On our planning day, ktrogrlic and I spent a lot of time talking about the components of balanced mathematics (modeled, shared, guided, independent) and what balance really means in teaching and in a mathematics program. We talked about how her practice is changing as she continues to participate in this project and about how our shared understanding of effective instruction continues to evolve as we work together sharing and implementing ideas.
In Katarina's class, lessons typically start with a concept, question or idea that students are asked to explore collaboratively. Student thinking is shared and the lesson that follows will be in response to the needs that students are demonstrating. Modelling is done as necessary, again, in response to the needs that students demonstrate through discussion. Katarina describes her guided practice as a chance for her to 'push students', whatever that may mean. For example, for students who are struggling with work at the grade 6 level, guided practice would be the support and the 'push' necessary to help close the gaps they've demonstrated. For students who are working at or even beyond the grade 6 level, guided experiences would 'push' student thinking even further. It's always a chance for the teacher to support and guide productive, necessary struggle.
Through our discussion we determined that, despite her strength with a flexible and responsive, "in-the-moment" approach, Katarina and I will work to build more intentional guided practice into her teaching. The guided practice would be a targeted response to information we gather through assessment for learning (like the Nelson pre-assessment that our board has recently purchased).**
Once we had discussed the technical elements of balanced mathematics, we ventured into a conversation around teaching mathematics (and balanced mathematics as it were) as a way of thinking, a way of 'being', and maybe even a way of knowing. If that sounds a little too philosophical for a grade 6 math discussion let me explain!
In order to reach our students, we need to truly know them. We need to know them through assessment in order to gauge where their understanding is in relation to curriculum expectations and, more importantly, we need to know who they are in order to reach them with the instruction we are planning. Here our conversation went off on a short tangent about student voice and the power of building relationships with our students, perhaps a great topic for another post. It was, however, during this conversation that we began to think: perhaps a balanced approach to mathematics is also, quite simply, a responsive approach.
**Our plans also include exploring the use of Screencastify to support communication and self-assessment which continue to be areas where our students can grow.
If we take the time to know our learners and constantly update this knowledge through assessment for learning, our responsibility is to plan instruction that responds to the student needs we're identifying. The components of balanced mathematics provide us with the tools that will make it possible to meet the needs of our students. Knowing when, how and with whom we should be using each of the four components is where our professional judgement comes into play and is done through analyzing our assessments - it's important to note that these assessments go well beyond a pre-assessment we might give and include our observations around a students' abilities and, again, who they are as a people and learners. Think about the math processes; this is where we, as teachers, select the appropriate tools and strategies to solve problems. The tools and strategies are the components of a balanced mathematics program and the problem we are trying to solve is providing the best, most meaningful and effective learning possible for our students.
With this metaphor in mind and the components of balanced mathematics alongside the rest of the tools in our toolboxes, we look forward to the next four months of work on this TLLP.