Mathematics Education as a Milk-Based Wine Drink

Creativity and mathematics in the standard, K-12 classroom are about as oppositional and unfavoring as milk-based wine drinks. There. I said it. We are taught algorithmic techniques meant to develop critical thinking skills (finding zeros to second degree polynomials, learning SOHCAHTOA, integrating horrible, horrible functions, etc.) and told that “this is what math is.” In my experience, students then ask: “When will I ever use this?” and they are met with, “Math is applicable in every profession! Look, here is an exercise on compounding interest. Isn’t that neat? Money!!” 

Look, in this technological day and age, students aren’t curious to know whether math is used in the real world or not (frankly, they all know that the answer is yes). What students are curious to know about is whether these skills they learn inside the math classroom, unquantifiable and indescribable as they may be, will or can be used inside their own version of the real world (since, it is also the generalized concept of a ‘real world’ that is absolutely ridiculous)!

While there are many kids (at all grade levels!) who enjoy the doing and learning of mathematics they encounter, the obvious majority of students in the States do not. For those kids that do: unless they attend some specialized boarding school, the mathematics they learn could still not be further from what real mathematics practice is like. If this is the truth, the following question falls naturally from the supposition: 

What is the purpose of mathematics in the K-12 classroom? 

I will omit now speaking in regards to educational policy (as is this is not the focus of this blog post) and on posing this question to upper division undergraduate/graduate math courses (since the purpose of teaching/taking these classes is, at this point, self-evident (though, to prune for a bit, there are concerns with required introductory courses in the tertiary mathematics sector—though not our concern for now). The assumption here is that anyone taking mathematics past the calculus level has already some pre-built know of why they are there, why they should be there, or why they would want to be there (none mutually exclusive), in regards to learning mathematics. These students usually (or luckily) find their own rationale for learning mathematics. At my alma mater, for instance (Harvey Mudd College) no student had to convince another that mathematics was "worth learning." The “worth-it” aspect, in the community, was a truism—whether mathematics was used a toolbox for other pursuits, or desired on its own as its own direction of study.

Many months ago, I tutored a high school student named “Ryley” in his Algebra II class. Ryley was learning about parabolic functions: finding zeros, expressing functions in standard and vertex forms, etc. Nothing a math grad wouldn’t be capable of handling. 

But I am embarrassed to say that the tutoring was a painstaking feat. Not because of Algebra II, no. But because of my own inability to give Ryley a lucid, satisfactory explanation for why he was learning these things. I mean, why would he have to use these techniques in the future? Ryley didn't know what he wanted to do for a living yet. I was a math major and went to grad school for two years for another math degree. I definitely hadn't ever used it either. And that's a perplexing thin: a math major (who went to a pretty STEM-heavy college) never once had to, say,  complete the square to a parabolic equation. What use could the concept have in being introduced to a 10th grade classroom, if it's material like that that is making students feel dumbfounded with mathematics? Sure, some K-12 math classes might be proficient at training students to apply methodology (perhaps for the sake of engineering, physics, medicine, etc.,), but I do not recall ever seeing an engineering or physics student ever needing to pull out Descartes’ rules of signs to figure out the problems they have had to encounter in their field. Most of these problems require different skillsets altogether (the real ones are perseverance, mindset, interest, exploration, patience, just to name a few); not ones accidentally picked up in the some of the more arbitrary choices of our K-12 mathematics curriculum. However. I am open to being proven wrong. 

The best case scenario for curricular choices like the rule of signs is a classroom full of students knowing they will pursue STEM in life. Because yes, there is beauty behind it. Abstraction. Symmetry. Patterns. All of the good stuff. But if the content being taught is used for neither applied nor pure purposes by students (meaning the student neither pursues math specifically nor a STEM more generally, which *surprise surprise* is the case for the majority of students who take calculus), then why the hell is math so behemothly emphasized in the pre-collegiate levels??

One might suppose that it could be for the for the sake of “proving your worth.” Say, for college applications. If this is the case, then I rest my own, as it would be equivalent to putting an equal sign next to the term "potential" and a letter grade from a homework-intensive course on the history of (not just music, not just rock music, but) alternative rock music from the 1700s. Why? It’s arbitrary. And in the end, what its most indicative of is a student's ability for a wicked sort of self-discipline at an early age (talk about a loss of childhood) and most likely higher than average parental educational attainment.

And if it’s not for the sake of entering college, then I wish to assume it’s for the sake of building intangible, largely insensible skills like "critical thinking. Which lands at me my proposal: could we change this pursuit, whatever it is (though I sensibly call it "critical thinking"), in K-12 math classrooms to be the pursuit of creative thinking? 

Imagine a world where math classrooms build agency in our learners. Where students come out of math courses feeling like they had a chance to learn and to create something of their own. To really experience mathematics for themselves. I believe the next revolution in mathematics education will be the one which personalizes the mathematics experience. We need a more human system of mathematics education, not a more correct one. The study of mathematics is no longer—and should have never been—a need in our society. I do not wish to abandon the notion of ‘correctness’—just de-emphasize it. 

When an art teacher judges the artwork of their students, the art teacher doesn’t scan for correctness. They scan for growth. For identity. For controlled risk and innovation. Unfortunately, K-12 math ed. has been placed as one of the most binary subjects to learn out there: you are either wrong, or you are right; the method is incorrect, or the method is correct. Though math is foundation-ally a deductive search for truth, the search component of its study has long been forgotten by the layman. 

We need more creative thinkers in our society, and the mathematics classroom is the perfect to place to foster these constructs: agency and creativity, in the illustrious and artistic foyers of the younger minds.