The Goal of the Lesson

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Brian Ryczkowski, Green Bay, WI,

What was I doing before?

No, not before COVID—though I did start this article in March of 2020. What was I doing in the classroom?

I have had the privilege of working with two great CPM coaches: John Hayes and Lorna Vazquez. In 2020, when with Lorna, we decided the coaching goal we would pursue would be: Elicit and use evidence of student thinking.  Specifically, the student behavior we wanted to consider was teaching practice 8: Students reveal their mathematical understanding, reasoning, and methods in written work and classroom discourse.

In 2017 and 2021, when working with John Hayes, lesson planning revolved around these questions:

  1. What is the goal of the lesson?
  2. Where might students struggle and how can we support them to be productive?
  3. Where does the lesson hinge?
  4. When can they get up and move during the lesson?
  5. What i the closure?

Through all of this work, everything revolves around the goal of the lesson. What is the goal of the lesson? It is what we have all come to know as Learning Targets, I can statements, Success Criteria—the multitudes of the verbiage used to get at the heart of what a lesson truly is.

At the start of every lesson, I have a student volunteer read the lesson opening, as CPM suggests. I use Activinspire, which is similar to SMART Notebook. After the student finishes reading, the next slide is one I have pre-generated, and it states the goal of the lesson. The goal is always written as a question, and I try to make it as short and student-friendly as possible. For example, in Core Connections Algebra, one of our questions recently was, What is y = mx + b? The learning goal comes from Learning Log prompts and the Lesson Objective in the teacher’s edition. Here is what they see.

In Secion 2.1 of your toolkt: What is y=mx+b?n Be sure to provide examples.

At Ashwaubenon High School, each student has a Toolkit where they write the answer to the goal of the lesson. Their Toolkit is where they write their Learning Log entries, definitions, examples, and all of the evidence of learning. One of the conversations we have early in the year is that our notebook is our “sloppy copy” and our Toolkit is our “final copy.” Everything that student teams read about and write intheir notebook–problems they complete and conversations they have—are all geared towards answering the goal of the lesson.

I am fortunate enough to have a whiteboard wall in my classroom. When we show students the goal of the lesson at the start of class, I go to the wall and write the question as high on the back wall as I possibly can. While I write the question on the wall, a student volunteer reads the question while everyone else writes the question in their Toolkit. Then, I tell them to hide their Toolkit under their book. We do this to promote the idea of “beginning with the end in mind.” Early in the year, I also say “You will know if you have been successful if you can answer that question at the end of class.”

During the lesson, I try to use several STTS to encourage students to talk and listen to each other. A few that I swear by are Board Reports, Huddles, and Swapmeets. While I circulate and work with teams, I make it a priority to ask them where they are in answering the goal of the lesson. More often than not, teams have something to contribute towards answering the day’s question, and I ask them to get a marker and add their thoughts on the wall. This is where I have made my most progress as a teacher. As I shift from team to team, I keep in mind the goal of the lesson and incorporate that into my line of questioning. And by having the goal of the lesson on the back wall with student evidence of learning, I am able to use that with struggling teams. For example, I may point to something on the wall and ask, “What do you think that means?” or “Does that begin to answer today’s question?” This gives teams a chance to think and share their thoughts during the lesson. Universally, we can all agree that this approach is most powerful because it is student work, not mine.

Here are some examples of what it might look like:

photo of y=5x+2 with arrow to 5x with caption increase slope growth and arrow to 2 with caption y-intercept start
Example 1
Example 2
photo of whiteboard with What is y=mx + b?
Example 3
photo of a whiteboard
Example 4

As I circulate, I file away who wrote what and how that would best be sequenced to share at the end of class. Sometimes, I see students answering the goal of the lesson in their Toolkit before closure. To me, that is quite potent because they trust what their classmates wrote.

At the end of class, we have students get their Toolkit out from under their book and I tell them it is time to answer the goal of the lesson.

As we look at each item written, I call on students to read what they wrote and explain what it means. There are times when I correct something on the wall, but I typically try to do this before closure. Also, there are days when students or I add something to the wall during closure that completes our answer to the question.

When we start or end a lesson, I often tell the class that if they can answer the question partway or completely they have made progress towards the goal of the lesson. It does not matter if they read something in their book, if their teammate said something or if they heard it or read it during closure; this demonstrates a growth mindset and progress towards understanding and learning

The days I feel are the most successful are days when everything on the back wall is student hand-writing and they can explain it all during closure. Not every day ends up that way, but I feel it gives us the best chance to be successful in reaching the goal of the lesson.

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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.