By Lizzy Skousen, *6–12 Curriculum Writer, IM Certified® Facilitator*

During a problem-based lesson, the teacher does a lot of listening while monitoring student learning. When teachers are introduced to a problem-based lesson structure, they may wonder:

- “Do we just hope that students will think about what we want?”
- “How will students learn the things they need to know?”
- “When do I actually teach?”
- “Is this doable with the amount of instruction time I have?”

One answer to all of these questions is a well-executed lesson synthesis.

There is an overall structure to an IM lesson. We begin with inviting students to the mathematics of the day, then dive more deeply into concepts and procedures. After the lesson activities and before the cool-down, there is a lesson synthesis when we consolidate and apply the learning. What does it mean to consolidate the learning of the day?

We need to bring together all of the learning that has happened with individuals and groups and make it explicit for the entire class. During each activity, students generate solution methods and then reflect and discuss how they solved the problems. There may be as many different ideas as there are students. Some students or groups will generate strategies or make connections that align with the learning goals of the lesson, but not every student will. Sometimes they may choose a more familiar but less efficient strategy or struggle to make a specific connection.

**“Do we just hope that students will think about what we want?”**

I like to imagine that teaching is a bit like taking my students for a wilderness exploration hike. I want the hikers to explore, see new things, and get to play, but I also don’t want them to get lost or wander onto a trail going the wrong direction. As the leader of the hike, I need to start by knowing the area. What are the major landmarks? Where do we start, where do we end, and what are some major pitfalls we need to avoid?

In a lesson, I need to know the same things. What is the purpose of the lesson? Where do I want students to end up? What do I want students to be able to accomplish?

The learning goals and cool-downs are really clear signposts to help answer these questions. The learning goals help the teacher know what students should understand and be able to do, and the cool-down shows how students will demonstrate it. With this information, I can go into each activity with a clear idea of where the lesson is going. During the lesson synthesis, I check in to make sure all students have heard the important takeaways of the lesson so I know they are ready to demonstrate their learning on the cool-down.

**“How will students learn the things they need to know?”**

When students are exploring mathematical ideas, they are not all going to do it in the same way. On the wilderness hike, some explorers will carefully follow a pre-marked path, while others will try hopping on rocks or logs, and still others may follow an interesting bug. During the lesson, some students will want to use a familiar representation instead of trying a new one, others will skip using a diagram at all, and some may get focused on a different approach. One group of students may already be showing that they can meet the learning goal, while another group is still unsure. This is why it’s important to consolidate the learning of the day.

The lesson synthesis gives teachers the opportunity to bring together students’ ideas and focus on the learning goals for the lesson. Targeted questions during the lesson synthesis highlight the learning that has already happened during each activity and help make this learning explicit for all of the students in the class.

**“When do I actually teach?”**

When I have my wilderness explorers hiking with me, I think of myself as a scout leader. We may be exploring and having fun, but there is also an intended direction to travel. With my students, they explore and play with ideas, but there is a mathematical direction in a lesson as well.

The lesson synthesis is a brief but vital component of the lesson where teachers can make sure that students have all heard and seen important vocabulary words, strategies, and connections. In this discussion with the students, the teacher asks targeted questions, and a few students will share their thinking. The teacher may revoice important ideas, highlight strategies that align with the learning goals, and explicitly state an important concept or vocabulary term. Most of the students will be listening during this part of the lesson.

**“Is this doable with the amount of instruction time I have?”**

Even on the most relaxed hike, there are time limits. If I know that we have to meet back at camp before sundown, I have to plan ahead to make sure that my hikers all get there on time. Since I’ve already looked ahead at the map, I know about where we should be throughout the day and can set a pace for the hike.

Pacing a lesson can be a challenge. It can seem like there is not enough time in a day to do the synthesis, but the lesson synthesis is critical to student learning. Each lesson synthesis should take about 5 minutes of class time before the cool-down. One way to pace the lesson effectively is to work backwards. Plan for the last 5 minutes of class to be the cool-down, and the 5 minutes before that to be the lesson synthesis. Then look at how much instructional time is left and adjust the pace for the other activities as needed.

Since the lesson synthesis brings together all of the learning that happens in each activity and makes it explicit for the whole class, it’s not necessary for every student to have completed every activity perfectly before moving from one activity to the next.

**Conclusion **

After students complete the cool-down, take a moment to reflect. If most students showed evidence of accomplishing the learning goals, what happened during the lesson synthesis that helped consolidate the learning for all students? If most students struggled with the cool-down, how could the lesson synthesis have gone differently? Connecting the day’s lesson synthesis with the cool-down can help you plan ahead for future lessons.

A well-executed lesson synthesis is essential to accomplishing the learning goals of a problem-based lesson. This is the point where teachers make explicit what students should take away from the lesson and give students the necessary preparation for the cool-down. When preparing for a lesson, make sure to plan time for the lesson synthesis and work backwards from there to pace the other learning activities.

##### Lizzy Skousen

Lizzy Skousen is a curriculum writer and certified facilitator with Illustrative Mathematics. She has a passion for connecting coherent learning materials with cognitive research. With a master’s degree in mathematics and an undergraduate degree in psychology, she thrives on leveraging the amazing processes of the brain in learning mathematics. She has been a speaker at NCTM addressing mastery learning and acts as an educational consultant for public and private schools around the country. She has taught mathematics at the middle school, high school, and undergraduate level in Arizona and Texas. She also volunteers with the band program at her children’s schools.