by Krista Sarmatiuk
As educators, we work tirelessly to improve outcomes for our students. We wonder what will be the difference that makes the difference. Tonight’s discussion made me think it might be about “being ready”.
Cathy Fosnot talks about math as a creative subject, though she admits that many students and educators don’t see it this way. If you can imagine a landscape of mathematical ideas – or even just allow yourself to think for a moment that such a landscape might exist – what would it look like? What tools would you need as you navigated this landscape? You would likely want to have tools that would help you to determine direction, to travel safely, to nourish you on the journey. These tools are models, but they need to be helpful to you. If not, they are just extra baggage that weighs you down and slows your progress.
As educators, we are tasked with helping students to select the tools and strategies that will help them to solve problems as they traverse this landscape. To do this successfully, they will need to reason, to communicate, to interpret what the landscape represents, to reflect on their journey so far and to adjust in order to reach their destination efficiently and safely. This is a journey that requires creativity, courage and determination. We need to be ready to embark on this journey alongside our students, to act as a guide, while giving them room to explore.
We need to be ready to navigate a landscape of mathematical ideas. Successful navigation requires knowledge, thinking and action. Cathy Fosnot said that “it’s about deeply understanding the development of the mathematics at hand. We need to know what the development of a mathematical idea looks like so that we can craft situations that will support kids to employ strategies they know already and then have new insights that will lead them to the next idea.” In this case, “being ready” means really digging in to the curriculum, thinking about the big ideas and how they develop over time. This is not an easy task in mathematics, as the expectations are interdependent. We see key ideas reflected across all 5 strands, and when we notice that we can draw on student strengths in patterning or geometry to build stronger number sense, then we have some of the leverage that we need to make the difference.
We need to be ready to engage learners in contexts that will help them to uncover big ideas. When a context helps us to see math, we begin to dig around, to explore, and this makes us think like mathematicians. Presenting a context with a low floor and high ceiling makes the idea accessible to all. Being ready also means anticipating the solutions and strategies that will bubble up in response to a problem or context, and having the questions that will propel student thinking to the next level in your pocket.
We need to be ready to empower learners to notice and name the strategies that they use as mathematicians, the models that help them to think, and the behaviours that they want to repeat or try for the first time, tomorrow. Increasing student ownership of models and strategies requires frequent exposure to powerful tools and models, lots of discussion and a strong math community in the classroom where everyone has a voice. We need to give students time to reflect, to talk and to journal about their own journey.
Just as every country and continent has similar and different features, each of the landscapes Cathy has developed is connected, and yet distinct. The first time you look at the landscape as an educator, you can easily be overwhelmed. Given time to build your own understanding, the whole picture begins to come into focus. This brings me to my last point. We need to be ready to slow down the pace of learning. For ourselves and for our students. Appreciate think time. Engage in discourse. Circle around again. Walk away for a while, explore other mathematical ideas. Do you see the landscape differently when you return? I bet you do.
Are you ready?