I have a bit of teacher-musing, and then I want to share a funny story that happened in calculus class yesterday.
Everyone is always saying “make math relevant for your students!” Well, great. Sure. Okay. Will do. I think that’s a bunch of hooey. It’s not about making math relevant, but making math into problem solving skills . I don’t care if students will ever have to use what they learn in my class in the “real world” (what world are they living in now?). But I do care that they can see a problem and break it apart into its component pieces. That they can go down dead ends without getting frustrated. That they can see that there are often multiple ways to solve a problem. Sure, sometimes one solution is more elegant than another, but that can be okay… because sometimes problems don’t have elegant solutions at all!
All this being said, I’m terrible at doing this. At least, I’m terrible at doing this in my non-accelerated classes (which are my Algebra II and Calculus classes). I stick close to the basic skills and concepts, we don’t do too much investigation; I’m focused on making sure they can do basic skills. That they can verbally explain the concepts. Which is unfortunate, because after students learn basic skills, they should be given the opportunity to draw connections, hit dead ends, and all that good stuff I just listed above.
As a teacher, it’s so easy to make excuses (we have a fast-paced curriculum, the class period is only 50 minutes, my students are working on so many different ability levels, there isn’t enough time in the day to design these classes) of why not to do it. I also think that investigative work doesn’t go well in the non-accelerated classes.
But that’s probably a function of me not knowing how to do it right — how to design and implement these sorts of lessons without spending too much time at home or in class working on them.
So back to what I was saying… the mantra “make math relevant” actually took a funny turn after my calculus class yesterday. To set this up, I have to remind you that I teach at an independent school. Tuition is high and students tend to come from wealthier backgrounds. It’s a different world [see my post about that here]. Anyway, after school, one of my calculus students said “Mr. Shah, I have a math question for you. It’s not related to what we’ve been learning in class.”
Turns out, he found out that he and one of the other seniors both resort at the exact same place in the summer. And after thinking about what a strange coincidence it was, he wanted to know “what are the chances that two seniors at this school both resort at the same place?”
So that’s math in context for my students, apparently.
(These are the sorts of moments that I realize that this world is so different than the world I grew up in. But I really like these kids.)
If you care, my answer was that we can definitely figure it out together. I then told him about the birthday problem (how many people do you need in a room before the chances that two of them have the same birthday reaches 50%?), and how we could use that as an analogy to solving our problem.
In the birthday problem, you have people in a room, and each of these people have a birthday from the calendar year (each person could have one of 365 birthdays). In our problem, we have 80 seniors, of whom “only “ resort. Each person who resorts goes to one of a certain number of places (we’d have to do a back of the envelope calculation/Fermi problem to find an approximate number of resorts that people from my school could go to).
Then the analysis would be the same as the analysis for the birthday puzzle.
If you’re curious, you need about 23 people in a room to have a 50% chance that two people in the room have the same birthday. Of course, you’re going to need 366 people in a room to guarantee that two people in the room have the same birthday. (Do you see why?)
 That’s not to say that I don’t think the the content is unimportant. The content is always my primary focus. And I guess when I say “relevant,” I mean specifically “real world applications.”
Thanks for your musing. I’m glad to hear I’m not the only one struggling to take my students that next step.
Great post. Your “Musing” is exactly my own thoughts lately, and exactly the thoughts I’ve expressed in conversation during the last month. Like Simon, I’m glad to hear I’m not the only one.
In my precalculus class I took an article on e (http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/) and made it into an investigation of sorts, rather than just asking them to read the article. (1) It took me forever to make it. (2) I’m not even sure how well it’s going to work.
I’m going to give you an “Amen” on your musing, too. The next thing I always wonder is – what can we do with inservice professional development to make more of us better at what we know we should be doing? Not that I have any answers, but I think there must be a way.
I kind of love when kids ask me about something math-y that doesn’t have to do with classwork. I wish we had the luxury of teaching by just exploring what they are curious about. I know I’m supposed to have ways to ignite their curiosity about specific things, but there’s a big difference when it’s their idea.
You say “you’re going to need 366 people in a room to guarantee that two people in the room have the same birthday.”
To which I respond “February 29th.”