Last night for a wide range of reasons, not the least of which is the layer of construction dust that can seep through plastic sheeting and is covering everything in my house, I had a bout of insomnia, and sometime around 2 am, I resigned myself to the inevitable being exhausted at work is never fun, but being exhausted while teaching five classes of high schools students on a gorgeous warm Friday can be brutally painful.
And yet it wasn’t.
In fact, some parts of the day were downright enjoyable. What madness be this?
Although we are deep in procedural land in Algebra 2 (polynomial operations), the vast majority of the work on the boards around the room, as well as the explanation of that work, was done by students. In fact, they spent most of the class time checking with each other, correcting each other, and discussing what order of operations was correct in a given problem. My ‘hinge question‘ from yesterday’s lesson became today’s warm-up [my timing isn’t quite there yet…], but it led to a lot of fruitful discussion, and uncovered some widespread misconceptions. The content right now is procedural to the nth degree [ouch! ; ) ] and I want to find some activities to spice things up, even though the loss of class time in September will most definitely create a painful shortfall later in the term. My departmental curriculum, to which I am fairly strictly bound, unfortunately follows a procedural rather than conceptual route through Algebra 2; adding depth and meaning to the prescribed pacing is always a challenge for me. That said, I’m pleased with the classroom culture that has been created thus far by the random groupings and cooperative/supportive table work.
I reworked the Race Around the World activity last weekend; I was not satisfied with my presentation to the students, and hoped that clarifying the process would re-ignite some interest and activity in what I thought was a fun and engaging problem – how fast can you travel around the world given time and air flight restrictions? I worked through the problem on my own, and redesigned the graphic organizer to better support the work the students would need to do in order to complete their trip. I demonstrated how I would proceed in planning and calculating the time required for my trip. It seemed as if a few more students understood the idea behind the activity, but many remained unmotivated to attempt the task. I think that in missing the right hook from the outset, not even my revision could reignite the spark. Very few students finished the task, and we were approaching the fourth day of class. I decided it was better to move to the more substantive work of the course rather than continue to push this activity. I’m not happy, but there were lessons learned for me, and for those students who chose to engage. Next time around…
But here’s the great part.
The day following this minor debacle, we began the major work of the class, exploring different problem-solving strategies. I distributed notebooks (love those mid-July Staples sales!), and we jumped right into solving our first problem: Virtual Basketball League. Using the Crossing the River book as a guide, I asked the students to attempt to solve the problem with a diagram. Clearly, many of them are not familiar with Borg philosophy, and thus thought that resistance was a great idea.
“Why do I have to draw a picture?”
“I don’t like pictures.”
“I just want to do math.”
“Can’t I do it my own way?”
And then some of them started to draw diagrams. And others looked over at their diagrams and began to draw their own. And students who hardly ever participated (I had many of these students last year in Geometry) agreed to put their pictures on the board. And THEN they began to argue. I refused to tell them what the correct solution was; I kept redirecting them to convince each other. I thanked all of them for sharingtheir work, and reiterated several times that mistakes were GREAT, and that anyone who made a mistake publicly provided all of us with the opportunity to learn, and should thus be thanked. This strategy seemed to appeal to the kids, because I got very little resistance (go Borg!) when I asked individuals to share their sketches. In fact, I find that students who traditionally don’t do that well in math are more willing to share their work without knowing whether it is correct than my ‘gifted’ track students.
We spent the entire period – in both sections of the class – talking about the Virtual Basketball League problem. To be honest, I was surprised (very happily) by the success of the lesson after egg laid by Race Around the World. When class began today, and I gave out the second problem in the series, only one or two students refused to draw diagrams (and I was able to coax one of those to sketch a visual of their solution after he arrived at an answer ‘mathematically’). Once again, different solutions to the problem were shared, and discussion ensued. I noticed that leaving the class completely to their own debate did run the risk of allowing a misconception to reign, and I asked some very pointed questions to draw their attention to the error. I’m hoping that as we move through the problem sets the class will uncover these mistakes on their own; I am concerned about ‘over-directing’. I want to empower these students to find their own solutions, and find them within each other.
We finished the class today with the problem Pool Deck, which goes like this:
POOL DECK Curly used a shovel to dig his own swimming pool. He figured he needed a pool because digging it hard work and he could use it to cool off after working on it all day. He also planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the deck?
Surprisingly (to me, anyway), many students were mystified. Stumped. They struggled to make sense of the problem (I did not give them the photo). They drew oval pools inside rectangles. They found surface area; one student found volume. Many who added on the deck did not subtract the area of the pool. What threw them? Was it that they needed to read about Curly (like from Oklahoma?) and his desire to go swimming before getting any pertinent information about the pool? I thought a rectangular problem would be a piece of cake. More to think about.
So the week ended really well despite my exhaustion. And I can’t wait to see what these problem solvers are going to do next week.