I don’t know much about being a good math teacher… I mean, I’ve seen good math teachers at work. And some days, I think I’ve been a good math teacher myself. But it’s depressingly difficult to pin down what it is that makes for good math instruction, or to train someone to be a good math teacher. When it comes to good math teaching, I guess I’m like the famous judge who, when trying to explain what counted as pornography for the purposes of the law, said simply “I know it when I see it“.
But while I’m not very knowledgeable about what makes a good math teacher, I know plenty about being a bad math teacher. I think most of us do, as a matter of fact. We’ve all had that math teacher who muttered into the board, with his back turned to the class, making the problems as clear as mud. As the department chair at my old school, I even got to be in charge of that guy, and let me tell you, he’s not any more fun for the adults at the school than he is for the students…I could probably sit down and write a 300 pg. book, off the top of my head, no re-writing required, if the topic was “Being a Bad Math Teacher”, and the only problem would be that no one would buy it because you’re all already experts on the subject, thanks to the national pandemic of bad math teachers.
I do think, though, that over the last couple of years, I’ve gained a key insight about bad math teaching that the general public has not yet realized: bad math teachers usually begin with a bad philosophy of math…
I first learned to love math from an old man with a “Santa Claus” beard, who rode a Harley and cussed like a sailor in front of his students. His name was Mr. Atkinson, and he was my 10th grade Geometry teacher, and it’s mostly his fault that I don’t teach literature or history.
Mr. Atkinson had a way of explaining math as if he was that one uncle you have, who was in the Navy, and uses that as an excuse for being inappropriate at the family dinner table. Once, when explaining that Side-Side-Angle congruency doesn’t prove that you have congruent triangles, he looked out at the class and proclaimed: “Side-Side-Angle congruency is usually abbreviated SSA. A lot of students like to laugh at that, because it’s ass, backwards. I’m ok with that, because as you’ll discover when you’re an adult, most things in life are, in fact, ass-backwards.”
Once, when talking to my best friend and I after school, Mr. Atkinson told us: “look, I know that at your age, all you’ve got on your minds is girls, fast cars, and alcohol. All I’m asking is that you think about math every once in a while.” For a man trying to reach teenage boys with the Good News of Math, this was pure pedagogical gold.
Mr. Atkinson couldn’t have given less of a damn about teaching us the real world applications of the math we were learning. Sure, he had been an engineer before becoming a math teacher, and so he new a lot about applying math to the real world. But for him math was first and foremost epistemology. Math wasn’t just a tool for your toolbox, it was a path to truth.
I don’t recall doing a single word problem in his class. We did proofs. We started with assumptions–called “postulates” in Geometry–and used logic to work our way to the truth. Truth, mind you, that would always be true, that you knew for sure now because you had proven it.
We live in a technological age. I don’t mean merely that we live in an age driven by computers and gadgets, though that is certainly true. I mean it in the sense of the Greek root word, technos: we are obsessed with skills. In an age where knowledge is cheap and easy to get, your ability to wield tools becomes paramount.
As a society, we value functionality over truth. We’ve been that way for a while now. Maybe it’s the Pragmatists fault. Maybe it’s just that we’ve had technological progress and economic expansion for so long, we’ve given into the natural human tendency to become obsessive. But whatever it is, this I know: math and math education have been reduced to teaching skills.
And I think that lies at the heart of a lot of bad math teaching. The bad philosophy of math that we have adopted is one which says that math is purely a functional set of skills, not the use of reason and logic in order to know. In fact, we no longer believe that reason is a path to Truth at all…if we believe that Truth can be known at all, we usually believe only in empirical truth, or in a blind faith kind of religious truth. Reason is right out, and with it goes math…
Math certainly is a useful tool for the real world, but that isn’t what math is at its core. Math is a subset of logic. Its part of a rational epistemology. It’s man using reason to know something that he didn’t know before. And if I teach math as if it is just a set of skills, just tools for a tool box, then I’m not really teaching math. And if I’m not really teaching math–rather, I’m just showing someone how to use a numerical tool set that apparently just fell from the sky, and which I have no more reason to find truthful than I do Greek mythology or the headlines on the National Enquirer–then it’s pretty hard to be a good math teacher.
‘That’s NOT to say that if all schools started going back to this tomorrow, we would suddenly have a lot of good math teachers. But we might just eliminate some of the bad math teaching that goes on…
Incidentally, this is also my complaint about the Common Core State Standards, the much-maligned federal list-o’-stuff-you-should-know-by-the-end-of-this-grade. It fosters bad math teachers and bad math teaching by reducing math to a list of skills to be acquired, rather than portraying it as it really is: a relentless pursuit of the truth. The funny thing is, that the numerical tool set is fairly easy to learn and use if I’ve pursued math-as-epistemology, but *extremely* difficult to do if I have no idea why the math is the way it is. And so, Common Core will inevitably turn out bad math students, in addition to bad math teachers…
And there’s a deep spiritual problem that can go along with bad math teaching. With reducing math to a set of skills, we risk undermining the value of finding truth. And And if we undermine the value of finding truth, if we convey that Truth and Knowledge aren’t worth pursuing with all of our hearts, then we risk adding one more stumbling block to our students, who are told by everyone around them that truth is entirely subjective, or that the pursuit of Truth is ultimately fruitless… and that belief has eternal consequences…
Once, Mr. Atkinson alluded to a mystical experience he had had. He wouldn’t go into the details. He wasn’t a believer in any particular religion, but he told us that after the “experience”, he became completely convinced that there was more to the universe than just the material. And he kept pursuing the truth.
I kept in touch with Mr. Atkinson until he passed away. I was in college, majoring in math at the time, so Mr. Atkinson never knew I went on to be a math teacher. But my friend and I went to his funeral, and had a chance to tell his wife how grateful we were to have had him as a teacher.
In his encyclical letter, Spe Salvi, Pope Benedict wrote this about salvation:
Yet we know from experience that neither case is normal in human life. For the great majority of people—we may suppose—there remains in the depths of their being an ultimate interior openness to truth, to love, to God. In the concrete choices of life, however, it is covered over by ever new compromises with evil—much filth covers purity, but the thirst for purity remains and it still constantly re-emerges from all that is base and remains present in the soul. What happens to such individuals when they appear before the Judge? Will all the impurity they have amassed through life suddenly cease to matter? What else might occur? Saint Paul, in his First Letter to the Corinthians, gives us an idea of the differing impact of God’s judgement according to each person’s particular circumstances. He does this using images which in some way try to express the invisible, without it being possible for us to conceptualize these images—simply because we can neither see into the world beyond death nor do we have any experience of it. Paul begins by saying that Christian life is built upon a common foundation: Jesus Christ. This foundation endures. If we have stood firm on this foundation and built our life upon it, we know that it cannot be taken away from us even in death. Then Paul continues: “Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, straw—each man’s work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. If the work which any man has built on the foundation survives, he will receive a reward. If any man’s work is burned up, he will suffer loss, though he himself will be saved, but only as through fire” (1 Cor 3:12-15). In this text, it is in any case evident that our salvation can take different forms, that some of what is built may be burned down, that in order to be saved we personally have to pass through “fire” so as to become fully open to receiving God and able to take our place at the table of the eternal marriage-feast.
From time to time, I pray for Mr. Atkinson. I’m hopeful for his soul, because I do think that, at least from my experiences with him, he retained in the depths of his being an ultimate interior openness to truth. He would’ve been a bad math teacher if he hadn’t.