The Debrief

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John Hayes, Eagle River, WI,

What if all your students were engaged in every lesson? What if they were excited to be in class? What if they were invested in their math learning? What is preventing those things from happening to their fullest in your classroom? It might be your debriefs.

It took a while, but I now know that CPM lessons are carefully crafted and designed with a larger purpose in mind. Because CPM lessons are purposefully planned and placed, changing the lessons will not promote deeper student learning. It also took a while for me to understand that the first problem of a lesson is often used to create more questions from students than answers. It is often a hook, to allow students to fail in the comfort of their well-managed team, and then wonder why they failed. While failing can cause tension and frustration, it is my job to support students in productive struggle so that the tension and frustration do not develop into a bigger problem. If I can pull that off, I know they will become curious, engaged, excited, and invested in math learning, provided my interruptions are carefully managed. In other words, when I interrupt their learning, it should be as unobtrusive as possible. Maybe the most obtrusive thing I can do during a lesson, is the debrief. In this article, I am defining the debrief as the practice of using whole class discussion to explain problems in the lesson as students progress through the lesson. Using my definition of “debrief”, there are three variations of the debrief that I have used in my classroom: post, pre, and during.

The most common variation is the post-debrief model. Usually the teacher sets an arbitrary pacing timer during classwork. I use the word arbitrary because many times we truly misjudge how long a problem will take our students to complete, so we just make up an arbitrary time or wait to see how long the students spend on the problem. When the pacing timer goes off, we begin the debrief of what the student should have learned in that problem. One issue with this approach is that the pacing timer may create stress that can actually slow down students’ thinking. Another problem is that we know that all our teams do not process in an identical amount of time. I would wager that there is a small population in each class that are always victims of the pacing timer. When the timer goes off, we can turn their excitement in the challenge of the problem into a disappointment that they were not able to complete it. There is a place for timers during a class period, but maybe not for each problem.

Another variation is the pre-debrief model, where we explain what is going to happen in the problem before the students are allowed to try it. The intention is good, “I want my students to experience success.” However, not only have we removed most of the cognitive demand by doing this, we may have also removed the excitement of experiencing the math storyline for the first time. In this variation students move through the problem more quickly, because we have already given them hints at the solution. Then students sit idle waiting for us to explain the next problem. Students can end up confused about what to write down when the pre-debrief model is used, as the solution is obvious and requires no justification. “I just wrote down what you said,” students might say. In addition we have significantly reduced the productive struggle the students might experience and thus negatively impacted their abilities to tackle unfamiliar problems later on.

A third variation is the during-debrief model. It is often initiated with a shout through the room, “Ok pencils down.” This variation usually happens because the teacher has seen a common math error in two or three teams, so stops all the teams, and a debrief occurs in the middle of the problem. It is difficult to get students to re-engage after this interruption and again, the students lose their investment in understanding the mathematics of the lesson.

Myths of the debrief:

Myth 1: “A debrief gives students valuable insights.” 

We work hard to get our students working well in their teams. It is challenging to get quality discussions started in our classrooms and it seems like the debrief will give them valuable insight into the next problem. The reality could be our debrief has interrupted their discussions and now we will need to rethink how to get students talking again. This uses time and interrupts a team’s investment in the learning they are doing as a team.

Myth 2: “A debrief refocuses our students on the math.” 

It is difficult to keep our students on task and focused on math. We hope that our debrief provides them with more focus. The reality could be that the debrief gave them permission to stop thinking about math because we are doing that thinking for them. Certainly this may reduce their engagement.

Myth 3: “The debrief enables teachers to demonstrate the best solution.” 

It seems like it is important to model the math so students know the best method to work through a concept. What if some of our students thought of an alternative method? Will they automatically discard their method because they have more faith in the method we teachers cling to? The reality might be that our debrief has inadvertently made their method invalid. Could this then reduce the excitement they feel about their own solution? If students are not excited about their own solutions, how can they be excited to come to class each day?

Myth 4: “The debrief speeds up learning and therefore the lesson.” 

It seems like it is just quicker to debrief a problem and get our students on the straight and narrow. In reality it might be more challenging for students to get back on task after a whole group discussion. They may be more likely to be off task after a debrief, and less likely to re-engage with their teams. After three to four debriefs in a period, some students may decide they do not want to re-engage at all.

Myth 5: “Students enjoy math more when the teacher validates their solutions during a debrief.”

Think about the last time your students lost track of time doing math. The period ends and they say something like, “Is the period over already?” Who was doing the math when this happened, you or the students? The reality is that our students may embrace the challenge of the problems in the lesson if we let them.

Debriefing every problem can contradict CPM’s problem-based learning pillar. Here is an excerpt from the Problem-Based Learning (PBL) Tab in the eBook. “Furtak et al. (2012) has done a comprehensive meta-analysis of various studies in science education, concluding that social interaction (some form of cooperative learning or with a tutor) is an important component of problem-based learning, a finding echoed by DeCaro & Rittle-Johnson (2012), which emphasized the role of teacher control of activities. (Note: ‘teacher control’ in this context means that the teacher is responsible for ensuring that students are working well and on the mathematical topic—not that the teacher is telling the students what to do.) The same results were found in an extensive German study of 100 mathematics classrooms at the eighth grade level.“

So what do we do instead of debriefing every problem? One alternative is to allow the students to fail without rescuing them with the debrief. The caveat with allowing students to fail and wrestle with uncertainty is to structure “teacher controlled” time to check in with students. If we do not allow students to check for understanding outside their team periodically, we may end up on the opposite end of the debrief spectrum which is to tell students “Go do these problems and if you struggle just ask your teammates.” Provided students are writing solutions, a Proximity Partner or Swapmeet study team strategy can be a great structure for students to gain confidence with their solutions. Another alternative is to have a Huddle, but allow the students to do the talking in the Huddle. Your job may be to guide them to take good notes during the Huddle, but not do all the talking. You may even take a chance with a Huddle that you do not attend. “I’d like the Resource Managers to have a Huddle in this back corner to discuss problem 9-20,” and then you just keep circulating.

As teachers we are compassionate people and we want to rescue our students from their math difficulties. We also love explaining math and dazzling our students with our mathematical super powers. It is thrilling for us, but that might be the problem. Debriefing is only thrilling for us. The reality is that our students may be thinking, “When is Mr. Hayes going to stop talking so we can work on our problems?” There is a great place for a daily debrief in your lesson: it is called the closure. An easy closure is to have your students reflect on what they learned through writing, and then to check for understanding by asking them to share what they wrote. Writing during a lesson launch and during closure helps hold students individually accountable to the learning and allows them to engage with the material at a deeper level. Another simple closure might be to ask them to reflect for one minute with their neighbor about what they learned today. Then follow up that conversation by asking them to reflect for one minute with their neighbor about what they still do not understand or even what they might wonder. Engaging in conversation about your students’ closure reflections can be a very powerful way to make connections and to formatively assess their understanding, without worrying about whether you are interrupting their learning. In addition, it is an opportunity to use your teaching super powers to raise the status of students that have made amazing connections by letting those students provide the debrief.

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.