Planning a Re-engagement Lesson

Background: Re-engagement lessons allow students to work with a task to build mathematical ideas. The purpose of the lesson is to confront misconceptions and see why they don’t work, learn how to make justifications, bring their strategies from what’s comfortable to more appropriate grade level strategies, and maximize the learning from the task. “After the answer is out of the way, the mathematics begins . . .” – Phil DaroThe style of this lesson is to maximize student conversation. There are plenty of times of teachers to do the talking – this isn’t one of them.

Re-engagement – Confronting misconceptions, providing feedback on thinking, going deeper into the mathematics.

  1. Start with a simple problem to bring all the students along. This allows students to clarify and articulate the mathematical ideas.
  2. Make sense of another person’s strategy. Try on a strategy. Compare strategies.
  3. Have students analyze misconceptions and discuss why they don’t make sense. In the process students can let go of misconceptions and clarify their thinking about the big ideas.
  4. Find out how a strategy could be modified to get the right answer. Find the seeds of mathematical thinking in student work.

A re-engagement lesson involves using student work on a task to highlight big mathematical ideas, different strategies for solving the problem, or confront misconceptions. During the lesson, I follow a 3-step protocol. First, when I ask a question, I give individual think time; so that all students have a chance to process the question and get some ideas on what to do before discussion starts. Then, I ask students to share their ideas with a partner. I want to maximize the opportunity for all students to talk their way into understanding and participate in the conversation. Finally, I have a whole class discussion so students can confirm their understandings or see why their misconceptions don’t make sense. I usually have students work on blank paper or mini-white boards. I don’t want their old work in front of them, because I want them not to need to defend previous ideas. I want thinking to be fluid or flexible.

Re-engagement Overview: The re-engagement lesson is designed to promote as much student discussion as possible. Students have already done the task on their own and now the important ideas need to be brought out, examined, and in the process have students confront and see the error in the logic of their misconceptions. Often, as teachers, we try to prevent errors by giving frequent reminders, like “line up the decimal point”. But actually errors can provide great opportunities for learning. Students don’t let go of misconceptions until they understand why they don’t make sense. To the student there is some underlying logic to their misconceptions. Instead of going back to re-teach a unit or lesson from scratch, we want to take advantage of the time students have already spent familiarizing themselves with a context and maximize the learning from that work, building on their previous thinking. By using student work, students are very engaged. They are genuinely interested in trying to figure out what someone else is thinking. This also ups the cognitive demand of the task and helps students learn to be more reflective about their thinking.

During the re-engagement lesson students do not have their work in front of them. This is so they will be flexible in their thinking and not married to defending their previous ideas. We are hoping that discussion will allow them to change their minds. Teachers often give blank papers or “think sheets” to students to write on as the lesson progresses. The idea is to allow students to structure their own thinking and processes, not to confine their solution strategies to the teacher’s way of thinking. Teachers often begin the lesson by talking about wanting them to have a discussion like mathematicians. We want you to discuss why strategies make sense. We also want you to listen carefully to each other to see if you hear something that makes you change your mind.

Classroom Norms: To maximize the amount of discussion in the classroom the following norms have proved helpful. Pose a question and then give everyone an opportunity for individual think time, before starting the discussion. This way everyone has a better chance of contributing, not just the quick processors. Before going to a group discussion, do a pair/share to maximize the number of students getting to share their ideas and to give students the opportunity to use and develop mathematical language for a purpose of convincing others. Then open the discussion to the whole class to allow divergent ideas to be shared and examined. Continue probing to allow ideas to be “almost” over-clarified, so students really solidify their thinking. Try to avoid feedback about the “rightness” or “wrongness” of their ideas. Let the group try to reach consensus about what makes sense and why. Feedback stops the discussion. Some teachers like to also use the quiet thumbs up signal to let them know when the students are ready for the next part. So the flow of the lesson: pose a question, think time, pair/share, class discussion, and then pose a new question. As a follow up, many teachers give back the original tasks with red pens a few days later to let students have the opportunity to edit their thinking.

Preliminary Questions: Before Designing the Lesson

  1. What are the big mathematical ideas of the task?
  2. How was the task designed? How did the design contribute to the cognitive demand?
  3. What are some common errors?
  4. What are some interesting strategies?
  5. How do we bring students along from where they are to “grade-appropriate” strategies?

Picking student work

  1. Start at basic level – even if students did well. It is important for them to really articulate the basics of the task that everything else hinges on.
  2. Pick pieces that create controversy or disequilibrium.
  3. Pick interesting strategies- some that work and some that don’t. Explore why they work or don’t work. Compare which ones are easiest to use.
  4. Compare and contrast justifications, so students develop their own internal standards about what makes a convincing argument.
  5. Write the work in your own handwriting, so scoring marks aren’t visible and students are trying to figure out whose work it is.
  6. Leave out parts of the work or parts of the labels, so there is something to figure out or discuss.

Basic Questions

  1. What is the student doing or thinking?
  2. Does it make sense? Why or why not?
  3. Is this a convincing argument? Why or why not? How could it be improved?
  4. Look at two justifications – Which one do you look better? What are the qualities that make it better? How could it be improved?
  5. What does this number represent? Or What labels could we attach to the calculations?
  6. What do you think the person wrote next or did next? How does this help?