To say twitter and the blogosphere have helped me grow as an educator is an understatement.
Second, there are numerous ‘first labs’ to choose from in order to start off the modeling curriculum. The goals are to ultimately establish a precedent for future labs, have students realize the value of a graphical representation, to come to their first consensous as a group, to realize that the slope of a graph represents something, and that they can form a mathematical representation out of our data. This is no easy feat.
My first year of modeling I started off with the circle lab. It worked ok for circumference vs. diameter, but the complexity of linearization for area vs. radius lowered the morale of the class during the first week. I have decided to hold off on the linearization until after the first model creation. My second year was worse with the knot lab. The situation required students to get data, get an equation, and do then use that result in another graph just to get the answer to the main question. Way too many steps, perhaps it would be a better first lab for an AP class.
Out of the choice’s I had for the first (and most important) modeling lab of the year, a new one presented itself through twitter and the modeling listserv. The bouncy ball lab.
Did the bouncy ball lab offer me what was lacking from my past two years of first labs? Was it something the students wanted to learn? Was it fun? Would they get it right off the bat, with little frustration? Well looking at my past choices it seemed to meet all of the criteria.
It is working amazingly. It is simple. The students get it. I have found that it is easier to push them to discuss openly due to this fact. The situation is non threatening. They haven’t seen it before, unlike the equations for area and circumference.
STARTING THE FIRST DISCUSSION
I went home yesterday. While thinking about what occurred in my classes, I was a little disappointed at the frequency of questions I was asking. I don’t want my students to be looking toward me as the go to oracle of the class. I needed a way to force them into conversation. These first discussions are so crucial to setting up the rest of the year. I needed help. It is hard because you really want to scaffold the questions until you get the students to conclusions you want them to have. I need to stop that. What did I do? I watched John Burk’s videos of his classroom board meetings.
Yesterday, the students left off at the point where they all decided to make graphs of their data and find the slope. I decided to use what I learned from the videos. Today I walked in and said ‘I am not going to say anything for 10 minutes. I want you to answer this question: What information can you get from the graph?’ It started with silence, then a few students rattling off one word answers (slope, data, relationships). Then silence. I discretely said ‘No one word answers’.
At this point the students started evaluating the relationships, they came up with what was different between the boards, this led to a series of statements about the slope, then the word bounciness came into play…….HOLY COW!!!! At this point I am gleaming, and students think I’m weird again. I’m only 7 minutes in…I couldn’t hold it any longer. I said ‘can we reach a conclusion about the slope?’ One group started to right it out, then another student said ‘wait I think thats backwords, shouldn’t the slope go down if the bounciness increased?’ Another holy cow, the students corrected each other, meanwhile I’m jumping out of my seat.
They wrote down a couple of conclusions, about the meaning of the slope and the relationships. They had to get to one last part, they needed to equation. I asked ‘back to our original question, what information can you get based off the graph’ by adding the word based, a couple of students later one said you can always get the equation.
Not sure where I read this, I think it was Frank, but in the center of my room I hung a hula-hoop smack dab in the middle of our board meeting circle. Students were wondering what that was about the whole period, perhaps it was a minor catalyst to motivate them for a conclusion? After one group made illustrated their equation on their whiteboard, a student of that group was trying to clarify it for another. She basically used the hula-hoop in the middle of the room! She said ‘if you know the height of the hula-hoop, then you can put use the equation to solve for the height you need to drop it from’ My job was done.
Less is More
That basically sums it up, I can count on one hand the amount of prompts I gave the students. As a result, I can see they had more ownership over what they have accomplished than I have ever seen. It was amazing!
Thank you everyone.