Are you using tasks with your students to promote mathematical thinking, but it falls flat? You know the tasks are high quality and your students are just not “getting” the math that’s intended.

The reality is, you spend time thinking about the task you want your students to think deeply about. You choose it to get them thinking about the math, but sometimes all they think about are the blocks, their drawings, or which friends they’re working with.

But what we really want is our students interacting with a task that leads them to a math conjecture or math understanding that can be built upon in future tasks. We want our students to notice patterns and use what they’ve done in previous tasks and apply it to the new task.

Somewhere, something is going awry… not because of lack of trying, so let’s break down what might be happening. 

In this episode about Debriefing Math Problems:

• defining math tasks 
• getting students to think 
• mistakes to avoid when debriefing 

Let’s Start with What is a Math Task?

In 5 Practices, Smith & Stein lay out a framework for choosing a rich task.
Here is the gist of the Task Analysis Guide found in their book on page 20.

They talk about lower level demand to high level demand problems, ending with higher level demand- doing mathematics problems. Specifically these are problem solving tasks. These tasks require exploration and active inquiry. Students must actively engage in sense making as they solve the problem. They have to be in a position to explore a mathematical situation and make sense of it, without being told in advance what to watch out for or how to approach the problem. They have to reason through those things.

Now this whole episode is about 3 mistakes we make debriefing math problems. But let’s start with what is a math debrief?

I love debriefs. I actually always say, “Never Skip the Debrief. That’s where the learning happens.” And it’s true, when you give students time to grapple directly following that productive struggle time we use a debrief or a math discussion to crystallize their problem solving experience. (We talked about grappling and productive struggle in episode 84). So, don’t skip the debrief or the discussion because that is where you can help students take what they explored and worked through and make sense of it all.

So what is a math debrief?

A math debrief can look lots of different ways and some ways are more effective than others. Sometimes it is a series of questions that go over students’ work. Other times it is a synthesis question in the lesson plan or on the lesson slides that helps students see what they were supposed to learn from the activities. Maybe the BEST way to have a math debrief is through a student centered discussion where questions are asked to help students synthesize their experience and formalize it into math understanding. Giving this opportunity to formalize understanding through explaining their reasoning ensures not only that student understands, but gives students opportunities to hear others’ reasoning and in turn to their own understanding.

It’s like this… kids are solving a fraction problem during grapple time. They come to the math discussion to share and discuss what they found as they discovered *hopefully how to add fractions with unlike denominators. Some students used fraction tiles and others used drawings. While other students are still trying to decipher what the problem was asking them to do. The teacher orchestrates (shout out to Peg Smith episode 80) a math discussion that allows students to share their thinking and demonstrate their breakthroughs with their models and strategies. Then, others listen intently to add to their own understanding. So, even if they come to the rug completely confused about the problem they are able to access the math discussion because we can’t discuss THEIR work, but asking them to think about others’ strategies and models. This relieves the pressure from students to “get it right” during productive struggle and emphasizes the importance of participation and showing up ready to learn.

Let’s discuss 3 Mistakes to avoid when debriefing math problems? 

1. Ask questions to get answers instead of thinking – If you want to level up your questioning go over to Math Insiders and grab the printable and audio summary of the questions you need to be asking. Math Insiders is a private, subscription podcast full of extras just for math teachers. It’s $5 a month and you can subscribe at MonaMath.com/Insiders
2. Your focus is on understanding, but students are focused on writing things down.
3. Unprepared for all the responses

Mentioned in this episode:

📕 5 Practices for Orchestrating Math Discussions

🎙️Episode 84 – Productive Struggle: Building Confident Problem Solvers

🎙️Episode 80 – Ambitious Teaching with Margaret “Peg” S. Smith

🆓 Guide to Engaging Math Discussion MonaMath.com/Discussions

📱 Sign up for Math Insiders HERE.  

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