Today my blog is about one of the most important things I’ve learned as a teacher, and specifically as a teacher of math. I’m going to start with a story about a kid I tutored for a while, many years ago.
When I was younger and just starting to realize I had a passion for math and for teaching, I firmly believed that anyone could understand math and be good at it. Some people took to it more readily than others, but I was certain that given enough time and effort, every single person could excel.
Then I met Lief (not his real name).
Lief came to me when he was in grade 6, and our first tutoring session was about math questions involving time. The question we worked on was something like “Harry leaves home at 12:05 pm and arrives at his destination at 1:30 pm the same day. How long did the trip take?”. Lief was really struggling with the question, but I knew that I could explain it in such a way that he would not only be able to determine the correct answer he would fully understand how we did it and be able to answer many more similar questions. As my students would say, I have mad skillz when it comes to explaining math.
Boy was I wrong. I spent an hour with Lief and I used all my powers of teaching and explaining to no avail. Strewn about us were diagrams, pictures of clocks, number lines, a watch and even part of a model Volkswagen Beetle (don’t ask me why, I don’t remember). Lief just could not understand what the question was asking and why the answer was 1 hour 25 minutes (see how I threw that in there so you’d know if you got it right? 😉 ). I learned a valuable lesson that day.
Some people just aren’t wired for math. And that’s totally OK of course. Contrary to popular opinion, math is not a critical life skill. Aside from people like me I can’t think of a single person that needs to be able to complete the square of a quadratic function given in standard form in order to determine the coordinates of the vertex of the parabola. Proof? You most likely have no idea what in the world I was talking about there and I bet you do just fine. I know at least that you own some sort of electronic device capable of connecting you to the internet. That says something.
So why is this blog titled “Sometimes, the Door Is Down the Hall”? What am I talking about, you ask? Well you wouldn’t be the first to ask that. Allow me to explain.
Where I live in Ontario, Canada, students attend high school for four years — grades 9 through 12. During that time, in order to be awarded their high school diploma, they must successfully earn three credits in math. For most students, that means a grade 9, grade 10 and grade 11 credit, though some do grade 9, grade 10 and grade 12. It means that math is optional in grade 12, if all you want is a high school diploma. If you want a post-secondary education however, like college or university, you will most often need to take math in all four years of high school, and also be sure to choose the right math courses for your intended post-secondary program.
At each grade, there are choices of which math course to take. There are different paths and they don’t all lead to the same place. For example, a student who intends to study math or science at university will take what’s called “Academic” math in grades 9 and 10, then “University prep” math in grades 11 and 12. Conversely a student who intends to go to college to learn a trade will likely take “Applied” math in grades 9 and 10, then “College prep” math in grade 11 and maybe also in grade 12, depending on the requirements of the college program. Some students take what’s called “Essentials” math in grades 9 and 10, then “Workplace” math in either grade 11 or grade 12. These students are either not planning to attend a post-secondary institution or else are planning to go into a field that has nothing at all to do with math.
Phew! So that was kind of boring to read, right? But if you read it you may have noticed the glaring flaw in the system. A student must decide on a career path in grade 9. When they are 14 years old. Actually they have to pick their grade 9 courses when they are still in grade 8, so they and their parents have to make the call when the student is 13 years old. Who the heck knows what they want to do with their lives at the age of 13? When I was 13 I wanted to look at girls, play video games, eat steak as an afternoon snack and look at girls. And then look at girls. I had absolutely no idea what I wanted to do with my life. As a matter of fact now, at 43, I still don’t know what I want to do with my life (except for the looking at women part — I still do that and am lucky to have a wife that is exceptionally fun to look at). But I do know that I am happy with what I’m doing right now. Maybe that will change, maybe it won’t. But the key to my happiness is that I am doing something I am good at and that in turn makes me good at it. Read that last sentence a few times. It seems confusing but it isn’t. Try doing something you suck at for a long time. Keep telling yourself that you’ll get better if that makes it seem worthwhile. But I think you’ll find out that when you’re not good at something you are miserable doing it and then you are not good at it.
So how does this manifest in high school? Well it may seem obvious that since very few 13 year old kids have any clear idea about what they want to do when they finish high school — let alone as a career — that they choose the option that keeps all the doors open. In Ontario, that means that they will usually choose grade 9 academic math, because if they don’t they are closing the door to a post-secondary program that requires math. They do it again in grade 10, 11 and even in grade 12. I can not begin to count the number of students I have taught who have struggled mightily in math who then sign up for the hardest math course the following year because they don’t want to close doors. I’ll illustrate with an example. Good ol’ Hanz.
You might remember Hanz from “Steer With the Skid”. Hanz is a hard-working kid who does not have a lot of natural ability in math. By not a lot I mean he’s terrible at it. And please, before you object and say nobody who works hard can be terrible at something, look around. Some people are wired to be awesome at certain things and terrible at others. Some kids are born athletes, some are born artists, some are born mathematicians and some are born poets. You can improve your abilities in almost anything but that doesn’t mean you can excel in almost anything. Personally, as hard as I might have trained, I would never have been an Olympic sprinter. My legs are too short and I don’t have the reflexes. I’ve made peace with it.
So back to Hanz. Hanz doesn’t want to close doors, so he takes Calculus in grade 12. Currently in Ontario the course is actually called Calculus and Vectors. It’s the two hardest math topics in high school grouped together in one spectacular ride. Hanz has been miserable in math class ever since grade 9. He works hard, and puts in the time, but the most he can muster are grades in the 60’s, and it eats him up. His hard work is constantly rewarded with what he considers to be mediocre grades. He’s miserable because he’s convinced that he can’t be successful in life unless he’s successful in math and his definition of successful in math is marks in the 90’s, something he’s never been able to do. In trying so hard to keep a door open, Hanz has missed the fact that for him, there is no door marked “math”. He can’t see that if a program requires Calculus and he takes it and earns a 51% he won’t get in anyway. It’s a fruitless exercise. Yet every time I talk about this with Hanz or his dad Franz, they both insist that Hanz has to stay in Calculus so that he can keep his doors open. That’s when I shake my head and say “Sometimes, there is no door. Walk down the hall.”
See, if Hanz could recognize that there is no “math” door for him, he would be compelled to walk down the hall and see what other doors there are. If Hanz would spend more time in situations where he has natural strength, he’d know what those doors are and what lies beyond them, and he’d be so much happier. Unfortunately it’s extremely difficult to convince Hanz of this, and he spends all his energy working at something he was not wired for, spiraling further and further into self-loathing and often depression. I’ve seen it many times. I’m not exaggerating.
Now please, before you go off wondering how I can call myself a math teacher and be so willing to write kids off, understand that’s not what I am saying. I teach all levels of math. I am just as happy teaching someone like Hanz how to plan a family budget and the evils of credit card interest as I am teaching him how to take the derivative of a sinusoidal function that has been composed with the square of a logarithmic function in order to determine the instantaneous rate of change on the curve at the place where it intersects with a given exponential function. I work just as hard either way, and my reward is always Hanz’s success. It just pains me to see kids like Hanz convinced that they will end up “homeless under a bridge” (this is a saying my students have when they decide they are going nowhere in life) if they can’t do the derivative question. Honestly though, how many people can? And why on earth would most people need to? The derivative question is an exercise in abstract thought that is beautiful in its way, and critical for people going into a field where they have to solve high level math or science problems all the time, but it’s not the definition of intelligence or success.
Students like Hanz often ask me what courses they should choose when they are picking for the following year. I always say the same thing.
Me: “What are you good at?”
Student: “Well I’m good at <insert non-math or science discipline here> but that doesn’t get you anywhere so I need to take <insert completely inappropriate math or science course here>.”
Me: “Why would you take something that makes you so miserable?”
Student: “Because I need it to be successful. I need to keep my doors open.”
At that point I generally ask them how they intend to become successful in a field that requires them to be good at something that makes them miserable. They really never have an answer for that. Except for the door thing. My advice then is for them to take courses they enjoy, and that they excel in. Happy people who excel at what they do are always successful. Find one and ask them. You’ll see what I mean.
Thanks for reading,