One of the fall outs of children not understanding mathematics and the associated failure which often follows at some point in their 500 hour tour of the salt mines of mathematics — aka math education — is that teachers, through no fault of their own, start to sell/hawk mathematics like it is some discontinued K-Tel kitchen product at a Saturday Flea Market.
Imagine reading in school for the sole purpose of filling out job applications and passing your driver’s license. Why the hell are people reading books in school? You don’t need to read books, do you? And, art — ha — good luck with finding any practical application for painting/sculpting in the cookie-cutter/cut-and-paste lives we help subconsciously manufacture for children in school. Driving, buying groceries, calculating time, measuring lumber and financing your home. In the banal routines of life is where we find mathematics’ Willy Loman. Here mathematics is sold at a discounted rate to already jaded and skeptical students. “Hey kids, you like flying kites? You know there is bucket of trigonometric fun here!” Gauss must be spinning in his grave seeing math prostituting itself as an overreaching and over zealous supporting actor in the comedy of the math classroom.
Mathematics is on the same level as literature and art — it takes creativity and resilience to produce these reason poems(Paul Lockhart). If we are going to stay in the goods and commodities metaphor, then this is how it should be sold. It shouldn’t be primarily pedaled around through intersections in our practical lives! Kids are frantically seeking adventure, mystery, and excitement. That has been the narrative of mathematics for…I don’t know…only its entire bloody history! We don’t just want students to be passive recipients of huge wads of undigested knowledge. We should want students to be active learners in not just the literacy of mathematics, but the history, thematic development and global contribution/current endeavors as well.
Most of K to 12 mathematics(save for calculus and parts of statistics) was known by the 9th century. It might be time for a status update, don’t you think? Put me down for the holy trinity of theories — number, graph and game — to be installed in elementary school:) Let’s hack into the duplicity of lotteries. Let’s laugh our asses off at Warren Buffet’s hilarious “risk” of offering one billion dollars to a perfect March Madness Bracket — when the reality was a mathematical expectation of around one billionth of a penny. Let’s stop using the diversionary butter knives that school offers, and lets get out the Miyabi knives and hack/slice/dice all the tomfoolery that is out there!
Do you think even one mathematician in the last 2000 years started exploring mathematics because they thought that some commercial application could follow? Don’t get me wrong. Without all the technological applications of mathematics, we would all be living like Fred Flintstone in Dickensian squalor. And yes, there are math folks deliberately using the advances of number theory/fractals to help society, but this is only after decades and decades of joyful and laborious investigation. But, showcasing mathematics for its practical uses tells only the end of the story. All the early chapters of curiosity, imagination and resilience are absent. This creates a sterile and inaccurate portrait of math. Its like mathematics had some kind of immaculate conception in a test tube and then had its purpose realized in terrorizing children in school with pretentious nomenclature, unexplained formulas and too many algebra questions concerning the bizarre amnesia of Mary and the ages of her brothers, sisters and other relatives.
Above is a beautiful shape that looks like a figure eight or the infinity symbol. How is that shape — a lemniscate — even produced? What “machine” are we plugging in random values to create such exquisite and symmetrical curvature? Most people might know what a tangent is, and most would be able to point to the four places where the tangent is horizontal. Pretty easy, right? What if you were asked to find the exact co-ordinates? The answer is not important. It’s actually quite anti-climatic. The real question is how would go about finding this mathematical gold? Calculus would get you a third of your way in this journey. Yet, understanding the highest level of calculus would only take you so far. The rest of the journey is a tricky trespass of algebra. Most students would be so fortunate to slip and tumble. Yes, fortunate.
This is where mathematics needs to be bought and sold — in its sometimes messy and intricate fun. In the early grades it should draw the same currency of curiosity and application-free exploration. Kids should be roaming around freely with the guidance of their teachers in the garden of numbers — discovering ideas about odd and even numbers, seeing the relationship between perfect numbers and triangle numbers, etc.
Heck, they should be breaking apart numbers and putting them back in ways that please their creative and imaginative minds! Numbers need to be like LEGO for children — and adults! Why not let them play with the Goldbach Conjecture and the Collatz Sequence — they are more than capable! The onus is on all of us to unshackle mathematics from the limiting and unexciting uses in our daily lives and instead, embolden people’s lives with the magic and beauty of mathematics. The practical applications will have far more meaning and lasting value if our first objective is for our children to love and value mathematics the same way we seem to value authors and artists — or do we?
When we guide children through the joy of a subject, pleasurable emotions of learning and discovery naturally come out. The currency of happiness has a much higher intrinsic value for motivation than does the heap of dried out carrots of assessments and miscalculated usefulness. To artificially change the trajectory of why and how mathematics has been explored not only results in a completely disingenuous picture of mathematics’ true value in our society, but it results in the slightly ironic, collective failure of our children truly understanding the world of mathematics.
Math is everywhere. That is both a blessing and a curse. We only have so many hours in our lives and, if we are teachers, even fewer with our students. Once basic literacy expectations are met, are we going to continue the prescriptive road of perspiration or the imaginative road of inspiration. I have no idea what the road less traveled looks like, but a millions of students have been telling us for years what the other road(paved with good intentions) looks like — boring.
Does everyone need mathematics? Maybe. I don’t know. But you lost me at need — especially if its a need out math education’s discount bin of faux trig applications, contrived algebra problems and lame proofs involving triangles. (leaving proofs until high school is kind of ridiculous…especially if the first introduction is going to be the “exciting” world of column proofs involving triangles…SAS, ASA, ZZZZZZZZZ…)
Can everyone love mathematics? This is the better question for society to explore. Even if the answer is no, this is the scenic hike we should be taking our students on. You will find me on this path somewhere, sitting on a rock, happily removing the mathematical mud from my boots:)