Math Pedagogy in Plato’s Republic

By Spencer Cawein Pate

This summer, I enrolled in a doctoral seminar centered on the standardization and corporatization of the curriculum in public schools. Our professor, Dr. Tom Poetter, had an ambitious goal for the class: to collectively write and produce a book on the course subject, drawing upon our own experiences and curriculum theorist William Pinar’s concept of currere, within a short and intense span of four weeks.

The book that resulted, Was Someone Mean to You Today?: The Impact of Standardization, Corporatization, and High-Stakes Testing on Students, Teachers, Communities, Schools, and Democracy, has just been published by Van-Griner. It’s an unusual and interesting volume: instead of each contributor authoring a separate chapter, we worked as teams to co-author chapters by weaving together previously-submitted essays and reflections on a common theme. I was in charge of the chapter on rhetoric, which contains three pieces of mine in addition to the chapter’s conclusion: a substantial exploration of the Freudian and Lacanian psychoanalytic foundations of currere, a strategic discussion of George Lakoff’s idea of linguistic reframing vs. Corey Robin’s advocacy for a “politics of freedom,” and finally a personal narrative about perennialist values in the math classroom. I would like to present a special expanded version of this last piece here, as I think it’s my most succinct and elegant statement of my educational philosophy and practice:

In the fall of 2014, I took a philosophy course centered on Plato’s Republic. Several books of the Republic concern the question of education in the author’s ideal society, and as a former middle school math teacher, I was delighted by how Plato places mathematics at the center of his educational philosophy. Plato, of course, would be an educational perennialist, concerned with passing down timeless / universal / transcendent truths to a new generation. Mathematics and geometry, which in Plato’s view are the very definition of archetypal forms (527b5: “it is knowledge of what always is, not of something that comes to be and passes away”), are ideal for this pedagogy, so long as they remain refined and abstract, divorced from any kind of measurement: “for the sake of knowledge rather than trade” (525d1-2). He goes on to argue the following:

“Then it would be appropriate, Glaucon, to prescribe this subject in our legislation and to persuade those who are going to take part in the greatest things in the city to go in for calculation and take it up, not as laymen do, but staying with it until they reach the point at which they see the nature of the numbers by means of understanding itself; not like tradesmen and retailers, caring about it for the sake of buying and selling, but for the sake of war and for ease in turning the soul itself around from becoming to truth and being. […] It gives the soul a strong lead upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies.” (525b11-d7)

Furthermore, the process of learning mathematics models the faculties or virtues of reason and logic that Plato attributes to the philosopher-kings of his ideal city: “More than anything else, then, we must require the inhabitants of your beautiful city not to neglect geometry in any way, since even its byproducts are not insignificant. […] And in addition, when it comes to being better able to pick up any subject, we surely know there is a world of difference between someone with a grasp of geometry and someone without one” (527c1-8). It exercises the mind in the same way physical training strengthens the body: 

“Now, have you ever noticed that those who are naturally quick at calculation are also naturally quick in all subjects, so to speak, and that those who are slow, if they are educated and exercised in it, even if they are benefited in no other way, nonetheless improve and become generally sharper than they were? […] Moreover, I do not think you will easily find many subjects that are harder to learn or practice than it. For all these reasons, then, the subject is not to be neglected. On the contrary, the very best natures must be educated in it.” (526b4-c5)

When I taught math, I would sometimes find myself being asked the inevitable questions by my students: “Why do we have to learn this? When am I going to use this in the real world?” The answers that math teachers typically default to are: “You will use math in your future job.” or “You need to learn math so you can get a good job in the future.” I find both of these answers to be unsatisfying and inaccurate; while many jobs (and everyday life itself, particularly in matters of finance) do involve more math than we often think, some jobs do not, and those that do will not necessarily involve all of the areas of mathematics that are commonly taught (because of specialization). And of course, when one answers with reference to jobs, students will immediately challenge you to specifically describe how the math they’re currently learning will be useful and relevant to a particular career, which is not always easily done.

Moreover, I especially dislike the corporatization and subordination of math education to the technical ends of capital, of being able to “compete in the global economy.” The use-value of mathematics infinitely exceeds its exchange-value; indeed, the study of mathematics doesn’t have to have a reason or a purpose: I believe that the contemplation of math, much like the contemplation of art, is its own reward.  So when students asked me those above questions, I tried to sidestep this trap by reframing what the questions presuppose. I would answer as follows:

“We should study and appreciate math for several reasons:

“1. Because math is beautiful and fascinating in its own right.

“2. Because math teaches us to reason, to think critically and logically, and in doing so, it makes us better and more literate citizens who can participate in a democratic society.

“3. Because math helps us to investigate and solve real-world problems and phenomena.

“4. Because math is connected to every other subject imaginable: science, history, economics, even art and music.”

And only after I listed those four reasons would I cite the fifth–to get a good and enjoyable job someday.

I would like to think that this is a rationale for mathematics education of which Plato would have basically approved. While doubtlessly he would not agree with my progressive pedagogical inclinations, my educational values are perennialist, like his own. Those eternal verities act as a bulwark against the corporatization of mathematics education (often under the guise of STEM), and they can help us to reframe what is considered normative or commonsensical in schooling. We teach and learn math not to serve the interests of capital, but rather for both public and private good.

Finally, I should note that seventh graders generally don’t find my answer any more satisfying than the default one. But we should expect this–after all, they’re still just middle schoolers. However, I believe that an intellectually honest if unconvincing answer is superior to a fundamentally dishonest and ethically suspect answer that is even less convincing. Who knows? Maybe I’ve planted seeds that, in the fullness of time, will flower and bear fruit. I would love to think that when my former students are, say, studying calculus and / or physics in high school or college, some will have an epiphanic moment of realization and exclaim: “Mr. Pate was right–mathematics really is beautiful!”

If you’re interested in reading more on-the-ground reportage and analysis of the disastrous effects of high-stakes testing on public schools–written by actual classroom teachers, informal educators, and college professors and administrators–be sure to check out the book! I’ll end with my reflection on the process of crafting the book:

This currere project reminded me of a quote from the final section of T.S. Eliot’s “The Waste Land”: “these fragments I have shored against my ruins.”  It seems contradictory that only gathering and marshaling fragments can stave off encroaching ruination, but in the wake of the corporatization of education, perhaps fragments–of history, of theory, of discourse–are all that remain. Fragments are something we can build with, in the empty spaces between the rubble and debris that capital has left behind. The currere method produced short, sharp fragments of subjectivity (which we called “bits”), that were then worked into longer and more rigorous academic treatments. The treatments were in turn woven and braided into narratives, the narratives into chapters, and the chapters into the book you have just read. But rather than subordinating all of these disparate melodies to a single harmony, the currere process allowed us to babble with a polyphony of voices, a kind of sinuous and riverine music with themes submerging into and surfacing from the flow of the text. For all the messiness of our journey as a course, something spontaneous and surprising and novel emerged. As Charles Darwin wrote in The Origin of Species, “from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”

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