes alike must be active and involved players in the game! Math, like soccer, must go “through you.” That’s why doing daily homework practice is so essential.
Math was created by a Living God Who sustains all things at every moment by laws that are also themselves “alive.” True math was not invented by man to torture or stupefy the rest of us. The concepts of multiplication, algebra and geometry were in existence long before man engaged in these himself. Man only discovered mathematical laws and concepts which God had long ago embedded within His creation. With Him is the original Source Code. Indeed, math is a peek into the mind of God as He created the universe and everything in it. More forthrightly, Math is the deep code found within everything in the natural creation, including within you and me, so that things can be accounted for, organized and explained. Math is God’s order imprinted on everything He touched in the physical universe.
Even a cursory glance of the first chapter in the Bible reveals God’s math in creation. In Genesis 1: 4, we see among the first acts of creation a separation – a sort of sorting: “...He separated the light from the darkness.” Acts of separation continue, as well as true addition of more created objects (sun, moon, plants, humans, etc.), and a numbering of creation days from 1 to 6. As God separated light from dark, waters above from waters below, and seas from land, He was decreeing that unlike terms cannot be truly combined (2x + 3y is not 5xy, but remain separate). There is also a naming or labeling that occurs “according to their kinds” so we can keep track of everything (let “x” represent the number of humans, let “y” represent the number of monkeys: 2x + 3y is still not 5xy). God was doing math at the very outset of creation. Sorting and grouping same kinds together (apples with apples) and keeping separate different items (bananas) is one of the first math lessons our Kindergarteners learn in our living math (Singapore Math) curriculum. They are our littlest mathematicians and, even at this age, echoing the acts of our Great Mathematician.
This accessibility to math for anyone leads me to confer that Math is good. The pre-Fall creation and employment of math by God permeated the 6 days of creation in which, after each day, God observed what he had made and called it “good.” Math is good because it comes from a Good God. James 1:17 states: “Every good and perfect gift is from above, coming down from the Father of the heavenly lights...”
Math is also good because it is so useful to us. Because we were created in the image of God, we find within us a small reflection of God’s ability to order and keep track of things. We are asked to be good stewards of what He has given us. So we balance our budgets, we try not to waste, we sort, engineer bridges, classify, make lists, plan, think logically. Basically, math helps us keep track of stuff in the universe. (Fortunately, we are not asked to keep track of everything in the universe. Take hair, for example. God has them counted on our heads- we don’t have to.)
Everyone can grow in math. Saying someone is “not a math person” is like saying someone is not a food-eating person. There is order and symmetry even in the way God created us, and because God created human beings in His image, He wired our minds and hearts to also seek and crave that order. You cannot avoid math in life. At some point, you will put things together, divide, count, go off on a tangent, circumvent a situation, take factors into consideration, distribute flyers, parallel park, view the symmetry in a work of art, realize that things can’t come together without a common denominator, realize that you can’t cancel a person even mathematically like you can cancel an appointment, and you will desire to be onewith God and have singleness of heart rather than division. If you can sort laundry or get ready in the morning in an acceptable order, you are a math person. If you can classify, make a grocery list, read from left to right, tell time, or share a meal with someone, you are a math person. In response to “I don’t get math,” math is not something “to get”; as we’ve seen, it’s something we already do every day, and missing the day’s goal once or twice has no bearing on whether we’re good; we just need more practice and coaching to master more sophisticated plays and grow from the point at which we find ourselves. All math students are “junior mathematicians”- working out the bent towards order that was put into them by God by interacting with and engaging in the laws God put in place: 9 x 9 = 81, the square root of 225 = 15, the derivative of 8x2 = 16x.
Let’s go back to James 1:17: “Every good and perfect gift is from above, coming down from the Father of the heavenly lights, who does not change like shifting shadows.” From this, we also see that Math is true. Math is a gift to us from the Heavenly Father, Who does not change like shifting shadows. Indeed, because 2 + 2 will always be 4, and the square root of 196 will always be 14, math is a reflection of the unchanging nature of God. We can rely on the truths in math because they came from the Solid Rock, our God. This is very comforting. In a world that is constantly changing, we can take refuge in the constancy of math. People can find security and comfort (and fun) in working out math. The bedrock truth of math is laid in the elementary years with memorization of math facts (addition and subtraction tables 0-20, multiplication and division tables 0-12) that become the air they will continue to breathe- therein lie the seeds from which all other beautiful math will sprout and blossom. In George Orwell’s 1984, the last bastion in the battle for the soul is math. If people could be convinced that 2 + 2 = 5, then they truly have sold themselves under the control of others. The times we live in are scary as the battle line has already creeped into the biological realm and encroaches on math with redefinitions and even a renumbering of genders. Let us hold firmly to this last bastion and uphold the truth of mathematics.
So we come to my favorite question: When will we ever use this stuff? As mentioned above, we use “this stuff” all the time. But I understand the student in middle or high school means more specifically, “When will we ever use Algebra? Or Geometry? Or Trig? Or definitely Calculus, especially if I have no plans on becoming an engineer, go pre-med, or work with derivatives in finance?” But they are asking the wrong question. Yes, math actually does have usefulness in some professions to a high degree. But our education in mathematics is not about how we can use it later. It’s the wrong question. The question, rather, is: When will mathematics ever use us? In other words, when will we bow and submit ourselves to the order of God and allow Him to refine us through the learning of math? Like taking vitamins, we may not feel anything, but it changes us. It does something to us. I took violin lessons for many years as a child- never got that good; certainly didn’t become a professional violinist and make a living from it. But that experience did something to me- it shaped me in ways I cannot fully explain, but I am more attuned to music and His order in certain ways. My own math learning also did something to me (apart from my “using it” to teach others math). Math made me more just. I have been so conditioned by “what you do to one side (of the equation), you do to the other,” that I literally hear myself saying as I strive to grade tests fairly- “What I do to one student’s test, I do to the other…”
When will math ever use us? I say to students: let math use you; let it consume you. Your affections will be better ordered; your thinking will get clearer and more sequenced; your logic will become sound; your writing will become more exact; your discernment will get sharper; your pattern-recognition will come more easily in all your studies; your problem-solving will be honed; and your room may even get cleaner. In his book, Mathematics for Human Flourishing, Math Professor Francis Su relates: “If, as the writer Kenneth Burke once said, literature is ‘equipment for living,’ then mathematics is equipment for thinking” (110). It’s no wonder some of our greatest thinkers were mathematicians also: Aristotle, Rene DesCartes, and Blaise Pascal were all philosopher-mathematicians. Dare I say, the student who submits himself to math may become a great thinker for our day?
Finally, Math is beautiful. The immense beauty of math betrays the contention that we do math primarily because it is useful. No- we do math because it is awesome and awe-inspiring in and of itself. We get to peek into the mind of God- it is infinite… it is amazing. Depending on the year, I answer the “When will we ever use this stuff?” question with the answer: “NEVER!!” Sometimes just saying that is easier. Other years, I don’t even answer the questionand we simply proceed with the year’s topics… Somewhere along the line, it becomes somewhat enjoyable. They get hooked into the story... They want to know what happens next… How does it build? What recurring themes will there be? Wow, we did long division in 4thgrade, and now you’re telling me in 11th grade we are going to do it again- but with letters? And with exponents? Man, I thought we were done with fractions- you mean I have to keep adding them with different denominators, and on top of that, they are all exponents? There is a marriage of conjugate pairs- and they aren’t even in the real world! There is intrigue, drama… In Algebra 1, not only do we solve for x, but there is a new character added to the story- who is this mysterious “y” we now also have to solve for? What are negative exponents? A host “X” invites guests “Y” and “T” over to his domain and gives them name tags so everyone understands just whose domain it is! In Calculus, we talk about Russian nesting dolls and remind ourselves not to forget to chain the babies(!?) In Geometry, we talk about parallel lines and how the Holy Spirit is our Paraclete- not the same as us, but going right alongside us. We debate whether an infinity-sided shape is the same thing as a circle, and our minds are blown away. New chapters open up when we are introduced to the parallel universe of imaginary numbers… Half the year in Calculus is based on something we learned in the 8th grade… (I must stop here, lest I give away and ruin the ending and too many more surprising delights we discover as we journey through this big story.)
Math at Chapel Field is a 13-year mini-series that unfolds for us as we progress from year to year to deeper and deeper levels. The same characters and events keep popping up with twists and turns. I love the connectedness from one grade to the next. By the end of 12th grade, every year of math learning has fed into the next and is used up- nothing is wasted! I love the backbone story stretching through the entire elementary school on up through the wiry middle school on to the freshmen in Algebra 1 and continuing to the higher and higher vistas that wind up the mathematical mountain to Calculus. It was said best a few years ago by then-Calculus student, Matt Harrison: “Nobody ever told me what all my previous math was for! Nobody ever told me! Now I know!!” I and my Calc students have the immense privilege of getting thatmountaintop view of math learning… I have often wished that I could tell everyone of the beauty and awesomeness at this level in 12th grade- but nobody apart from our small class would understand. But then, I visited the elementary school and was reassured- 2nd graders were happily making constructs to aid them with their division learning. Around Christmastime, 5thgraders were joyously ladening their workbooks with strings of fraction multiplication. 7thgraders proudly went beyond the textbook agenda and learned perfect squares and perfect cubes!At every grade level, there is a vista to be discovered and enjoyed. The grand story of math has within it, progressively more complex sub-stories of coming together, breaking apart, fast action multiplying, friction, tension, resolution, and enough recurring themes to keep students at every grade fascinated. And the students are getting so hooked they could do acrobatics… they are alive and living math. This is a story to be told for years to come…
********
This is a rather simple Calculus problem solving for the volume of an area under a curve that is rotated all the way around the x-axis, but you can find every year of math from grades Kindergarten through 12th grade in the working out of this problem:
Esther Park serves as Chairman of the Mathematics Department at Chapel Field.
