Recently in the american media, various articles discussed the social mobility barriers that mathematical prerequisites represent in higher education. Much of the discussion centered around remedial algebra in community college. Statistical evidence indicates that intermediate algebra is the main culprit that prevents many workers from graduating from highschool and community college. Some of the writers and technocrats cited in these articles suggest scrapping many of these mathematical pre-requisites.
Polarization arose in websites, social media, and comment sections. In one side, some people argue that removing these mathematical pre-requisites would contribute to the cretinization of the general populace- akin to removing writing and reading classes from curricula. The other side of the debate pretends to take the pragmatic side, by arguing that these requirements are empirically holding back social mobility for the underclasses.
I find these debates often infuriating, informed by the theory-less barbarism of technocratic bean-counters. The pragmatists that want to cut the mathematical requirements do so because some “expert” with a fake master’s degree fitted a line through a scatter plot that somehow signaled that mathematics is insurmountable for black people. Yet, the other side of the debate is also very simplistic; it reacts out of conservatism because it conceives of an already established body of vetted knowledge – in this case, mathematics – that will be diluted by the administrative paper-pushers. I do agree that the admins and their lackeys should be opposed; they are willing to throw anyone under the bus in their fanatic drive for metrics and vulgar empiricism – as they have done so for countless of students, adjunct professors and teachers. Furthermore, at least superficially, there seems to be a very problematic schism between the humanities and the hard sciences, as diagnosed by C. P. Snow almost 60 years ago, which diminishes the creative potential of humanity at large. Yet, mathematics, as it is currently taught is deeply alienating – for it is not the mathematics of the visionaries that unfolded the symmetries of the universe – but the mathematics of accountants and assorted paper-pushers. Therefore, I will try to describe in this post why mathematics is important outside the sphere of commodity circulation and technocracy – within the realm of leisure, art and creativity.
Innumeracy constricts thinking, as it blocks a path to the totality. In the same way illiteracy denies the individual access to accumulated thoughts, memories, and disciplines, innumeracy denies entrance to a whole gradient of human experience: from aesthetic considerations about symmetry and beauty, to the laws of motion that regulate both the physical and human universe. Not only innumeracy closes a window to large wells of human knowledge, such as the natural sciences and mathematics, but also constraints the ability to synthesize thoughts about the world. In the same way sociology, history and the arts immerse people in a rich context that will affect how they vote and relate to humans from different creeds and ethnicities, the abstractions of mathematics influence how individuals navigate fundamental aspects of reality such as space, time, inter-connectedness, and change. For example, an idea that I frequently explore in my writings is the complexity and non-linearity of human society –properties that have deep implications in our ability to conceive ourselves as political beings. For instance, the mathematical volatility of human society and the nonlinear, economic coupling that connects spatially separated humans across oceans and continents calls into question the philosophical foundations of nationalism and borders. Another example of the conceptual power of mathematics is how mathematical physics connects different natural qualities through minimalistic equations, such as newton’s second law, which relates force, mass and the rate of change of velocity (acceleration) into a differential equation.
Yet, the current pedagogy of mathematics is driven by the necessities to produce technical workers or professionals. The lesson plans for calculus and algebra in universities and high schools are designed as pre-requisites for STEM; the imperatives of professions such as engineering or finance dictate the content of these lessons. For example, fluency in number crunching is necessary in many of the hard sciences – where solving non-trivial algebra and calculus problems is business as usual. However, such facility is only achieved by alienating problem sets and repetitive grinding. which discourages the uninitiated. Yet the deeper dimensions of mathematics as a bridge between consciousness and symmetry, beauty, and change are not explored – it’s only the mathematics of balding men in cubicles and spreadsheet theorists that make their way into curricula.
The answer is not removing higher mathematics from the curriculum – unless one wants to shrink the consciousness of marginalized individuals. Nor it is keeping the mathematical pre-requisites as they are – which are the pre-requisites of accountants, engineers and bankers. As it stands, much of higher education is a means to social mobility, and it’s obvious that the current spiritually draining approach to mathematical pedagogy is acting as an obstacle to achieve that function. Perhaps, the answer is to have alternative classes of mathematics for non-STEM students that highlight conceptual reasoning over computational fluency. A mathematical pedagogy that describes how the symmetries sketched by artists are the same symmetries found in the movement of the heavens and in the interior of an atomic nucleus, will do much more good than emphasizing how to compute the cubic root of a function. Much of mathematical innovation and inspiration arose from observing the natural and human world – perhaps that same inspiration can awaken in unmotivated students when teachers and pedagogues bridge the relationship between mathematics and the totality.