What the Educational System Gets Wrong About Math
“Math sucks.” As a mathematics tutor here at Sage, there’s not a day that goes by that I don’t hear this statement from one of my students. The fact of the matter is, I can’t disagree with them. Math does suck. Hardly anyone goes on to remember their mathematics education fondly, and there’s a reason for this.
Our education system is 100% wrong about mathematics.
Wait, but how can our schools be “wrong” about math
By simply missing the point completely.
As our schools present it, math is about memorization and repetition. Here is how you solve for x. This is the distributive property. These steps will find the derivative. Now do that over and over again. Page 252, 1-31 odd.
What we’re teaching is manipulation of symbols divorced totally from meaning, repeated ad nauseum. Assignments are rote drudgery, inflicted on students by omnipotent textbook authors whose will they must bow to. Students find themselves pleading to these faceless architects: “What do they want here?” “Do they want me to divide?” Our math curricula are bloated with countless rules, definitions, and symbols presented without motivation or context, whose sole purposes seem to be to appear on test problems, only to be forgotten the next week.
No wonder students find themselves throwing their hands up in despair! What’s the point of it all?
English mathematician G.H. Hardy said it best: “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”
A mathematician as an artist? Math and art are basically the antitheses of each other. Left brain versus right brain!
There’s certainly no art in the current state of affairs. Mathematics, as taught by our schools, reduces students to glorified calculators. Kids are given a process and are made to execute it over and over again every night under the guise of learning. That’s not learning. It’s memorization.
At its very core, mathematics is a means of human expression that requires creativity.
It is a means of conveying ideas, creating patterns, discovering solutions to puzzling questions, and forming beautiful structures. The fact that reading that sentence probably made most readers inwardly smirk is indicative of how effective our education system has been in squashing this idea. To call mathematics an art that prizes creativity is laughable to us because we haven’t had the chance to experience it as such; our school systems drown our innate satisfaction at the simple beauty of patterns with complex notation and rules to be memorized and regurgitated.
Consider a world in which music received the same treatment as mathematics. Music is a ubiquitous human phenomenon, and the little black markings on staff paper must constitute the language of music. Therefore, from a young age, we indoctrinate all of our children in this system so that they might be well-rounded music students. In 1st grade, they practice drawing rows and rows of treble clefs, quarter rests, eighth notes. 3rd graders are introduced to the circle of fifths. By 8th grade, they’d better have all of their modes memorized if they want to test into advanced music theory (which looks great on college apps).
In high school, they are taught how to compose a fugal passage according to the rules of the western system of tonal harmony. If there’s a “V” chord, it is a dominant and must lead to a “I” chord. Don’t forget the correct inversions to insure proper voice leading! Fill in the notes on your staff paper. Page 252, 1-31 odd. All without allowing students the liberty of listening to and appreciating music on their own terms or, god forbid, encouraging them to hum their own melodies.
I don’t take any stock in this creative mumbo-jumbo. Aren’t students learning practical skills? In the real world, everyone should know math!
How often do adults need to know trigonometric identities? When was the last time a job required you to do polynomial long division? Find x-intercepts? The second most popular phrase I hear at Sage is “When am I going to use this?” The answer is probably never, and students know this.
The secret fact behind it all is that mathematics was developed purely as a human diversion. For fun. Pythagoras discovered a theorem relating the sides of right triangles, but I’m sure he had loftier things in mind than building a coffee table in his living room.
But math has practical applications! That’s the whole reason it’s so important!
You need to know how to read and write to fill out forms at the DMV, but that is not why we teach kids those skills. We understand that at their core, these disciplines are about so much more than their practical or commercial uses; they teach us about communicating ideas and exploring ourselves. Anything else is a by-product.
Imagine if the only motivator schools gave for becoming literate was to be able to understand the position of your state’s representatives. Though that is a necessary part of being an informed voter and citizen, if the only reading students did in school were excerpts from public policies, it would be no surprise that many would grow to hate English class. Sure, maybe some students would excel at parsing political jargon, but others would throw up their hands, saying “I guess I’m just not an English person.” Why do we attempt to motivate our math students in this way?
Instead, our math classrooms are devoid of any mention of beauty, creativity, or history. In this unrecognizable format, the subject has become simply a means of climbing the academic ladder, of portraying oneself as a competitive applicant, of discriminating between who is a “math person” and who is not.
Okay, so then what alternative is there? How do we teach students to do math?
I couldn’t put it any better than American mathematician, Paul Lockhart: “By choosing engaging and natural problems suitable to their tastes, personalities, and level of experience. By giving them time to make discoveries and formulate conjectures. By helping them refine their arguments and creating an atmosphere of healthy and vibrant mathematical criticism. By being flexible and open to sudden changes in direction to which their curiosity may lead. In short, by having an honest intellectual relationship with our students and our subject.”
A music student must develop a love of the art itself before pursuing the tools with which to better understand that music and to communicate their own ideas; in the same way, a math student should be allowed to develop a love of inquiry and exploration. Only then will they find the motivation to pursue the tools with which to improve their understanding.
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