Author: Chad Topaz
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If you are reading this, you are very likely an instructor of math at the college level. I probably don’t need to convince you that mathematics is a worthwhile discipline. But please, humor me, and let me remind you. The challenges and opportunities of human existence increasingly require quantitative tools. Math helps us build efficient power networks, create effective medicines, develop intervention strategies to support public health, animate movies, understand the workings of the human brain, and much more. If you don’t believe me, believe the National Research Council’s Math 2025 report. Though mathematical tools are pivotally important for society, we are still finding our way when it comes to embracing the subject. After all, while the U.S. literacy rate is estimated at 99%, it remains socially acceptable to proclaim that one is simply “not a numbers person.” Much like Chef Gusteau of Ratatouille fame insists that anyone can cook, it is also true that anyone can do math.
To better prepare our nation and our individual students, improving college math teaching is only part of the puzzle. We face complex issues related to K – 12 math teaching, equity, government policy, taxes, and much more. Nonetheless, college math teaching is what I am going to write about.
The fact that I am writing about it is somewhat surprising to me. Recently, a few people have encouraged me to write a book about college math teaching. I find this to be hilarious for at least two reasons.
First of all, I feel like books aimed at professional development are sort of… over. Who has time to be professionally developed by reading a book? Who wants to pay money for a book? What author wants to have to shop around a manuscript? Am I willing to write with enough gravitas to make publishers take me seriously? Who wants to be limited by the paper format? After all, in a book, you can’t include videos of adorable talking mice. Still, I am going to refer to this mess of web pages as a book, even though it isn’t. Occasionally, I will call it a non-book.
Second of all, I feel like I am not really the person to ask about how to teach college math. I mean, I do teach college math, and I am occasionally lauded for it, but I take no credit for this. All I do is do what I am told by people better-informed than I am.
By “people better-informed than I am,” I am not referring to other college math professors. Don’t misunderstand me: other college math professors are, no doubt, more informed than me on nearly every matter. But on the specific topic of teaching, they are not necessarily the ones I have in mind. The premise underlying many of the subsequent chapters is that teaching and learning are a science. So the people I listen to are scholars whose expertise pertains to education, or else other mathematics faculty who listen to those aforementioned experts. Also, I am married to an educational psychologist. This has been immensely useful for my teaching, and I highly recommend that you yourself marry an educational psychologist at the earliest opportunity.
You know who else is more informed than me? The National Research Council (NRC). I already mentioned them once. If you don’t know them, you should. They bring together experts of ridiculously high quality and using the total amassed brainpower, produce syntheses on various topics that lots of people pay attention to, but more still should. As for teaching, there are two NRC reports that I am especially fond of. Notice that I carefully called them “reports” to comport with my previous statement about nobody reading professional development books. You can download these two reports for free if you create an online account, and I highly recommend making the time to at least skim these at some point:
The primary goal of my non-book is to present basics of learning science rather than delving into applied research that is focused on the classroom. Though I might sometimes suggest specific teaching strategies, I will more often just try to explain features of human learning. Why? First, because it is dangerous to implement teaching techniques without understanding the theory behind them. Things can go awry. And second, because if you understand the theory, you have the power to find and develop the teaching techniques that work best for you, in your context, with your students, your department, your institution, and your community.
It’s predictable that I would think this way as a mathematician, yes? We want our students to understand concepts rather than memorizing formulas and blindly executing procedures, right? So we should approach ourselves the same way as teachers. My title of this book, “The Inappropriately Secret Life of Awesome College Math Teaching,” is likely to raise some hackles. (Apparently, this is an expression people use. I looked up what hackles actually are, and they are “erectile hairs along the back of a dog or other animal that rise when it is angry or alarmed.”) I am not saying that we are bad teachers, though I fully admit that I suck (more on this later). What I am saying is that for many of us, when we do things that work for our students, we don’t all understand why they are working. Good teaching need not be mysterious. There is plenty of evidence about what works, and yet our field often seems to engage in discussions and debates about teaching practice that have already been resolved by other fields.
A secondary goal of this non-book is to get you, the instructor, to view yourself as a learner, where the thing you are trying to learn is how to teach. All of the expert evidence about student learning applies equally well to you if you want to spend your career working towards being an ever-more-awesome teacher.
Isn’t it funny that I say I listen to the experts, then proclaim myself not to be an expert, and then presume that you should listen to my advice by reading my book? Yes. Yes, it is funny. But life is funny. Still, what I will do in the future chapters is to try to maximize reporting of well-grounded research (put into friendly and practical terms for you) and minimize opinion. Though anyone who knows me knows that keeping my opinion totally out of it is a futile quest.
Here’s my first opinion. Fundamental to successful teaching is admitting that you suck.