y=mx+b

Algebra has become a newsworthy subject once again, after slumbering for decades in freshman high-school classrooms undisturbed. We are, as a society, suddenly energized by this new research claiming that algebra is unnecessary as a broad-based mathematics course, and should be tracked only for college-bound individuals. Everyone’s dropping out, we’re shouting from atop the local schoolhouse bell tower! They need easier math so that they can stay in school! 

To do what, exactly? Continue on a course of delayed-maturity middle-school mathematics? Do we really think that stunting the mathematical curriculum will ensure us that we don’t need to suffer questionable life choices like this and this and this? This limb seems strong enough to support me, so I’m going to inch out to the very leafy end of it and counter this statement with another potentially confrontational one: algebra is not only necessary, but serves us in life areas beyond mathematics. To further that point, I think that the frustration and ambiguity that algebra engenders in high-school freshmen is, in fact, a good thing – because they will need it later.

Algebra is to elementary- and middle-school mathematics as creative writing is to the five-paragraph essay. These tasks – writing something new, solving a complex system of equations – are the first moments in our lives in which we’re truly asked to go beyond what is given to us, to go outside the prescribed and well-worn path to results. Algebra, in particular, asks us – for the first time in our educational careers – to deal with imperfection and lack of clarity. Just as creative writing asks us to set sail upon the windswept terror of a blank page, that foamiest and angriest of literary seas, algebra tasks us with navigating between Scylla and Charybdis, and making safe landfall on mathematical shores beyond. For the first time, there are unknowns to be brought to heel; there is ambiguity in the route to the outcome. It is left to us to make sense out of what we’re given, to think about what it is we’re going to need to do to get to a solution. Point B, that friendly buoy bobbing in the harbor just a few hundred meters offshore, is no longer the destination. Now, we are only given a compass, a nautical chart, and the position of point Q. Managing sails and wind and drift, sailing by starlight, is left to us.

I call that life.

Moreso, I think, for parents of gifted kids. Do you recall flipping past your child’s NNATs and CogATs and WPPSIs and WISCs to find, at the end of the document, a neatly-bound roadmap for you to follow for the next twenty years? When you’d need to consider acceleration, and when you’d want to prioritize intensities and sensitivities over the need for intellectual goodness of fit? What combination of work flexibility and income will maximize your children’s social well-being and emotional health? Or maybe, just maybe – and it’s OK to allow yourself the full sinking-feeling sensation when I say this out loud – has life perhaps turned out to look something like a word problem?

Child E will be ready for college a full four years before your college savings fund was planned to be fully-funded. If x represents your current monthly savings rate, solve for your revised savings rate in terms of x-prime.Extra credit: solve for y, the number of extra billable hours you will need to summon forth from the fabric of the charitable universe to make x-prime a reality! (Note: you are not allowed to violate the space-time continuum.)

Child H, our resident dyscalculic, has completely lost sight of whether she is actually doing above-grade, at-grade, or below-grade work in math. If H enrolled on time for kindergarten at age 6 in a program that teaches math one grade level above, and was then accelerated a full grade at age 9, express the grade level that would best address her dyscalculia in terms of x, where x would be appropriate age-level math. (Extra credit for not confusing the high holy hell out of the child along the way.)

Sound like word problems yet? Anything like this going on in your household? Do you really think a sound familiarity with the times tables is going to make a difference in working out issues like these? See, this is the point.  I don’t credit algebra with preparing me to do any particular sort of mathematics with respect to dealing with life (although it’s sometimes handy); I credit algebra for preparing me for a life of unstructured ambiguity, in which I don’t start with all the information I need to solve the problem. Maybe the problem is going to have to be solved in stages. Maybe the answer is undefined – that black hole of vertical slopes and division by zero and infinity to the zero power – and there is no way to solve the problem. Maybe I’ll need to take the issue through two or three transformations before it becomes solvable. Are these really lessons that can be learned in elementary-school math? Much as I love him, am I really going to learn how to manage the ambiguity of modern life by following this fucking rabbit around all day?

These are cold, deep, often frightening waters. Take it from me; I have signed on as the crusty sailing-master for E’s voyages into algebra at age nine, and there are tears and frustration to be dealt with as she realizes the challenges inherent to algebraic problem-solving. My goal is to let her make as many mistakes as possible now; my hope is that by the time she reaches college, she is used to sailing these waters confidently. The future for her, as it will be for all of them, is fraught with precisely this sort of uncertainty. That’s what makes me laugh out loud when the New York Times article cites a Georgetown study indicating that “… in the decade ahead, a mere 5 percent of entry-level workers will need to be proficient in algebra or above. ” Really? Does that imply that they will need to be ‘proficient’ in arithmetic? Will they really be doing wedding-cake long division on the job, when the basest of crappy mobile handsets comes with a calculator app better than most of the calculators I had prior to 1987? What does ‘proficiency’ even mean in the context of mathematics in a world where everyone with Internet access now has a free spreadsheet program available? This entire line of thinking is reminiscent, for me, of Sugata Mitra’s comments in Future Learning. 

Here is my counterpoint to the fine researchers at Georgetown: what the next decade will require from our nation is an unprecedented level of creativity, in every line of work, every vocation, every professional discipline, in order to build a new America that is survivable in the realities of a truly global economy. I don’t guarantee that the type of creativity that is forged in the fires of algebraic manipulation will manifest itself in everyone who takes high-school algebra. But five percent? That seems like a shockingly small proportion of young learners who would benefit from exposure to algebra – and it seems to suggest that 95% of the world population will somehow be able to advance human society forward with nothing more than a four-function calculator. I would no more make a ludicrous suggestion like the ‘Georgetown five percent’ than I would, oh, say…suggest that critical thinking should not be taught in schools.  (Sorry, had to.)

What we’re going to need is more adaptive thinking, more creativity, more willingness to turn the ship away from the twinkling lights of the harbor and into the chilly, foggy expanse of blue water that lies out there. For me, that begins with a troika of analytic creativity, literary creativity, and critical thinking. I’ll be talking more about the latter two in other blog posts to come – but given how prominently the ‘algebra debate’ has figured in our nation’s recent educational discourse, this seemed a logical place to begin; with the variable a, the role of algebra in our country, to be solved for by the generation to come.

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