Thinking in the Math Curriculum

Area(s) of Focus: math, curriculum
Division(s): Primary, Intermediate
Level(s): Grade 3, Grade 7

The project identified thinking in the math curriculum. It Increased teacher efficacy by deepening their understanding of the cognitive demand on student thinking when solving a math problem (process of thinking).

  • Identifying thinking in the math curriculum by categorizing thinking questions
  • Identifying and naming the thinking (cognitive demand) in a given math question/activity
  • Naming the types of thinking (e.g., representative thinking, conceptual thinking, etc.)
  • Creating questions to target certain types of thinking
  • Exploring what makes a good thinking question

Team Members

  • Tracey Brent

    Peel District School Board

  • Sonia DiBiase

    Peel District School Board

  • Christine Kohse

    Peel District School Board

  • Ariana Khan

    Peel District School Board

Professional Learning Goals

  • Deepened our understanding of mathematical thinking
  • Examined what is thinking in the math curriculum (develop categories of thinking such as representative thinking, structural thinking, conceptual thinking, etc.)
  • Developed questions and tasks to target a variety of thinking

Activities and Resources

  • Name the thinking (i.e., creating categories of thinking)
  • Make connections between math processes and mathematical thinking
  • Develop questions and tasks to target the categories of thinking
  • Research current articles and books related to mathematical thinking
  • Breakdown the thinking in math questions/tasks before giving them to students

Unexpected Challenges

  • Documenting student thinking in the moment
  • Changes to participants on the project (e.g., sick leave and maternity leave)
  • Time (e.g., need additional days and scheduling)

Enhancing Student Learning and Development

  • Expose students to different types of thinking
  • Students are more comfortable with talking, sharing their thinking and disagreeing with others
  • Some students are more aware of their thinking (e.g., students are pausing to think before responding)
  • Students are developing different types of thinking skills (e.g., using their procedural understanding to solve constraint thinking questions or to make connections between different concepts)


  • Share with colleagues at leadership conference in Peel
  • Share with colleagues at OAME
  • Share with colleagues at staff meetings
  • Share the learning process on Twitter

Project Evaluation

  • Cross-school collaboration allows for exchange of different/alternative ideas
  • Increase teacher knowledge about thinking (e.g., different types of thinking)
  • Encourage teacher discussion and reflection on thinking in the math classroom
  • Expose students to different types of thinking
  • Students are more comfortable with talking, sharing their thinking and disagreeing with each other
  • Teachers will be more proficient in providing a variety of thinking questions to address student needs
  • Support teachers in intentionally planning and thinking about math questions differently and varying the types of thinking
  • Differentiating thinking in the classroom allows students to develop other areas
  • Additional time to continue to develop questions to be used in the class

Resources Used

Krpan, Cathy Marks. Teaching Math with Meaning. Pearson, 2017.

Fiore, Mary and Lebar, Maria Luisa. Moving Math: How to Use Thinking Skills to Help Students Make Sense of Mathematical Concepts and Support Numeracy Development. Pembroke Publishers Limited, 2017.

Small, Marian and Tomlinson, Carol A. Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom. Hawker Brownlow Education, 2017.

Hattie, John et al. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning. Corwin Mathematics, 2017.

Small, Marian. Teaching Mathematical Thinking: Tasks and Questions to Strengthen Practices and Processes. Teachers College Press, 2017.

Sousa, David A. How the Brain Learns Mathematics. Corwin, a SAGE Company, 2015.

Carpenter, Thomas P. et al. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Heinemann, 2017.