One of the true joys of being a teacher is it necessitates being a lifelong learner. Any teacher will admit they learn more from their students than they teach them – although the lessons can be disconcerting to say the least! Part of the recertification of a teaching license – an every five year process – is taking another college course. Not having a master’s degree, as I did not for the first twenty-five years, meant the course had to involve mathematics. This meant I got my first experiences with online courses and was pleasantly surprised by some of them.
About twenty years into teaching I tried a University of Phoenix course entitled “Teaching Mathematics with Art”. At that time U of P was the longtime leader in online education and the experience changed my view of what was possible online. The course involved over twenty students and one professor from at least five different time zones and twenty different schedules, so needless to say we didn’t have a ‘class time’ – yet the course was both rigorous and challenging.
The content – art is a critically important part of both brain development, and therefore teaching mathematics – made a lasting impression. The distinct types of art: Visual; musical; physical; each contribute to different types of brain development and tying your subject to both the art and the brain development creates a synergy which we typically ignore in our theories of education. This course came at a point in my teaching career when I had enough time and experience to observe realities of how students reacted to my teaching efforts – and to recognize the idiocy of much of what was laughably called ‘Professional Development’ promoted by ‘experts’ who had never spent day one in front of a class of students.
The clearest evidence of how little the powers that be understand education can be seen in the response to budgetary shortages – a distressingly repetitive reality of public education. Whenever money is tight, paring the curriculum is a primary ‘go to’; and the art programs, as well as other ‘extracurricular’ studies, are axed. The damage done passes unnoticed because BS (Big Standardized) testing does not and cannot measure brain development.
As a mathematician the breadth and depth of mathematical topics never ceases to amaze me. Equally amazing is the narrow, stultifying approach used to teach ‘Rithmetic. I used to tell my Algebra students that we taught them all the boring stuff – because we did! Unfortunately Algebra is incredibly important and useful for the study of a broad range of math applications – and hence quite necessary. What doesn’t make sense is why we choose to teach it in such boring ways, and we do! That can be said for the vast majority of math instruction – topped off with standardized tests which are worse – which is hard to imagine. If our goal was to make math education as daunting and unexciting as possible I’m not sure we could accomplish that any better than with the curriculum being pushed on today’s children.
Let’s take just one example – fractions: Everybody’s favorite! An understanding of fractions and the mathematics that define them is of critical importance to virtually every use of math in everyday life. The widespread use of calculators in the elementary years was hailed by education reformists as ‘eliminating the humdrum boredom inherent in math education’, and students were encouraged to use calculators to do all computations involving fractions; or any other numbers! The result is that teachers in higher level math courses in high school, where fluency with how numbers – including fractions – behave is crucial to understanding the more complex concepts being presented, are left feeling sorely betrayed.
In a Pre-Calculus course I had a number of sophomores meaning they took Algebra I and Geometry in middle school. These were the best and brightest math students our school system had to offer. In a quiz on probability I did not allow calculators because the computations were simple. One student added 2/5 and 2/5 and got 4/10. As amazingly wrong as this is, I said to myself: “Well, it’s just an oversight; I’ve made the same kind of mistake myself.” However two problems later the student added 7/8 to 7/8 and got 14/16 – or almost a whole added to almost a whole is still less than a whole! This is a student who doesn’t understand numbers or how they work. The next course – Calculus – would require an understanding of ideas like ‘infinitely close’ and ‘as x grows without bound’. At that point viewing numbers as abstracts one enters into a calculator which then magically produces a correct answer, moves from difficulty to impossibility.
After my art-math course I became more attuned to students who had an interest in, and studied, art. Nobody who studied music failed to understand fractions. Likewise students of drawing readily grasped the mathematics of geometry and shapes. Art magically associates knowledge with the beauty surrounding us on this incredible planet: Why do we not use it?
Art teachers have always inspired deep inspiration in me. Having your chosen career viewed as unimportant is belittling; but at least math – as one of the three Rs – has a little respect. Art lies below the low – except to the art teacher; and now this math teacher! When education was the exclusive preserve of the privileged – which is not really so long ago – the arts were considered of at least equal importance to the other subjects. The loss of that appreciation in public education – in my humble opinion – lies at the base of the failings of public education.
Mathematics is rigorous – in a way that can be hard to understand for those who don’t study it. Few other subjects involve this rigor and the discussions involving these subjects are likewise lacking in rigor. A requirement of such rigor is very clear definitions for terms used and unwavering adherence to those definitions. As I have – through this newsletter – delved into the debates on education the lack of rigor has become the primary characteristic of these debates. What is the purpose of education? Even a cursory glance at the proposed ‘solutions’ for what’s wrong with education will quickly expose that those arguing do not define ‘purpose’ in any way the same. If the purpose is to train one for the working world, at least half the curriculum can be ditched immediately as superfluous. If the purpose is improved standardized test scores then test-taking strategies is clearly a much higher priority than anything involving an understanding of concepts. Suppose the purpose is to prepare one to enjoy life more fully: Then what about the arts?
For the sake of argument, let’s assume the purpose of education is to learn to THINK! From my perspective the initial difficulty is there is NO rigorous definition of what ‘thinking’ is. From experience I can assure you calculators don’t think. By any definition AI doesn’t think, although the hot topic of the day is whether AI will ever be capable of such – an argument doomed to irrelevance if we can’t rigorously define the term! In the course on art we learned of studies that measured brain activity, including where in the brain the activity was occurring – where synapses were firing. This was tied to the different areas of the brain where different types of art fired synapses. The highest levels of brain activity were measured in the brains of professional football players in a game (so goes the ‘dumb jock’ myth). The second highest was for a member of an orchestra during a performance. By any definition, these people are thinking! Where was the lowest level of brain activity measured? In a person seated while performing a repetitive activity. My mind immediately conjured an image of a classroom full of students – taking a standardized test!
Loved this post, Steve! Art, math, critical thinking—an integrated whole. Bring poetry in, too, the cadence and precision of a sonnet, the multiplying power of an image in free verse. That famous path diverging in the yellow wood. We need to educate the whole miracle sitting in each of those seats (as squirrelly and resistant as those teenagers may seem). Because that is what the human mind is.