When I observe effective teachers of mathematics, there is one characteristic that they all have in common. It is the space they provide for their students to voice their ideas, reflect on their thinking and explore mathematical concepts. This may seem simplistic. But I argue that it is not. Space is time. It is the precious real estate in the classroom schedule of which we never have enough.

Ineffective teachers rush through their space, filling it up with lots of limiting tasks that students complete, on their own, following rigid rules and formulas which they have memorized with limited understanding. Ineffective teachers believe that if their students complete the math, their students understand the math. Teachers who hold on to their space want to control everything. They strive to control the strategies and solutions their students produce all the while rendering mathematics a subject that is monotonous, predictable and uninteresting.

It takes a lot of courage as a teacher to share your space – the space which you would normally fill with your mathematical ideas, your mathematical explanations and your questions. Effective teachers realize that sharing their space with their students means that lessons will take longer, but they also know that their students’ learning will go much deeper. Effective teachers realize that deep learning is messy; sometimes students’ answers are hard to follow and their strategies may not replicate those that are found in commercial math resources. These incredible teachers believe that the messiness is the joy of mathematics; it is the freedom to explore and think. Effective math teachers share their space eagerly with their students as they facilitate rich discourse and help their students to value mistakes as part of learning in mathematics. Teachers who share their spaces know that it is by listening to their students’ ideas that they will gain insight into their students’ thinking. They know that just because their students do the math does not mean that their students understand the math. These teachers also know that by providing wide spaces in which students can investigate, pose questions, and share their mathematical ideas, they are helping their students to celebrate the beauty of mathematics on a daily basis. Their students see themselves as mathematicians and value mathematics as a meaningful part of their lives – all of this because their teachers cared enough to share their space.