I went to UBC for my undergrad, an experience that changed my life for many reasons.
The biggest shift was the immense beauty of ocean meeting mountains. Never had I experienced this before, and to be thrown in and living in this beauty was something I never really became totally comfortable with. It was almost always to good for me.
I grew up in Southwestern Ontario, where the Canadian Shield grounded me in safety and security in terms of natural disaster worries. Suddenly I had to learn and be prepared for tsunamis and earthquakes. It was strange and different for me, and although I loved and appreciated the beauty of B.C., I was always constantly thinking about the next possible earthquake. Would I be in B.C. when the “big one” hit? What would my reaction be? Was there really any ‘safe’ place?
Perhaps silly, I had to mentally find a balance between appreciating where I, at the time, lived, and not constantly worrying – that small nagging voice in the back of my mind – of an earthquake of epic proportions.
The Fault Line in Teaching
At this point in my teaching career, I am having this giant existential-like questioning about why and how I am teaching. In my mind, I am constantly not ‘doing it right’. There is always something better I could present to my students, always a question I could have asked, and always a connection that was not made.
It’s like I am back living in B.C.: I love teaching. I enjoy the beauty and energy of teaching. But I am standing on a fault line where that huge earthquake could come at any moment. I am never truly comfortable.
Tectonic Math Plate Movement
In Mathematics, I feel that this is especially true for me. As I learn more about Mathematics, as I do my best to bare my misunderstandings and misconceptions, as my personal philosophy of Math is developing (math is play!), I know that my ideals in education are shifting. There is movement below the surface, and I just don’t know where to take this movement, and how to channel it.
What I mean is this: I am a bigger picture teacher. I teach in order for students to find meaning for themselves; to develop a sense of self in this overbearing world. I want my students to be ok with not having the right answer; to not have to be perfect. I want math for them to be interwoven in their lives, to be problem solving — to be an action they take with pride and honesty.
The shift is happening as I stand on the fault line of giving my students the bigger picture experience, and keeping my instruction focused and channeled.
Can really doing the math create successful EQAO results?
I asked the question.
Here is where I am at, and what I mean by that question: My students will be writing EQAO this year. I am not about to discuss EQAO in itself, I am going to discuss how the act of performing EQAO is generally approached.
Here is an example.
Teachers engage students in using EQAO released questions (or EQAO like questions – focusing on application and thinking) to guide their instruction in a variety of ways, for a variety of reasons. For example, to see if their students are able to understand the problem, if they can apply a workable strategy to solving the problem (was the student able to identify that this problem required more than one mathematical ‘step’ in order to be successful? If not, what is our next step as educators?). Are students able to reason and work their way through multiple choice, and have strategies if they are not sure of their choices?
Yet, my question is always this: Will I be able to let students go deeply into all the math content so that they are ready for EQAO?
This is where I stand. On this fault line of giving my students a rich, immersive math experience (and, I am still working and learning this!), and wanting them to feel like they can apply their learning in a testing setting.
I tried something different this year. Rather than make EQAO something students would “have to do, so we had better be prepared”, I had them examine the math in an EQAO released question. I had them determine which tasks and problems in the past we had worked on and make connections.
This was me trying to bridge the fault line.
An example of this would be proportionality, and unit rate. I started by asking students what was the best deal in a morning activity through grocery store photos I had taken (nothing new here), and to my surprise, students self taught unit rate — through no instruction. Obviously students used other strategies (adding/multiplying the number of items until they came to the total cost, or estimating a reasonable cost of what one would be, then multiplying until they came to a close total), was one strategy, but many figured out the price of one by dividing number of items/weight and cost.
I gave them time to talk and share strategies, and discover if this was always true. We played with the idea of proportion and rate, and compared it to ratio. We made connections between ratio and rate — and how results can be effected by ratio.
But the nagging fault line struck me again: Would students connect this new, and, believe me, we could still go a lot deeper into proportionality, learning to an EQAO question?
For a Board/Ministry Initiative I am involved in (Renewed Math Strategy), we were asked to give students a unit rate (well, a problem that can be solved through unit rate) problem, and at first my students had no idea how to go about solving it.
Even though they were disappointed at first, they begged me to go over the problem. They wanted me to walk them through how it could be solved. They wanted to know. This struck me — if anything, I had created a classroom where, sure, they didn’t know what to do, but they had a desire to know. They didn’t get wallowed in defeat. They understood the yet — they weren’t sure how to go about solving it…yet.
Weeks later, after some exploration into unit rate, I decided I would have them own this problem. I would let them figure it out – and on their own. They would try the problem again, and they would self evaluate. I gave them the codes; I had them lead the conversation, I had them determine and compare their previous work to their current understanding. I had them discuss and identify what math they would need to use and apply in order to be successful.
I admit I did this rather randomly. My purpose was for them to own the math. I wanted to walk on that fault line. I wanted to prove to myself that them as a team experiencing and feeling and playing with proportionality would transfer to a place where they would have to explain and justify in a testing manner.
Students are conferencing and working together to figure out the math they needed to use and apply. They themselves shared strategies.
Amazingly, the dialogue was rich. My students were saying things like, “Oh! I see how when we found the best deal with the store prices, we had found the unit rate – we can do this here!”
“Oh, I see how you and I came up with different strategies, and I see where I went wrong – I forgot the last step of subtracting. I see now how that makes the total cost make more sense.”
Before and after my students investigated and played with the bigger ideas of unit rate.
My students proved something to me — that really immersing in the content of mathematics, even though it is slow, and I feel a major pressure to go fast and cover more, is important.
My fault line fear — the earthquake of pressure to make sure I cover it all, and well enough that they can do well on EQAO, is still nagging me, but I can breathe a little more knowing that I am at least giving my students positive math experiences.