As we explore the value of collaboration and inquire into effective learning, the most valuable discovery that I have made this year is that children have a lot to share; the more I listen, the more I learn and - beautifully - the more they learn.
I started the year with the expectation that I would help them discover what it was that I wanted them to know; I expected that I would never lose sight of where we were going and my goal was to track their progress and ensure that their path was tracking in the right direction. I wrote a blog earlier in the year on how the process of inquiry was like climbing a mountain where the destination was the peak, identified by the 'teacher' but the path was freely chosen by the 'learner'. The first time the kids went up a mountain, the paths were varied and hesitant. By mid-January they were almost exclusively ploughing ahead without much need for re-direction. Most recently, I have been discovering that the peak is not where I thought it was, it reaches higher, to a destination originally obscured by the clouds of my own prior knowledge and prejudice. Nine-year-old students have been taking their learning beyond the ends I envisioned and they have been finding faster routes to the peak. It is to the point where when we ask a question, their thinking takes them places I never expected it could go.
A week ago we started a conversation about characteristics and terminology for 3D shapes drawing on their previous knowledge. We had managed to define a point as a location where 3 edges meet which led to a conversation about cones and how to explain the point on a cone as there are no clear edges. Based on previous conversations in class related to the concept of infinity, one of the students defined a cone as a 3D object with an infinite number of edges. Boom. Grade four.
A few days ago we had a conversation about the differences between 3D and 2D in which they were easily able to engage, in particular drawing from their experiences with 3D films and video games. Definitions ranged from descriptive and sensory to mathematical. One student defined 3D as a piece of paper and 2D as the writing on the paper which led to a counter-argument that writing exists on paper as a result of ink molecules which are 3D on a miniscule level but nevertheless 3D. The question was then raised whether anything not 3D could exist in the world. One student responded with: "Nothing in the world is 2D. 2D is just an image in your brain. 2D is a thought, not a thing." Boom. Nine years old.
Yesterday a student suggested at the end of a Math period that we refocus our discussions by defining as a class units of measurement for 1, 2 and 3 dimensional entities. Today a student suggested we use Google Sketchup to expand on our exploration of three-dimensional shapes. "I'm thinking you could challenge us to construct a building within some parameters, maybe we could only use certain types of 3D shapes..." Another student had been researching 4th and 5th dimensions and wanted to talk about the ambiguity of chance. We are becoming accessories in their learning. It's beautiful.
I continue to understand the inquiry process through the mountain exploration metaphor where we do not drag students to the top or march them up the well-worn path as might typically have been done in a more traditional system. As the guide, not the prison guard, I have come to understand that we are constantly engaged in empowering students' own decision-making such that they discover the peak for themselves. Most recently, I have realized that the more we let them think, the more they think, the more they know, the more they understand and the more we learn together. I wish I could have explained multiplicative commutativity with their conviction when I was in elementary school. Maybe I could have if someone had given me time or permission to play with rotating arrays. Opportunity is everything: tell them that the sky is the limit, point them in that direction, and they will land on the moon. Cheesy. Cliche. Fact.