This has clearly been an insanely hectic month as neither Jessica nor I have blogged. So today I have made it my priority.
I attended a session at OAME2013 Free-Falling – Letting Go Of Textbooks, Worksheets And Units by Bruce McLaurin (@BDMcLaurin) which left me with much to think about. I intended to blog about it immediately after returning from the conference but I am now glad that I didn’t get a chance to because I think I’ve benefitted from thinking about it a bit more.
Early in the session Bruce asked us if we had ever asked a question in class that we didn’t know the answer to. He gave us time to share with those around us and then we discussed as a group. It took me a bit to think of an example of when I did this. I think I thought I did it more than I actually do. Interestingly, those in the room that have taught computer programming said they do it often in that class but not in math class.
The example I shared is one that I did quite a few years ago, when I had my own class still. With all the learning I have done since then I would do it quite differently now, but I will share my “beginner version” with you because I think its important to be honest with where I started.
The problem came from a visit to the grocery store back in 2007 when I saw a sign that looked something like this:
It was in the early days of moving people to using re-usable grocery bags instead of plastic bags. I read the sign and then went on my way but on my way home I started thinking…
“Is eliminating 1 billion plastic bags really that impressive? Plastic bags can be squished up pretty small. Would eliminating 1 billion of them from a landfill make that much of a difference? Is this company just using the number billion to make it sound good? How much space would 1 billion bags actually take up?”
So that September I shared that poster with my students and I told them about all of the thoughts going through my head. (I’m already cringing at typing this because it is so obvious to me know how much better I could have done this… but I said I would be honest about where I started).
I asked my students how much space did they think 1 billion bags would take up. They were having a hard time explaining their ideas so I gave them something to relate it to – a classroom. I simply said, “Do you think it would take up a whole classroom, part of a classroom, many classrooms?”. I had them all make a prediction and I made one myself as well. I told them I really had not tried the problem yet – we were going to explore this together.
I think provided students with the collection of plastic bags that I had accumulated over the years (which I still have, in case I do this problem again). I also gave them some plastic storage containers of various sizes and rulers and tape measures. Students then worked in groups to determine how much space 1 billion plastic bags would take up.
They persisted quite well, although working with large numbers gets challenging at times. I found I often had to suggest to groups that they label their calculations along the way because they were losing track of what all the numbers on their pages represented.
We were all quite surprised with the result (I won’t spoil it for you) and it was nice to be genuinely surprised with them.
I have since run into other plastic bag videos, promotional info, etc. that could fuel a similar exploration in classes such as this one:
As I was thinking about this blog post I was having a bit of an internal struggle. I like the idea of asking questions that I don’t know the answer to because I think it helps students see me acting like a more true mathematician who is working with them. However I know that I always encourage teachers to work through a problem themselves before giving it to students so that they can think about: the mathematics that will come out of it, what questions might arise, how they will facilitate the conversation, what strategies they might expect to see, etc. Although I didn’t know the answer to the problem, because I hadn’t worked through all the calculations myself ahead of time, I did spend time thinking about all of those questions above as well as where it fit into the curriculum I was responsible for.