I have been quiet on the web for the last couple of days. I had an interview for and was hired into a grade 6/7 long-term occasional (LTO) position, and it has been a whirlwind of prepping and trying to teach a very challenging group of junior/intermediate students. Today was day 2.
I planned a math lesson the way I wanted to do it, knowing that with my group it could flop miserably, but to my delight, it went off quite well! First we did our first WODB (Which One Doesn’t Belong) for the non-math-teaching-geeks out there. They had to sign their name to the one they thought didn’t belong and write in their reason. They were reluctant at first, but loosened up when they realized that they were allowed to use the same reason as some of their classmates. Knowing that they might be tempted to cluster in their answers, I provided an incentive for original thinking: as a class, they had to try to find my secret teacher choice. If they did, they would get a small prize. Here is the board for the day:
Students came up with all kinds of great reasons, some of which I hadn’t even considered! A few of their reasons were not well explained, so we discussed what they meant, and I clarified and made visible their thinking in green (my teacher colour). Despite their best efforts, they did not come up with my secret teaching reason. I chose 2×2 because it is a perfect square. I picked this one, because it tied into exponents (which the grade 7s had learned in the fall), and it opened up the idea of an array, which should open up their view of multiplication. After saying that it made a perfect square, another student said that it didn’t have to be a square and separated the two groups of two. I should have paid him. It got the class talking about another way in which we could talk about multiplication. Overall, we had a great discussion. The image to the right shows some additional insights and reflections on student thinking.
I followed this up by splitting them into visually random groups and having each group take one of the multiplications and representing it as many ways as possible on a sheet of chart paper. They struggled with what this meant at first, and I had to call them back in to model it a little in the middle, but they seemed to wind up with a broader conception of multiplication by the end.
For grade 6/7 students, the multiplication was a little simple, but I noticed during my transition day of observation that students did not seem to have a lot of flexible thinking when it comes to the idea of multiplication so I wanted to back them up a little and try to open up their minds a bit. I think it worked, even if it did take a while. They now have a base from which to add in an extra digit.
Today was a good day. I guess all days have some good in them, but today had more exceptionally awesome moments than most. I had a grade 7/8 class in an alternate program here in Ottawa, which afforded me the privilege of a co-teacher and an EA, both of whom were AMAZING! Because we got a fair amount of snow today, many of our students were late, which gave my co-conspirator and I a little extra time to go over the day and do some planning. Originally, the plan was to go outside after lunch and then come in for history. But then the magic started to happen. Somehow, we got talking about how great it was outside with the snow. The first couple students had arrived and we were talking about making snowmen, but then the conversation shifted to forts and how we could use the idea of forts to move the history lesson outside. After that, things started to snowball.
My co-teacher said that we could put the students into groups of First Nations, British, and French, and then we could go out and build forts and simulate the fur trade which was a topic the grade 7s were studying. Then we had to figure out how to simulate the trade and what we could use to stand in. (Rubber chickens were beaver furs, colourful soft golf balls represented knowledge of the land, and pattern blocks were used by Europeans to represent fire arms, ammunition, blankets, and spices from Asia.) The First Nations got to go and set up their fort first because they were already on the land when Europeans arrived. At the last minute, we added a couple extra rules. First, you could speak English within your group/fort/nation, but not to the others to simulate the language barrier. Second, you needed all of the items to survive, but especially knowledge of the land. Finally, only one person at a time could go and trade because at the time, the leaders would tend to speak on behalf of everyone. We both contributed ideas to these rules, and each time a question was raised, we conferred and went with the consensus.
This is where it got really interesting. Part way through the game, the frustrated British asked if they could use their ammunition and fire arms to attack the First Nations and steal their furs. After a brief consultation, we decided to let it play out because in history, it did sometimes go down like that. But they could still only send one. The First Nations were startled at first, but quickly fought back, “killing” the initial emissary. We had not planned on this approach, so how a person “died” was pretty much made up on the spot. The British then tried to steal all the golf balls (knowledge) to try to get all the points and win. I had to tell them that you couldn’t get knowledge from someone who wasn’t alive, and took them back. In the end, all of the British group perished and were killed, the First Nations population was greatly reduced, and the French, seeing the war, sat back and let them kill each other, taking the loot in the end. While I would never condone killing each other at school, that element of the game led to some great discussion in the follow up session.
The debrief is where this lesson gained all it’s power. We sat around United Nations style in our groups and discussed what happened. First we talked about how the game was similar to actual history. It was interesting that resorting to violence was brought up first, and how that introduction changed dynamics and strategies among the parties. The British acknowledged that greed played a major role in that decision, and that greed was probably also a major factor in history as well. We discussed supply and demand and the fact that not everyone was willing to trade. We talked about the rivalry between the British and the French. We talked about the language barrier, how it was difficult, and the many strategies to overcome it, but that led to a conversation about how they knew that each group wanted to trade in a way that the initial peoples would not have. Historically, they wouldn’t approach a situation knowing each other’s intentions.
This led to differences. First, the British lost. They were wiped out. Our world might look radically different if that were the case. We will never know. Also, the First Nations were all lumped as one group rather than their smaller groups. We thought that next time, the British and French should be slightly smaller and there should be more smaller groups of First Nations. There were other differences that I am currently struggling to remember.
Finally, I asked a number of what if questions…. First, what if the smaller teams and more First Nations? What if, when the First Nations acquired a gun, they suddenly got more beavers to trade with? How could we keep the realistic element of being able to attack someone while acknowledging that killing one wouldn’t eliminate an entire group? Students had some very valuable and thoughtful answers to each of my questions, probing deeper and thinking things through, questioning each other where appropriate.
After school, I thought that using a fire arm on another group should come with an element of risk as fire arms were not as reliable back then. (Add in a dice?) As I sit here, I think about how we might add in the element of European disease. What if I didn’t tell the First Nations groups that they were supposed to trade…. what if I had them build their forts and hunker down with their stuff and let the Europeans be a surprise? What happens when you struggle? How do you form an alliance with someone if you don’t speak the same language? How can we make knowledge of the land a more useful and real element to the game? Do it in the gym where there are a number of different types of markers and they need to know which areas are safe and which are treacherous?
One of the students suggested that they all make alliances and that the land be governed by a council consisting of leaders of all the nations. The group as a whole decided that probably it wouldn’t work because eventually somebody would get greedy, but I can’t help but admire the ideal in this. How can we work together for the prosperity of all rather than the few? How can we protect against a small group getting greedy and not playing by the rules?
Why was this lesson so great? First, there were many contributors: three adults and several students all input ideas into the final outcome of the game. Second, we all had an open mind and allowed things to evolve naturally. This gave a nice sense of flow to the activity and the learning. Students asked great questions and were able to share remarkable insights. There were a lot of small group probing discussions throughout as I checked on the groups. The hot chocolate while debriefing didn’t hurt either! It was an honour and privilege to be a part of it!
My parting thoughts for today are these…
- How can we work together for the prosperity of all rather than the few? What paradigms need to shift in society for this to happen?
- How can we improve upon this simulation, either to make it more real or to increase the learning opportunities?
- I have this hypothesis that part of the success of today was that students were up, outside, and moving! How can we add more opportunities to get up, out, and move on a daily basis?
- Finally, many students had input into the way today’s activity was shaped. How can we include student ideas in this natural way more often? We had a fantastic student:adult ratio today… could this work in a class of 25 or 30 kids in the same way?
I would love to hear your suggestions!