If you’ve been using Math Medic lessons, you know that every EFFL lesson follows the same basic structure:
Activity
Debrief Activity with Margin Notes
QuickNotes
Check Your Understanding
The Activity is the engaging, accessible task that students work on in small groups to explore the big idea of the lesson. But the Debrief is when that big idea becomes explicit, and students see how their work on the task is linked to the mathematical principles the lesson is designed to convey.
Imagine if you were trying to teach somebody about the constellations. The first step would be to provide an environment where they can actually see the stars, an open field in a remote area without light pollution, on a clear night. The Activity portion of an EFFL lesson is that open field. It is the right environment for learning to happen. It gives students the opportunity to explore, wonder, and conjecture.
The debrief of the EFFL lesson is the constellation map that “connects the dots” for students, helping them name and notice the constellations (i.e. the big ideas of mathematics). The debrief, like the constellation map, trains the student’s eye to notice certain landmarks (skymarks?) and helps them make sense of what they are seeing.
Activity Debrief
We cannot overemphasize the importance of the debrief, as it is generally when the deep learning of the lesson happens. It is also the portion of the lesson that requires the most teacher skill. Today we’re going to look at 3 principles that will help you take your debrief to the next level.
Debriefing the Activity is NOT like going over homework.
Every part of the debrief should be connected to the main idea.
The teacher’s role during the debrief is to help students name and notice.
Debriefing the Activity is NOT like going over homework.
When we go over homework problems in class, this often looks like working through a problem and showing the necessary steps needed to get to the solution, whether that is presented by you or by another student. The hope is that students who didn’t know how to get started would glean a way to make sense of the problem and students who got stuck in the middle would be able to figure out where they went wrong. The focus is on how to solve the problem. You have probably noticed that the students that already knew how to do the problem and were able to arrive at the right answer on their own tend to be checked out during this time. There is not a significant value add for them in seeing the problem worked out again.
The debrief is not intended to be focused on how to get the answers to the activity questions. We expect that the majority of the questions will have been solved by students using the intuition, strategies, and prior knowledge that is available to them, before the debrief starts. If the debrief just goes over all those questions again, students have no real reason to pay attention during this portion of the class period because nothing new is being added. Even if there is a challenging question that not all groups were able to solve, the debrief of that question is not just about making sure students have a correct answer written down, but identifying what that question is all about, how it differs from others on the page, and what features of the question make it more challenging. These are usually the features that motivate a new strategy or method that the lesson is designed to unpack.
The debrief, then, isn’t just for the students who struggled in the activity, it is designed to help all students organize, formalize, and generalize the processes they used in the activity. Students will often be able to successfully answer the questions in the activity using their reasoning skills, but that doesn’t mean they have a full grasp of the underlying idea or that they can clearly articulate the impact of what they have learned. This does not mean that the lesson was a flop; it means that the students are in a perfect position to learn from the debrief.
Tip #1: Don’t just ask what they got or how they got it.
To signal to students that the debrief is not just about “going over” the answers, pay attention to how you ask students to share about their work. Below are two ways a teacher could ask a group to share out.
Option 1: Lara, can you tell us what your group got for question 4?
Option 2: Lara, can you tell us about your group’s thinking when you were filling out this table in question 4?
Notice the subtle difference in the teacher’s question. The first asks the student for the answer and how they got it. The second invites a discussion around a general strategy or approach.
2. Every part of the debrief should be connected to the main idea.
The goal of an EFFL debrief is not just to “go over answers” or even talk about how a group calculated a certain answer, but to connect the group’s strategy and answer to the main idea of the lesson.
Let’s take a look at a specific lesson from our Algebra 2 course titled “How Much Does My Pizza Cost?”. This lesson is in the first unit on sequences and linear functions and is designed to help students learn the point-slope form of a line. We suggest pausing to work through the lesson before continuing on with reading this post.
First, we need to establish the main idea of the lesson. Before you say “point-slope form of a line”, remember that the main idea of the lesson is not the topic or standard being taught, but the conceptual idea that you want to help students develop. It can usually be stated in a sentence and it is specific to that particular lesson and audience. While I may teach the same topic in Algebra 1 and Algebra 2, for example, it’s more than likely that I have a different intended take-away for that lesson in each course. When I teach “How Much Does My Pizza Cost?” to an Algebra 2 class that has never before seen point-slope form, the main idea I want students to understand is that:
Knowing the slope of a line and any point on the line is sufficient to determine all other points on the line.
How will we do this? By figuring out how far our desired point is from the anchor point and adding or subtracting copies of the slope.
My priority when I debrief the lesson, then, is to connect student responses to that main idea, rather than just going over how students got to their answers. Here’s what this might sound like when debriefing question 2 on the activity.
Approach 1: Focusing on the “how”
S: I got that a 5-topping pizza is $20.74.
T: And how did you get that?
S: I knew the 4-topping was 18.99 and then I just added the cost of 1 more topping.
T: So you took the 18.99 and added 1.75 and got $20.74 for the 5-topping pizza.
Approach 2: Connecting to the main idea
S: I got that a 5-topping pizza is $20.74.
T: And where did that come from?
S: I knew the 4-topping was 18.99 and then I just added the cost of 1 more topping.
T: So you noticed that you could use the information you already had about the cost of a 4-topping pizza and the cost per topping, and just add on one additional topping to get to the 5-topping price.
Notice how in Approach 2, the teacher zooms out from the specific numbers in the problem and focuses on the strategy itself, emphasizing the “information you already had” and “adding on” which are key components of the main idea.
After a student has shared their idea, we want to respond in a way that
makes explicit key aspects of the strategy
invites students to see underlying structure
helps students generalize their approach
advances students toward the main idea of the lesson
In most cases, when students share out their strategy, they will talk about their specific strategy for that particular question. This often includes a calculation. The teacher’s role is to help them articulate the reasoning behind the approach and then generalize it.
Tip #2: Generalize, generalize, generalize
In this lesson, the completion of the table is a key aspect of the task. When debriefing this, a teacher might ask a group to share their group’s thinking when they were filling out the table.
S: For the 9-topping, I just added on 5 times 1.75 to the 18.99.
T: Why 5?
S: Because I already had the price of a 4-topping, and I need 5 more to get to 9.
T: So first you figured out how many additional toppings you needed to add on. Then you added on that many copies of 1.75 to the 18.99 price.
Note how the teacher uses the student’s specific answer to highlight a more general way of thinking about any value in the table. How does the order compare to the 4-topping pizza we already know about? How many more or fewer toppings does the new pizza have? Add or subtract that many copies of 1.75 from 18.99.
The questions themselves encourage students to make use of structure. But the debrief is critical for helping students connect the dots. Do not assume that a group with a correct answer has fully internalized the mathematics behind what they are doing.
Tip #3: Zoom out.
Not every part of the debrief has to be linked to a specific question. In fact, the most effective questions are directly linked to students’ work and leverage the actual things you saw during the lesson, making comparisons and connections between strategies and between questions.
For example:
T: Now I noticed that when you were filling in the table, you all used the 4-topping pizza as kind of a starting point and then just added on or subtracted from there.
But when you wanted to write the equation, I heard a few groups debate about if we needed to find the price of a 0-topping pizza first. What do we think?
Tip #4: Show how different parts of the Activity are connected.
Let’s suppose for a moment that students were able to fill out the table but were not yet able to write an equation for x toppings (or perhaps they all resorted to slope-intercept form). It is okay to tackle this as a whole class and help students connect the table to a possible equation.
That might sound like:
T: I wonder if we can write an equation that reflects the strategy you used for filling in the table. I noticed we always started with 18.99, since that was the pizza we were basing everything off of. Then what did we do?
In this interaction, the teacher is making an explicit connection between the students’ strategy for completing the table and an analytical representation of that strategy in an equation.
3. The teacher’s role during the debrief is to help students name and notice.
The debrief is all about making ideas explicit, calling attention to the reasoning students used intuitively during the Activity, and providing clarity and structure. In other words, it is to help students name and notice.
The margin notes are essential for adding new vocabulary, i.e. naming, the ideas students are talking about. In this lesson, we name this new equation “point-slope form” of a line. We might also name that the cost per topping is the slope of the line, or we might name Lara’s strategy of comparing each pizza in the table to the 4-topping pizza we already know about.
Through our revoicing and questions, we also help students notice key ideas. For example, to help students arrive at the (x-4) component of the equation we need them to notice the structure of all the pizza calculations in order to help them generalize to any number of toppings. We might use a line of questioning like this:
For the 7-topping pizza, how many toppings did you need to add on?
For the 9-topping pizza, how many toppings did you need to add on?
What about for a 100-topping pizza, how many toppings would you need to add on? How do you know?
How do we do that in general? How do we find how many toppings we need to add on?
Tip #5: Add additional “cases” to emphasize structure.
It is often helpful to add a few more examples not already in the activity to solidify the point. Using a more “extreme” number (like a 100-topping pizza) can help make the general calculation more obvious (using subtraction to find the number of additional toppings).
Tip#6: Purposefully address misconceptions.
Another way to help students notice is by offering a nonsolution or what I like to call “playing devil’s advocate”. If we know that students often default to y=mx+b when writing an equation for the line, we might purposefully illuminate this misconception.
“Wait, I thought that for a 7-topping pizza, we would need to add 7 copies of $1.75, since there are 7 toppings and each topping costs $1.75. But you’re saying we only add 3 times 1.75? I don’t get it.”
Having to convince someone else of why their method works is key to understanding it properly. The more you can help students articulate the meaning of the quantities in their calculation, the more likely it is to stick.
By making explicit the mathematical ideas embedded in students’ solutions, you allow students to see the world in ways they may never have before!
Want to see a full debrief of this lesson? Check out the video!