Activating Math Schema

In addition to working with grade K-5 teams on numeracy collaborative inquiries this year, I have been fortunate enough to also participate in literacy collaborative inquiries when they happen on the same days. I have very little literacy background, so I'm learning tonnes! I find it very exciting to see and hear how our students are learning, particularly in ways I've never stopped to consider.

Earlier this year, I met with a group of grade K-3 teachers as they explored students' ability to predict what might happen in a story. Starting in Kindergarten, the teachers introduced a book to the students by showing them the cover, and then worked with students to access three factors in order to make predictions: they look at the picture on the cover, they consider the title, and they activate their schema.


Aside... 
Schema (SKEE-mah): relevant background knowledge, experience, or prior knowledge within a context. 
I was blown away to learn that students as young as 4 or 5 years old are learning about the brain, and how they can "access their schema" (and yes, they even use that word!) to think about what they already know and give context to a situation or to make a prediction. Students learn so much more about the brain, and about learning in general, than I remember learning when I was in school. 


Back to the collaborative inquiry... 
We looked at examples of how students were able to make, and then refine, predictions as more and more information is acquired (for instance, as they start reading the book together). We talked about the students' ability to gather information from a picture and/or a title (or just a title, if there was no picture), as well as their background.

As is often the case when we talk about students' ability to infer (a skill developed as they get older), we talked about how each student's background knowledge is going to contribute to what they already know about a topic, or make a guess as to what a story might be about. I'm wondering about how these same ideas can be used to help students attack problems... in math.

Math Schema

When students approach problem solving in math, we often jump right to determining what is given in the question, and what is required for the answer (the first two steps to GRASS or GRASP - you read more about that in this lesson), but we don't often take the time to consider what students are already bringing to the problem.

So often, students who struggle glance at a problem and immediately ask for help or give up. When presenting students with a math problem, would it be worthwhile pausing for a few minutes and encouraging them to access their own schema about the task? What if we got into the habit of asking...

Where have we seen a question like this before?

How could we re-word this problem?

How could we draw this problem?

Can we create a context for this problem?

What is another context/question/problem that is similar to this one?

What representations have we used to help organize problems like this one?

What do we think a reasonable answer to this problem might be? (predict!)

To enforce the pause, a problem could even be initially presented without numbers/expressions (there is an interesting primary example of this, here).

The metacognitive piece is that we share with students that the reason behind all these questions is to both activate their schema (connecting the problem with what they already know) and build on their schema (so that they can recognize similar problems in the future). 

It's a small piece to the overall problem-solving puzzle, but one that might build over time to improve learner confidence and the ability to mathematize, as well as open up new entry points to solving problems.