This week, I've tried a few things with my two math classes (honors juniors and standard seniors). One, a scaffolded proof of the Sine and Cosine rules, went horribly for some very mysterious reasons. The other, a Binder check procedure I've copied from another blogger, is going very well.
What didn't work: First, on Monday, the seniors were learning about the Sine and Cosine rules. I hate how their textbook presents these, like they are some inscriptions on stone-tablets, and even thinking about proving or questioning them is heresy. My students typically have the confused and bewildered "wtf" expression when they see such things, and last year I had a successful class with students in groups proving these rules with some little scaffolding from me along the way. Scaffolding such as "maybe pythagoras' rule would help?" was enough, but the students took a full 90 minute class to complete the proofs, and this year I wanted to save time by providing more (much more) scaffolding.
So I made these worksheets. I'm trying to figure out how to include them in a post such as this, so bear with me while I experiment with different options.
Here is the file with the two worksheets, in pdf format.
I was particularly happy with having the students first try a specific case with rulers and all. Especially when it turned out that trying a specific case wasn't all that easy for them. I think by actually measuring and trying it out, they gained a good understanding of what the rules actually say. I will keep doing this type of "physically trying the rule" for other trig or geometrical rules.
The rest of the worksheets however, went not as good, to put it very mildly.
Above all, the students (even the stronger students) immediately complained they didn't understand what to do. I explained, and they moved one step along. Even though they were sitting in groups and usually have no difficulty discussing with each other, this time they didn't discuss, they kept just calling me over and asking questions, and I had the impression they just wanted to be spoon-fed stuff. The breaking point was when one student wrote the Sine rule and when I asked how he arrived at it, he just said that it was obviously what I wanted them to arrive at so he figured why not just write it already?
Oh well. That's when I gave up. The activity was taking too long time anyway and so I interrupted their "work" and, after I cursed at them for being so passive and not thinking for themselves (I'm not proud of this, but my relationship to these kids is good enough that it can withstand occasional lapses in judgement on my part), I quickly went over the proofs by myself on the whiteboard. The remaining ten minutes of class students worked on exercises, very quietly, and I demonstratively sat and played on my iPhone.
If you're wondering, the following class (starting sequences and series) went great, and so I feel no lasting damage was done.
Now, this experience has me a bit disappointed and confused. I often work with this type of scaffolded investigative material, though rarely with proofs with this class, and most often it works very well - students enjoy the process and feel ownership over the formulas they are then asked to apply in various problems. Why didn't this work? Was it too difficult, as my colleague J claims? Was it poorly formulated? Was it just a bad day for my students (and me, obviously)? Maybe it's just the students' expectations and interests? They are not taking math because math is fun, rather because they have to and this is the lowest level IB lets them get away with.
I'm going to try this same activity with my honors juniors in a month or two, and will write more about it then.
What did work, or is starting to, is the Binder check procedure Sam wrote about a while back. I use it with my honors juniors, and yesterday was the second check (I plan on checking every two weeks or so). Results dramatically increased from the first check, as Sam said happened in his class as well, and I feel that this way of checking homework is giving me some great information about the students' work between classes.
An important difference is that I do NOT grade homework. Because my students will be assessed ONLY on the final exam (in May 2012) and two investigative portfolios, neither the homeworks nor the test they'll have on Monday actually counts for their final grades. I'm happy to say that the students know this, and that still they take both the binder checks and the tests very seriously indeed.