School is back in session! Are you lamenting the end of summer vacation (or maybe celebrating it)? I’ve been out of school for a few years now, and it still feels strange not heading back to class after Labour Day. Looking back on high school, I definitely learned a lot, both inside the classroom and out. But there are a number of life lessons I wish we’d all learned in high school. If you’re a student, know a student, are a teacher, or know a teacher, let me know if you agree! Continue reading
For the last few months, I have been tutoring my sister in Grade 12 Math. That’s Advanced Functions and Vectors, so far.
My sister and I are very similar in a lot of ways, but when it comes to academics, we are very different. I’m a solver, not a memorizer. When I come across a question structure on a test that I don’t remember (which is likely), I’ll solve it from scratch, using whatever methods and facts I do have. That doesn’t work in chemistry, biology, or history, which are all very memory-heavy, so I avoided those courses in school. Physics, math, and English, on the other hand, are great for solvers. My sister is more of a memorizer, which is great for memory-type courses, but when it comes to math, not so helpful. And math is a pre-requisite for a lot of university courses.
As we’ve been working through the curricula, we’ve obviously had to work through the obstacle of different learning and test-taking styles. However, I have noticed one thing about high school math course structure in general that I never noticed as a student.
It seems that many upper year high school classes start with the how of a particular mathematical concept, rather than the why. Sure, if you were to read the textbook cover to cover, you would get an explanation of every concept and how they all link together. As it stands, students seem to be introduced in class to the solution method first. Then comes the application: the “word problems”. And I imagine the lack of context and deep understanding is the reason why so many students I know hate word problems: because if it’s not exactly how they’ve seen it in the past, it’s very hard to connect the dots and realize what mathematical tool is useful in the new context.
Of course, if a teacher only has two periods to introduce the dot product, for instance, they’ll need to spend one class on how to calculate it, and one class on how to use it to solve more complex problems. It wouldn’t be a stretch to provide a ten-minute introduction to the meaning behind the concept in that first class, before getting into the nitty gritty. But another barrier is the time that now needs to be dedicated to “work periods”.
So many students, my sister included, have become so heavily involved in extracurricular activities that they have less time to spend on homework in the evenings, or are too burnt out to function when they finally get around to their math. These activities have become more prevalent and necessary than ever, with the need to bulk up university applications (and, perhaps, appease over-achieving and vicariously-living parents?). Because of this, many teachers start regularly holding “work periods” during class time. This also serves as one-on-one time with the teacher, but only for the couple of students that happen to get their attention. So what ends up happening is that the students have a solid half-hour or hour to work on their homework in class, but they don’t quite understand what it is they’re trying to accomplish as they work through a problem. Then they get to their tests and have to extend their understanding to new problem types (for Ontario students, this is usually in the form of the dreaded TIPS questions), and they have no clue where to begin.
I’ve also found a couple of instances in which the textbook or the lesson will introduce a “shortcut” of some kind, without really explaining where it came from. My theory on these is that the teachers and mathematicians that write curricula and textbooks were also the kinds of students that excelled in math, in general. So they would have breezed through high school math, and probably loved using shortcuts to get through their homework and tests more efficiently. The problem is that today, many students are now using these shortcuts without the proper foundation that comes from a full understand of a mathematical concept. Most of these students will simply memorize, regurgitate, and move on. As a “solver”, this drives me nuts
This is all a new realization for me. In high school, I had a fairly easy time grasping the concepts being taught, so I appreciated having time to get my homework done before heading off to band after school. I was also very self-motivated and self-regulated, so I rarely struggled with getting things done on time.
But now I’m seeing my sister and her colleagues look at math as a course to be loathed and feared, and it’s confusing for me. (Yes, third year math was awful, but that’s a different story.) I don’t have a solution here, but I wonder how many high school math teachers have wrestled with this issue, and what they’ve come up with. I’m sure there are many schools of thought on this, but I’m also curious as to whether the structures of standardized math curricula allow enough freedom for teachers to combat the issues.
Did you struggle with math in high school? How did you tackle the challenge?
When people find out I studied Physics at university, the first question I usually get is something along the lines of “…Why?!”
(The question is usually preceded by a statement like “Wow, I was terrible at physics in high school,” at which I just smile and commiserate.)
Up until about third year, I used to give a canned answer – something about transferable skills, problem solving, mysteries of the universe… Blah, blah, blah. For a while, I think I may have actually believed it. But now that I’m neither studying nor pursuing a career in Physics, it begs the question: honestly, why did I do it?
Reason #1: Physics was my best subject in high school.
With no clue what I wanted to do with my life at seventeen, I looked to my report card for guidance. And actually, my top mark was a tie. My choices were Physics or English. Which brings me to my next point…
Reason #2: It looks good.
I’d spent 13 years in school trying to get top marks and excel academically, and I wasn’t about to stop there! I felt that saying that I’d majored in Physics would look good to relatives, peers, and potential employers. This was especially in comparison to English, which was my other best option at the time. I’d grown up hearing that Arts degrees wouldn’t get me as far in life, so I wasn’t about to take the chance.
If I were to spin this reason in a more positive way, I’d say it was more about the transferable skills from taking on a difficult set of courses. But that wouldn’t be true. When I was choosing a major in Grade 12, it was all about whether I would look smart, not about if I would actually be smart.
Reason #3: Interest?
I’ve had a mild interest in Astronomy since I was a kid, fueled mostly by my dad’s interest in the subject. Contact was my favourite movie, and I even got my own telescope! (Well, okay, I got it for free. But that’s a topic for another time.) I figured if I immersed myself in the subject, I would become more passionate about it. Turns out that wasn’t quite the case, because most of my interest boiled down to Reason #2: it looked good for me, the self-professed Queen of the Nerds, to be into Astronomy. I still do have that mild interest, but not enough interest to keep me coming back day in and day out.
In examining the reasons I chose my major, it’s no surprise I didn’t end up going on to an MSc, PhD, and/or career. I’m not ruling those things out forever, mind you. And I don’t regret studying physics, because it did help me gain those skills, meet new people, and get a better idea of who I am. For now, though, I’m still on the hunt for my real passions.
How did you pick your major? Is it still the love of your academic life?