In the Ontario curriculum we have many expectations (standards) that tell us students are expected to, “Determine through investigation…” or at least contain the phrase “…through investigation…”. In fact, in every grade there are many expectations with these phrases. While these expectations are weaved throughout our curriculum, and are particularly noticeable throughout concepts that are new for students, the reality is that many teachers might not be familiar with what it looks like for students to determine something on their own. Probably in part because this was not how we experienced mathematics as students ourselves!
First of all, I believe the reason behind why investigating is included in our curriculum is an important conversation! I’ve shared this before, but maybe it will help explain why we want our students to investigate:
The chart shows 3 different teaching approaches and details for each (for more thoughts about the chart you might be interested in What does Day 1 Look Like). Hopefully you have made the connection between the Constructivist approach and the act of “determining through investigation.” Having our students construct their understanding can’t be overstated. For those students you have in your classroom that typically aren’t engaged, or who give up easily, or who typically struggle… this process of determining through investigation is the missing ingredient in their development. Skip this step and start with you explaining procedures, and you lose several students!
Traditionally, however, many teachers’ goal was to scaffold the learning. They believed that a gradual release of responsibilities would be the most helpful. Cathy Seeley in her book Making Sense of Math: How to Help Every Student Become a Mathematical Thinker and Problem Solver explains the issue clearly:
In the two pieces above Cathy explains the “upside-down teaching” approach. This is exactly the approach we believe our curriculum is suggesting when it says “determine through investigation,” and exactly the approach suggested here:
At the heart of this is the idea of “productive struggle”, we want our students actively constructing their own thinking. However, I wonder if we could ever explain what “productive struggle” looks / feels like without ever experiencing it ourselves? How might the following graphic help us reflect on our own understanding of “productive struggle” and “engagement”?
I think it would be a wonderful opportunity for us to share problems and tasks that allow for productive struggle, that have student reasoning as its goal, problems / tasks that fit into this “zone of optimal confusion”.
In the end, we know that these tasks, facilitated well, have the potential for deep learning because the act of being confused, working through this confusion, then consolidating the learning effectively is how lasting learning happens!
Let’s commit to sharing a sample, send a link to a problem / task that offers students to be confused and work through that confusion to deepen understanding. Let’s continue sharing so that we know what these ideals look like for ourselves, so we can experience them with our own students!