I take a bus to work, and as with most buses it contains a cast of regulars and assorted cameos. One of the regulars on this bus is a math professor, which I know because (a) she grades papers that I nosily read over her shoulder, and (b) she has a math symbol tattooed on her foot.
The papers that she grades are not usually math papers, per se. Instead, they are "Reflections" from the members of her class about their experience in the last week's lessons. Such as:
"I really enjoyed this week hearing about the Fibonacci series. For a long time I didn't understand how it related to what we were doing in class, but then Maria explained it and all of a sudden it clicked into place for me. It was really neat. Although I didn't participate in class much this week because of some other problems in my life right now, I still felt as though I learned a lot."
This sort of thing continues for a page, usually a page with wide margins and 11-pt Courier. The professor then writes something at the bottom, such as, "Sorry to hear about your life problems but I'm glad the math made sense to you! Checkmark" and moves onto the next Reflection.
I hardly need to say that this is a rather different type of math homework than any I ever had.
The calc geek inside me says, "This is the problem with education in America today. We're too wrapped up in how the student is reacting to the classroom rather than in whether or not they've learned the damn concepts."
The inner bleeding heart says, "This is clearly a math class for students who don't have a good background in math [a lot of the Reflections have mentioned learning about simple probability, like drawing a red card, or an ace, from a deck], and these students have maybe always been afraid of math because of their weakness in it. This provides an opportunity for the prof to find out what works and what doesn't in her teaching style, as well as to find out which students need more help."
Calc geek: "But wouldn't both the student and prof time spent on these Reflections be better spent, I don't know, doing math problems? Reinforcing concepts?"
Bleeding heart: "It doesn't do students any good to reinforce concepts if they're all at sea anyhow. This is where the professor gets to find out whether her teaching is getting through."
CG: "You know, this is what I really hate about you. All nicey nicey, no results."
BH: "I'm sympathetic to your feelings. Should we talk more about this?"
Ok, ok. Point being: I can see reasons to do this sort of thing, but really--wouldn't it be better to make the homework Math rather than Mathy Feelings?
Then again, I've never done any teaching, so maybe this is the new way to run lessons and I'm just ignorant.
Though not about the probability of drawing a red ace (1/26).
6 comments:
Somehow, students acquire a tremendous fear of math. This is probably because some math experience gone horribly wrong in grade school. So, we should get rid of the fear. Then, those students need to do some math problems! :-)
This is weird. I don't think I can really comment on the validity of this approach because I have never required motivation to learn math. Perhaps these people need significant encouragement, or else they won't be able to do it at all. I do have to wonder what the professor thinks of her own approach. Does she feel totally lame assigning such stuff?
Reflections are all the rage in my department. When done well, they are intended to force the students to actually think about the material, rather than just perform some rote operations. (Of course a side-benefit and sometimes the goal is, like you say, checking in with the students to see what they understand and don't understand.)
In heavily equation-based disciplines I think it is sometimes easy to help the students learn to use the equation well, and yet totally miss helping them understand what they are actually doing.
In my own undergraduate career, I was really good at using equations and getting the right number to come out of them, but half the time I had no clue what any of it really meant.
I dunno, I like the idea of doing weekly updates on what's working/not working about the style. It certainly is impressive for the teacher to take that much time and mental energy to pay attention to everybody's needs like that.
I am really bad at math, it is mostly opaque to me process-wise and I have to pay a LOT of attention to following through math procedures. It's almost number/spatial reasoning dyslexia sometimes for me.
My strategy in college (having to go all the way up through Calc II and P. Chem. with some crazy derivations for a chemistry degree) was to initiate my own "reflection" type sessions with my professors where I went to their offices and got their extra help with this stuff. That's because I'm a go-getter, though, so pulling along some of the non-go-getters by gentle force is probably helpful to them (even if approaching more heroic of a feat than is probably good for the professor). But what about natural selection processes...
While I agree that doing practice problems for math is the best way to figure out how to manipulate and combine equations to solve your problem, I will say that problem sets often don't do much for helping students understand why they should actually care about math and how it's useful. Maybe if I had had to write these reflections someone would've tried to explain math in a way that made sense to me. I always assumed I was bad at math through high school and even college calc, because I never felt like I "got" it. I could take an equation, plug the #s in and get an answer, or take a derivative, but I never really felt like I knew what I was doing or why, especially when it came to calculus. Then I got to grad school and had to derive Darcy's Law in 3 dimensions (oh no! differential equations!), and realized "huh, there actually is a practical application for calculus..." I vote for teaching more math in an applied, rather than theoretical context.
IMO, fear and disempowered beliefs about ourselves will stop us dead in our tracks. I have increased my learning capacity, concentration and productivity 10-fold just by taking on a new, more empowered belief about myself -- but no one in academia is going to teach you how to do that. So if this exercise is helping her students move beyond where they would otherwise stop, more power to her.
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