Using Thinking Tools to Promote Deep Mathematical Understanding

Area(s) of Focus: math
Division(s): Intermediate
Level(s): Grade 7, Grade 8

Using thinking tools and meaningful rich tasks to support students’ conceptual understanding of big ideas, as well as improve student engagement and learning.

We were seeking time to learn, co-plan and create meaningful, rich tasks using a variety of thinking tools that provoke critical thinking, problem-solving, innovation and creativity. We believe the use of these thinking tools deepened students’ conceptual understanding of the big ideas. We then shared our learning to colleagues across our school community in order to better student learning experiences and deepen equity and inclusive education practices.

Team Members

  • Heidi Schrier

    Peel District School Board

  • Vesna Kacurov

    Peel District School Board

  • Valerie Lyon

    Peel District Schhol Board

Professional Learning Goals

Our overall goal was to understand how to effectively teach different math concepts by using a variety of math thinking tools in order to deepen the students’ understanding of mathematics. We wanted to co-create cross-curricular rich tasks (with multiple entry points) that provoke critical thinking and problem-solving, innovation and creativity in the solutions from two or more math strands (and possibly other subjects). Our idea was to deepen our understanding of learning outcomes so that we can notice and name the specific learning demonstrated by students and share our learning with other interested colleagues. With the use of differentiated learning strategies, we were able to include all learners and deepen equity and inclusive education practices and increased competency in assessment for, as and of learning.

Activities and Resources

Our TLC team met on regular basis and participated in a variety of sessions that aided in achieving our goals. Release days were the key to achieving our goals. Our team was able to work collaboratively to test-drive thinking tools, co-plan and co-teach lessons, co-create meaningful rich tasks that involve social justice issues and Indigenous people,  and had time to get creative exploring/learning through reading, “doing” and “making.”

Many of the activities, tasks, and tools we explored were incorporated into our daily teaching practice. Here is a list of the activities and resources from our project:

  • PD with instructional coach (creating rich tasks and spiralling the math curriculum)
  • Time to co-plan, co-teach, team-teach and work on assessments
  • Time to explore and discover (play with manipulatives and thinking tools)
  • Read books/articles and watch online tutorials to help us use additional apps/technologies in the classroom
  • Math newsletter (see picture of samples): student choice of math concept
  • Different manipulatives and math tools for kids to use (including “thought journals”)
  • Conduct teacher-facilitated sessions (for teachers and parents – Math Night)
  • Use of  Makerspace where students applied learned math concepts
  • Attend board PD opportunities
  • Opportunities to share our learning with grade-level colleagues

Unexpected Challenges

Since all the activities were purposefully planned and timed, we really didn’t feel that were any activities that were not helpful. We do feel we met all our goals. One challenge that we had was working around the different busy schedules and finding time that works for all of us.

Enhancing Student Learning and Development

Our project enhanced student learning in many different ways. First, student learning and development was enhanced through the use of thinking tools, manipulatives and thinking journals in the classroom. These tools helped deepen the students’ conceptual understanding of many different math concepts and big ideas. Next, students were more engaged and more motivated through the use of cross-curricular rich tasks (with multiple entry points) that provoked critical thinking, problem-solving, innovation, collaboration and creativity. Through 21st century learning such as inquiry- and design-thinking, as well as knowledge building, students demonstrated deeper conceptual understanding of the big ideas through using the thinking tools. The student learning environment fostered a safe space for co-learning and encouraging a growth mindset. Through spiralling the math curriculum and including cross-curricular connections and Indigenous and First Nation resources, students were able to make authentic connections to real-world ideas, thereby enriching student learning.


Share Out #1: Our TLC group met with grade-level teams in a day-long PD session to introduce staff to the math spiralling which gave teachers time to learn and perhaps try and integrate into their classrooms. As a team-level group, we continued to add resources to the already existing framework and which will be used in the coming school year.

Share Out #2: For the upcoming school year, we are planning to share our learning and project results with our grade-level colleagues during grade-level team meetings. Since there are a few new colleagues who are teaching math for the first time (or are teaching the integrated model for the first time), we think that it is a great idea to share our learning as well as our resources and projects with them.

Project Evaluation

We consider our project successful since we achieved the majority of our goals. We now feel very comfortable working  with meaningful, rich tasks using a variety of thinking tools that provoke critical thinking, problem-solving, innovation and creativity. We believe the use of these thinking tools deepened students’ conceptual understanding of the big ideas. Not only did our students enjoy using the tools and working on the tasks,  but they were also more engaged and involved in their own learning.

If we were to do anything differently, it would be to integrate more subjects (e.g., art) into the rich tasks. This is something that we will continue to work on during the upcoming school year.

Resources Used

From Patterns to Algebra: Lessons for Exploring Linear Relationships by Dr. Ruth Beatty and Dr. Catherine D. Bruce

Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching
by Jo Boaler