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?