I’ve been trying to sort out how to incorporate the problem based learning model in my teaching (most recently advocated by Chris Lehman during a session for ECI 831). I find it much easier to do when teaching computer science than when teaching math (just so you know, I teach about 90% senior math, 10% computer science). I’ve been pondering why that is, and I think a lot of it comes down to the fact that I haven’t been indoctrinated as much in my teaching of CS.
Although I was trained in computer science during my university days (in C++, no less), the vast majority of what I do now has been a result of teaching myself. When trying to sort out what language to teach my students in an introduction course (CS 20), I did a bunch of research and ended up choosing Python. In the process, however, I tried out a number of languages, enough to become semi-fluent in about 5 or 6.Since I’m a geek, I randomly get the urge to create a program to automate something or solve a problem I’m having. This lets me keep my skill level up in a variety of languages, as they all have strengths and weaknesses. All this has contributed to me becoming rather proficient at learning whatever I need to know by researching it on my own. I want my students to be able to do this.
As I said, this easy for me to do in CS. I can give the students a few basic nuggets of info, then let them go to it. For example, we’re using PHP to learn how interactive websites work right now. I taught them some basics about how PHP works, just enough to get their feet wet, then gave them a few simple assignments. The students have access to the net (obviously), and can therefore research methods of solving whichever problem I’ve set for them (say, creating a web form and spitting out the submissions to a text file). I essentially float around, acting as a resource, and occasionally will grab all of their attention by showing them a quick tip or trick on the projector.
In math, I’m at a loss. This is crazy, as I was a mathematics major at university, and took way more math courses than CS. However, the curriculum is so much tighter in a math course (it’s a struggle to finish it all), and the pressure to conform to the accepted way of teaching is so great (by students, parents, nearly everyone…), I find problem based learning really hard to implement. Not only that, but the sequence of high school math courses is such that if I don’t get around to teaching them something, they are completely lost in their next class (which I may or may not be teaching them).
Because of this, I don’t really use PBL in my math classes right now. What I do, however, is make my students construct the math that they learn on their own. I’m there, and I ask questions, but it’s rare that I will give an answer without dishing it off to one of them. So, if you were to visit one of my classes, you’d see me at the front of the room a fair bit, but I’m really conscientious about only writing what the students tell me to write. I make them put the pieces together.
This takes engaged students, however. I get them to buy in by being ridiculously excitable about math. Seriously. I tell them about Ug the Caveman, who created all of our number systems (some of them actually go for this, believe it or not). I point and gesture like a madman. I play random YouTube videos just for the heck of it. We have fun. In return, when I ask them a question, I get answers. Lots of answers. If it’s right, great. If it’s wrong, great. We figure it out together.
The downside is that I don’t ever get to sit down during a class. The upside is that I’m pretty sure that by the end of our time together, my students are better at thinking than they were at the start. It just so happens that I use traditional math knowledge to make them better thinkers. I don’t believe that teaching them to think this way is any less valid than teaching them how computers and the web work, even if the material is esoteric and will be used by only a few of them. The thinking, I keep telling myself, they can all use.
Sounds like I needed to be in your math and/or CS classes. There is some great stuff on YouTube and TeacherTube for math and science.
I agree that it is more difficult to incorporate an inquiry learning model in senior math becasue of the curriculum constraints and the political as you mentioned. It would take a much more concerted effort to be able to implement this, at least here in Sask.
Check out this blog that I came across.
http://blog.mrmeyer.com
Comment by Dave Bircher — April 2, 2008 @ 7:17 am
Dan, I think your approach is amazing given the curriculum constraints. Here are a couple ideas from Tom Barrett: Google spreadsheets and Using Twitter. Tom teaches elementary in the UK, but might help get some ideas flowing!
Cindy
Comment by rdrunner — April 3, 2008 @ 10:46 pm
I think I would you like to be in your class too! Our new math curriculum and math resources “Math Makes Sense” incorporates a lot more inquiry and discussion. My students work in groups or partners to complete their math. There is more questioning and the word “why?” is heard quite a bit. I like the new program but it takes time to changed the way I’ve been used to teaching math.
Comment by Kimberly Brown — April 6, 2008 @ 4:57 pm
PBL is really an ideology when it’s all said and done.
PBL embraces teachers like Vigotsky, Sigmund Freud, Pioget, and John Dewy. On the other hand, PBL shuns teachers such as Isaac Newton, Pascal, Einstein, Descartes, Edison, Bell, and Heisenberg.
The first set of educators breaks-down “learners” into psychological components so that they can be “managed” as groups; the second set of educators build upon pre-existing knowledge that students have arming them not only with knowledge, but educating them on how and when to use it.
Instructors forced to implement PBL are less educators than they are psychoanalysts who ask “deeper more probing questions” as to the learners “feelings” and so, “manage” their classroom.
Mathematics, especially AP mathematics, is in contrast and by its nature — very rule based. We can play the PBL psychobabble game all we want to in the classroom, but the AP assessments and the books that go with them are hard, specific, and unforgiving of inexactness.
We may detest the fact that the algorithm 2 + 2 sums to 4, but no amount of “feelings” on the part of the “learners” will alter the reality. The algorithm works. “Learners” may loathe the notion that multiplying a negative number by a positive number results in a negative product, but the fixed algorithm works as it always has regardless of the “learners” feelings. Feelings don’t score high on AP exams; but immutable facts, algorithms, exact nuances to rules — as well as their exceptions — always prevail on AP exams. (Or do I exaggerate on this last point? I think not.)
PBL and Constructivism are in high style today but I’m not sure that I would want to traverse a suspension bridge designed by teams of engineers who “felt” that the laws of physics could be disregarded because they were steeped in a pedagogical ideology that dictated that “reality exists only in the mind.”
Perhaps it would be better not to travel on the bridge at all, but rather sit around in a fairy-circle, holding hands, singing kumbaya while watching the rescue workers pluck bodies from the water.
At least that way, all the engineers involved could get in touch with their feelings while their attorneys figured out how to use PBL to get their clients out of a class action suit.
Comment by J. P. — July 16, 2008 @ 2:02 pm