Collaborative Accountable Talk

Establishing a Culture for Mathematical Literacy

Inquiry Theory of Action

How can accountable talk in a collaborative learning environment enhance student mathematical literacy and help develop more explicit communication of thinking processes?

The Reflective Practioner:Student Work Study Initiative (SWSI)

Garthwood Park Public School


Collaborating Teachers (CT)


Kimberley Allevato-Burt, Grade 1, Garthwood Park Public School


Julia Armitage, Grade 3, Garthwood Park Public School


Student Work Study Teacher (SWST)


Salima Khan

Collaborative Inquiry:

Through the inquiry process teachers have discussed student work to determine GAPS in numeracy. The findings indicated a need for engaging students in collaborative inquiries and Accountable Talk in Mathematics in order for students to become better able to communicate their thinking.

The greatest areas of need were in students’ articulation of their thinking and comprehension of information received either from text or from auditory lessons, keeping in mind ELL and Special Needs learners. Instructional strategies were reviewed and teacher reflection indicated a need for establishing positive collaborative learning environments and explicit instruction of accountable talk strategies, such as talk moves. Students are provided with rich, problem solving tasks that are responsive to the culture and learning styles of individual students. Greater engagement in 'accountable talk' through establishing cooperative learning norms in the learning environment enabled students to make their thinking visible and demonstrate a growth in mathematics levels.

Grade 1

We first establishing a cooperative learning environment where students felt safe and accepted in order to share their mathematical thinking. It began by asking the students to brainstorm what Cooperative Learning looks, feels and sounds like. The students generated many ideas which were recorded and then in three groups with a teacher-helper, the students grouped them to determine common themes. After the students generated with guidance 'learning stems' to assist with common language and vocabulary around mathematics discussions.


An image of the bulletin is found in the reflection section below.

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Grade 3

The teacher and students used accountable talk prompts or sentence starters called "Learning Stems" to help students find words to discuss math problems together.

Learning Stems Looked like:

I agree with ____ because...

I disagree with ____ because...

I want to add to what _____ said about ....

I still have a question about ...


*These stems and more found in the Accountable ToolKit Resource found in the above HaikuDeck on resources*

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Reflective Discussion: Theory into Practice

In traditional collaborative inquiry, the Theory of Action, follows an "If...Then" statement where, if this is put in place, then there will be a specific result based on that action. Kimberley and Julia have been a part of the SWST initiative since 2013. They have engaged in collaborative inquiries through the SWSI and upon reflection of this experience have come to realize that while the theory of action in essence is valid, there has been a shift in the mindset of the casual relationship. Based on the needs and the experiences of the individuals, many foundational practices and strategies were implemented. They realized that while there was one cause, it yielded multiple effects.

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Reflective Discussion: Scaffolding and Descriptive Feedback

According to Jo Boaler's 7 Positive Norms in Math Class, "Depth is more important than speed" where providing students with opportunities to engage in math at their level and in their zone of proximal development allowed us to go deeper into the learning. In addition it allowed for descriptive feedback to be more impactful as students were given many opportunities to act upon the feedback provided, as opposed to providing feedback but no opportunities to try out the suggestions.

Reflection Discussion: Learning Stems

Our experience is the students weren't engaging in meaningful talk around mathematical problem solving. When the' Learning Stems' were introduced to facilitate cooperative learning the students had great ideas and they now could vocalize them in a common language. Some scaffolding and modeling was required to reach every students at their entry point. There was mutual understanding and students were learning from each other.

The students used the learning stems in Grade 3 to interact with each other and in Grade 1 they were co-constructed with the students in friendly-language. The students were also becoming more comfortable sharing and talking with their peers with and without the learning stems.


The following are the student generated learning stems from the Grade 1classroom

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Digging Deeper into the Inquiry Going Forward

The three of us engaged in rich discussions about what we are noticing in the inquiry and where we would like to see it going in the future. Here are some of our wonderings:


How are we closing the gaps in assisting students in becoming mathematcians who can engage in mathematical discourse?


How much opportunity are students given to practice accountable talk? We have taught them the language, how do we get them to internalize and make it their own?


How can the common language become a part of their schema so they can apply what they have learning about cooperative learning into all areas of subject matter and the world?


The thinking process takes time to develop and sometimes are we asking a lot? How do we assure we are meeting students in their zone of proximal development and still maintain the curriculum and high expectations?

Critical Thinkers

How are we assisting students become critical thinkers?

Critical thinkers as defined as:


"Critical thinking is constructing your own meaning and learning based on what you have just learned where the processes is more important than the answer"


What we noticed is that the answer is still very important for the students and they are not asking questions to understand how they got there or how their peers got there. When they ask more questions for clarification and for greater understanding they fill their backpack with more strategies they can use in other problems.



Our next inquiry is to look at how to ask good questions for understanding processes? How to ask effective questions for deepening their understanding?

Developing Critical Thinkers through Questioning


Our next inquiry is to look at asking effective questioning:

How to encourage students to ask good questions for greater understanding?

How to ask relevant questions for deepening their learning and collecting more ideas and strategies that can be used in real world problems?

Rubik's Cube: A question, waiting to be answered

Authors: Peel District School Board Teachers

Kimberley Allevato-Burt - PDSB Teacher

Julia Armitage - PDSB Teacher

Salima Khan - PDSB Student Work Study Teacher