Mistakes = Ideas Worth Talking About

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Pam Lindemer, Rockford, MI  pamlindemer@cpm.org

Fall is my favorite season, primarily because it is when everyone goes back to school. My students and I begin the year with a clean slate. The possibilities are endless and with the right classroom culture, the sky is the limit. I am a big fan of Number Talks as an aide to establishing the right classroom culture. Not only do they help students build number sense and fluency, but also when teachers use Number Talks, they model their expectations for classroom discourse and culture.

I was initially reluctant to implement Number Talks because of the uncertainty that comes when students are allowed to share their strategies. What if I am unable to make sense of the ideas that a student decides to share? I have come to learn that this concern is greatly diminished by properly planning for every Number Talk. Part of that planning includes anticipating student responses. I had the good fortune of being able to share my passion for Number Talks with a group of teachers in San Francisco at the CPM National Conference last February. We were preparing to anticipate student responses to the prompt: 16 x 35. I shared the problem with my colleagues and asked them to solve it using mental math. I would like for you to solve the problem yourself now, before reading any further.

I asked for answers from the group and their responses were 330, 560, and 791. At this point we worked in pairs to come up with the thinking that lead to each response. The next step was to come up with a way to visually represent the thinking that we identified. If you would like, take a moment now to think about each response. What thinking lead to each answer.

I was feeling quite confident with the thinking that had lead to answers of 560 and even 330, but the response of 791 stumped me! Everyone at the session that morning struggled with the response, but no one was able to come up with the thinking that led to 791. While Sal, my colleague who offered up the response, was working diligently with his partner to make sense of his strategy, the rest of us were very curious and becoming more and more anxious to hear the thinking that lead to his answer.

When Sal was ready to share, we all listened eagerly as he explained his strategy. Sal had decided to use friendly numbers, numbers that would be easier to multiply. He rounded 16 up to 20 and 35 up to 40.

16 + 4 = 20
35 + 5 = 40
Sal then did the easier problem.
20 x 40 = 800
When rounding up to the friendly numbers, Sal added 4 and 5.
4 + 5 = 9
He then subtracted 9 from his product.
800 – 9 = 791
We all now understood how Sal had arrived at an answer of 791. Friendly numbers are a common problem solving strategy. WHY didn’t they work in this case? The area model provided just the framework Sal needed to help us make sense of what went wrong. Sal’s mistake was fascinating, exciting and thoroughly engaging.

Value mistakes as ideas worth talking about.

~Jo Boaler

I am inspired by teachers like Sal, and the others who joined me in that session on Number Talks last February. We did not shy away from the mistake, we faced it head on and I know that I am a better teacher because of that experience. Number Talks present teachers with an opportunity to model the way we want mistakes to be handled in our classrooms. I want my classroom to look like that session on Number Talks last February. I am looking forward to my first day of school and sharing my passion for Number Talks with a new group of students. If you have not tried Number Talks in your classroom, what are you waiting for?

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Algebra Tiles Blue Icon

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.