Developing Collaboration by Sharing Authority

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John Hayes, Eagle River, WI

As a Professional Learning Specialist, I have had more than 80 individual implementation support meetings with teachers and 20 team meetings this fall. When I ask teachers to reflect on their biggest challenge this year, the overwhelming response is collaboration. I do not doubt that on the surface collaboration appears to be a challenge to implementing CPM as intended, but discussions with teachers have revealed another challenge: shared authority. Shared authority is a key component of CPM’s Problem-Based Learning Pillar as mentioned in Section One of CPM’s Implementation Progress Tool (Image 1).

Problem-Based Learning

Students and teachers share math authority as they value and engage in productive struggle. Teachers guide without taking over the thinking.

CPM’s Three Research Pillars of Collaborative Learning, Problem-Based Learning, and Mixed, Spaced Practice might be seen as silos of best practice. One possible reason for this belief might be the visual image of pillars or it may be how teachers learn about the pillars in workshops. The reality is that these three pillars are intertwined in actual classroom practice. For example, most CPM teachers would agree that using a Swapmeet Study Team and Teaching Strategy supports the Collaboration pillar. In fact, a Swapmeet supports shared authority with students taking ownership of the mathematics by helping them see alternate solution strategies (Problem-Based Learning). Also, the solution strategies used are likely a product of students engaging and re-engaging with concepts over time (Mixed, Spaced Practice). The pillars are a foundation such that if one is absent, the others will suffer. If we disregard shared authority (Problem-Based Learning), students will struggle to have meaningful conversations (Collaborative Learning). This is precisely the challenge teachers face when teaching virtually or in socially distanced situations.

As teachers wrestle with what seems to be a constantly changing classroom structure–often moving between teaching virtually and teaching in a socially distanced classroom–sharing authority may seem the least of their concerns. As a matter of survival, teachers may resort to teacher-led discussions as the primary mode of instruction. Yet this can undermine a culture of students owning their learning. The culture of sharing mathematical authority with students can take months or even years to build. Now, amid the ongoing crisis, it may seem necessary to take a giant step back in creating that culture in order to get information to students while we secretly hope they understand. Think beyond the mathematics classroom, however. How many hours a day is the average student spending in a “sit and get” instructional mode? The next question to ask is, “What practices can teachers use to transfer ownership of learning back to students?”

The first step in sharing authority with students is to recognize that it is something worth working on in our practice and this work is a continuous process. Write the words “Shared Authority” on a sticky note and put it in the middle of your desk. This will remind you that every day you need to take one tiny step toward that goal. Team roles are a familiar strategy and a good place to start to get students to take responsibility for their learning and in sharing authority. Think about one responsibility you can give to students when they are in breakout rooms. Remember, however, that sharing authority is not just giving students responsibilities, it is also allowing them to make mistakes and supporting them to productively struggle without taking over their thinking.

Another practice that I often share with teachers is Talk Moves. To create a culture where students value each other’s thinking as a stepping stone to their own learning, we must first use strategies to get them to listen to each other. Then we need to support them in building from each other’s thinking. Talk Moves can help teachers address many of the student actions listed in Section Two of CPM’s Implementation Progress Tool (Image 2). Teachers who use Talk Moves and reserve their own evaluation of a student answer are transferring math authority to students and creating a culture where collaboration drives learning.

Problem-Based Learning

Students and teachers share math authority as they value and engage in productive struggle. Teachers guide without taking over the thinking.

Students demonstrate and value both conceptual and procedural knowledge.

Students look for, compare and connect multiple models and solution strategies.

Students recognize that incorrect work can be a stepping stone to learning and are willing to share and investigate their thinking.

Talk Moves


The most common type of teacher-led discourse is IRE. The teacher Initiates a question, the student Responds, and the teacher Evaluates the response. This type of discourse is a widely used technique but valuable only in a limited number of situations. Here is an example: 
Teacher: “Can someone tell me when the test is.” 
Student: “Tuesday.”
Teacher: “Correct.”

However, in most cases IRE is not very effective at getting students to think or, for that matter, motivating them to try. There is too much risk and it casts failure as a negative experience. In addition, it positions the teacher as the only one in the room who can determine what is correct. Talk Moves are a better choice. These ideas were presented by Dr. Leslie Dietiker at the CPM National Conference in 2018. Dr. Dietiker is a professor at Boston University, a CPM author, and the principal force behind CPM’s curriculum storylines.

The secret to Talk Moves is not to evaluate, but to get students to build on each other’s thinking without acknowledging if the response was right or wrong. Talk moves can work at the small team level or in a whole class discussion. Here are the four types of talk moves. (O’Connor, Andersen, Chapin)

Elicit Student Thinking (What are the students thinking and saying?)

  • Turn and Talk: “Share your thinking with your partner”
  • Revoicing: “Are you saying that…?”
  • Say More: “Could you give us an example?” or “Would someone else say that in their own words?” or “I’m not sure I understand what you are saying. Could you say more?”

Orient Students to the Thinking of Others (Are the students listening and understanding what others are saying?)

  • Repeating: “Who can repeat what was said?”
  • Sharing Out: “What did your partner think?”
  • Surveying Access: “Can everyone hear what is being said?”
  • Focusing Attention on Student Thinking: “As we listen to this response, think about how it is the same or different from what we talked about yesterday?”

Deepen Student Understanding (How can I make this more meaningful?)

  • Press for Reasoning: “Why do you think that?”
  • Having Reasoning Repeated in Multiple Ways: “Who can put that in their own words?”
  • Find a Student Who is Unconvinced: “Erin is not convinced. Who can explain why that is true?”
  • Turn and Talk (prompting students to make sense of reasoning): “Talk about Marla’s idea.”

The pandemic has forced many teachers into systems where circulation and study teams are difficult. Teachers have had to try to transfer many practices that successfully allowed students to take ownership in their math learning to virtual or socially-distanced environments. These practices may now seem a low priority, but it is more important than ever to focus yourself and your students on what it means to share authority. Carefully examine the Problem-Based Learning pillar on the Implementation Progress Tool for ideas on student and teacher actions that would support this work.


Michaels, Sarah and C. O’Connor. (2015). “Conceptualizing Talk Moves as Tools: Professional Development Approaches for Academically Productive Discussions.”

Chapin, S. H., O’Connor, M. C., Anderson, N. C., & Chapin, S. H. (2013). “Classroom discussions in math: A teacher’s guide for using talk moves to support the common core and more, grades K-6.”

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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.