A Collaborative Math Inquiry

Making Thinking Visible

Deepening the Understanding of the Student Learning Experience

"The process of building a community of numeracy practice requires a collaborative approach; it begins in conversation about how we might support one another in working with students to develop their full potential in mathematics and it leads to further exploration of the numeracy links across the disciplines."


This report will describe classrooms where students and teachers were engaged in exploring ways to improve their communication skills by making their thinking visible to others. Students’ thinking was made visible through discussions in which students presented and justified their interpretations and solutions to problems presented by their classroom teachers. The Student Work Study Teacher and the host teachers identified the goal(s) for students and developed problem solving lessons using the three part lesson design and rich and engaging problems. The development of students’ skills, abilities and attitudes were followed through a series of classroom observations, conversations and examination of student products. teachers were responsive to students’ needs throughout this collaborative inquiry by making changes to their instructional practices based on what the student work and actions were telling them. The Student Work Study Teacher concluded the inquiry with a reflective questionnaire for host teachers and students.

This qualitative research was conducted in two schools in Mississauga in the Peel District School Board. The time frame for one site was October 2012 until June 2013 and the other was from February 2013-June 2013. It involved students from a combined grade one/two, two grade 3 classes, two grade 4 classes and a grade 5 class. The schools were part of a complement of 22 schools selected by senior administration to participate in the Student Work Study Initiative this year.

Supposition Statement

When students are supported to make their thinking visible they improve their ability to justify and communicate their thinking in authentic problem solving activities.

Definition of Terms:

  • Fostering thinking requires "making thinking visible"- Effective thinkers make thinking visible, meaning they externalize their thoughts through speaking, writing, drawing, or some other method. These thoughts are documented for later reflection so they can be directed and improved upon.
  • Justify: to give reasons, evidence and/or calculations to show why an answer, argument or conclusion is correct. Student achievement and engagement are improved when students have an opportunity to explain, compare, and justify their mathematical thinking. (Fosnot & Dolk, 2006; Kazemi & Stipek, 2001; Turner & Meyer, 2004). When students justify their solutions to others who think differently they gain a better understanding of mathematics.
  • Authentic: The term “authentic” is used to describe using mathematics to genuinely solve a problem as opposed to using it as a “vehicle for practicing some mathematics” (OECD researchers, 2006, p.81).

Purpose and Goals

  • to lead teachers in a collaborative inquiry to determine what strategies are effective for supporting students to communicate their thinking orally, visually and in writing in problem based mathematics.

Students will:

  • be able to explain their thinking clearly so others understand what they mean
  • use math words correctly when they explain their thinking
  • identify the strategies being used and explain why they work or do not work
  • listen to others' ideas so they can learn from each other and provide feedback based on co-constructed criteria

Research Supports and other Resources

"The climate had to be established that it was okay to take a risk; we needed to have a venue to have courageous conversations...the climate is so important because...we were able to talk about our struggles."

"The data or the 'student work' is actually more than just the finished product, (it's) the process, the behaviours, the conversations and the non-verbal and verbal communication."


  • two schools
  • seven host teachers
  • two days a week for four to 8 months
  • document student actions and work using iPad, document camera and field notes

Making Thinking Visible

Students were supported to make their thinking visible using a variety of strategies...

Learning from the Work

What was the difference that made a difference?

Student Voice

“Knowing that you could make mistakes helped me in problem solving”

“As a learner, I feel that I am getting smarter in math and understanding more.”

“It is hard to write down all you are thinking, it is getting easier when I practice.”

“The teachers should continue giving feedback to me ‘cause then I would know what to improve and hopefully I will improve.”

“Try other people’s ideas because there is more than one way to get an answer

Host Teacher Voice

“explicitly teaching and reviewing the learning goals”, “more time spent sharing and reflecting”, “giving students lots of opportunities to practice”

“Revisiting math terms and math bins in order to make connections to math concepts”

“Making math talk valued and important”

“Taking time for students to share their thinking and listening and talking about different strategies”

"Through watching their peers present/share their solutions, my students working through level two became more aware of how to show their math thinking more clearly.”

Key Learning

  • Learning by teachers and students are inextricably linked
  • It takes time, explicit instruction and repeated practice for students to make their thinking visible
  • Focusing on reasoning/justification rather than right or wrong answer allows us valuable insight into student thinking
  • Observation and documentation of student work creates conditions for powerful and engaging professional learning communities.
  • As educators we need to value, create and preserve time for professional learning communities

Created by Avryl McKoy

Peel District School Board