Number Talks

Michael Parham, Adams-Friendship High School, Adams, WI

In our district, we had the fortunate opportunity to have a CPM math coach help us implement effective strategies with the curriculum. A lot of good discussions have come out of the work with our coach, including how to use teamwork more effectively by revising team roles, the importance of writing common assessments as a math department, but most importantly, how to conduct Number Talks with my classes. Usually Number Talks occur in the elementary grades, but we asked ourselves: Why can’t we use them at the high school level? That is exactly what we wanted to try. So our journey began.

My classes are composed of various levels of students with about 75% being classified as special education or having behavioral issues. Many of my students lacked mathematical fluency and confidence in the classroom. We pondered what we could do about helping them. The plan we came up with was to do a Number Talk on both Tuesdays and Thursdays for at least eight weeks. We knew that this needed to be part of our regular routine and not just a short trial.

We started off with Dot Talks to get everybody used to the process. Dot Talks are about students developing strategies for counting without counting by 1s. For instance, for the picture at right, some students will see this as 4 + 3 + 4 = 11 dots, while others might see this as 2(4) + 3 = 11. Both give the same answer, but with different approaches for counting the dots. We want the students to be able to use a variety of strategies to improve their math fluency. As they become more comfortable with numbers and the different strategies, students will be able to use them to explore deeper concepts during class. There are multiple strategies possible with any Dot or Number Talk, but only one correct answer.

For all of our talks, we came up with a few guidelines:

  1. You have to justify your answer by explaining your strategy, not just giving an answer.  
  2. Mental math only! You cannot use a calculator or paper/pen.   
  3. You should respect others when they share their ideas, but challenge them if you do not understand or disagree. 
  4. The Number Talks would be limited to no more than ten minutes.

Most Number Talks were just a little bit longer than five minutes. After ten minutes, the amount of engagement was diminished.

After two weeks of Dot Talks, we switched over to Number Talks. We started off with two-digit addition problems because addition is one of the first concepts students learn, and so most students feel comfortable with addition. The process started off very slowly, with only a few students contributing comments. The students that did contribute were using the traditional algorithm in their heads, imaging one number above the other, as they added the columns. Every once in awhile, a student would share a unique strategy, but this was not the norm. I knew there had to be something else I could do to promote more critical thinking about these problems. I wanted the students to enjoy the problems and have an informal conversation about the multiple ways that we can find a solution.

The first breakthrough I had was when I realized that I had to have an open mind. Students were coming up with so many different strategies including some that I did not even see myself. I emphasized that there is only one right answer, but many different ways to get there, and that you can only use “legal moves” in your strategy. During a Number Talk, my role is to write down exactly what the student says. It is not easy to write down an incorrect strategy without making a face, but I had to do it. I know from personal experience, as well as my professional development time learning about fixed versus growth mindset, people learn more from a mistake than they do when they are always getting an answer correct. For example, I would record a student’s strategy, and I would leave it as it was. I would move onto the next student’s strategy. Once several people shared, someone would challenge an earlier strategy, or a student would correct his own strategy.

Even after discussing these methods, students till seemed to rely on the traditional algorithm. The second breakthrough I had was to write down the name of the strategy as the students used it. All of a sudden, students started using more of these new strategies. A student said to me, “I think most of us were looking for the weird strategies, instead of the easy ones.”

This might sound great in theory, but how did it actually work in my classroom? We saw a lot of progress. Students were using more strategies on a regular basis, more students were responding to the given problem, and students were displaying more confidence with their explanations. These improvements were not limited to the Number Talks. We saw improvement in student confidence while working on their lesson/homework, while working with their teams, and when I would ask them questions related to bigger concepts covered in the classroom. So where do we go now? When our math coach has moved on, my class will continue to use Number Talks and modify them to connect directly to higher-level concepts that we see in algebra.

On a special note, I could not have done all of this without the help of my math coach Mark Ray. On a weekly basis, I would record my class, share them online using Swivl software, and then he would comment on my videos. The following week we would Skype and talk about how the week went and what changes we could do to make things better. For example, the last change we made was to have everybody share, even if it was a strategy that was already introduced.

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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.