Fostering Mathematical Inquiry and Critical Thinking in Grade 9 Curriculum

Area(s) of Focus: math, well being, curriculum
Division(s): Junior
Level(s): Grade 9

Teachers from Markville set out to revise and enhance the Grade 9 course to incorporate sustaining inquiry and critical thinking with the aim of fostering • Students’ ability to think • Growth mindset • Modern learning • Student achievement

This project addresses the needs of students in Grade 9 applied and academic math.

Research has shown that students have a fixed mindset and fear of math as a result of early experiences learning math in traditional classroom settings.

They believe math ability is determined by their intelligence which cannot be changed.

Continuous lack of success negatively affects students’ self-concept and self-esteem leading to disengagement and further failure.

Successful students in math also suffer from fixed mindsets believing that math requires memorization of algorithms and formulae resulting in a lack of strategies to think and problem-solve in unfamiliar contexts.

Inquiry-based learning has shown success in improving students’ confidence in math problem-solving by providing contextual and relevant tasks and providing richer opportunities for collaboration.

Students need to be taught strategies to think critically.

This project aims to:

  • Engage students in math curriculum through sustaining inquiry with a critical thinking approach
  • Increase teacher skill set in delivering curriculum using sustaining inquiry
  • Foster growth mindset and implement modern learning strategies using digitally enhanced activities
  • Improve student’s ability to problem-solve by teaching students to think critically

Team Members

  • Chris Achong

    York Region District School Board

  • Gordon Li

    York Region District School Board

  • Sonia Joseph

    York Region District School Board

  • Kassie Kei-Baxter

    York Region District School Board

Professional Learning Goals

  • Improved ability to create and implement critical thinking challenges in pedagogy, assignments and assessments
  • Improved ability to used modern learning spaces and the use of non-permanent vertical surfaces
  • Improved ability to engage students in authentic challenges and foster growth mindset in mathematics
  • Revised about 50 per cent of the Grade 9 course and unit plans to incorporate critical thinking activities and assessments to date

Activities and Resources

  • Meetings with Laura Gini-Newman from The Critical Thinking Consortium on numerous occasions throughout the school year
  • Received training on creating sustaining inquiry challenges and how to implement in the classroom
  • Reviewed critical thinking challenges and tasks developed for the Grade 9 curriculum
  • Revised an inquiry-based project deployed in semester 1 and improved upon in semester 2
  • Frequent meetings as a team to create resources for Grade 9 curriculum
  • Created a Math Fair project for the Grade 9 course through which students had a goal of raising money for charity
  • Attended professional development sessions hosted by Peter Liljedahl on “Building Thinking Classrooms” which had a large focus on vertical surfaces
  • Shared classroom observations on implemented strategies and revised pedagogy to improve courses from semester 1 to semester 2
  • Collaborated with another school (Westside Secondary School) to share ideas and resources on critical thinking

Unexpected Challenges

Developing Sustaining Inquiry tasks proved to be challenging as there was a steep learning curve in understanding the framework. The vocabulary from the framework required in-depth unpacking for both teachers and students.

Once a sustaining inquiry project was selected, all pre-existing lesson plans to support the project had to be modified and/or created. This resulted in teacher discomfort as lesson plans were changing daily. Homework that was normally assigned for certain lessons now had to be revised and in some cases homework handouts had to be created to support the new learning goals. Teachers were learning how to implement “on the fly.” Lessons were certainly not polished when delivered in the classroom and it was uncertain if the new lessons were providing a smooth, cohesive understanding of the curriculum expectations.

A Math Fair was created to foster inquiry-based learning. A challenge was not knowing if the outcome would be successful as it had not been done at the school before. Students were allowed to choose their own topics based on linear relations and data management. Unfortunately in semester 1, many of the relationships investigated did not result in a correlation. In semester 2, the teachers investigated known positive and negative correlations, but allowed students to decide how to implement the investigation at the Math Fair. In both semesters, student interest and active participation was high. Grade 9 students gave positive feedback and students in other grades that participated also commented on the uniqueness of the event.

The team had an opportunity to attend sessions on vertical surfaces by Peter Liljedahl arranged by the board.

While these strategies appealed to many teachers, it became a challenge to decide which thinking strategy to keep focussed on. Strategies from Mr. Liljedahl’s sessions were quicker to implement in the classroom, but did not seem to incorporate an inquiry-based model using authentic tasks.  More exploration between the two thinking strategies will be helpful in the future.

To measure success, it was originally planned to anecdotal data from students on their perceptions and view on their ability to think. The challenge was developing appropriate questions in a survey that would provide meaningful measurable data. The team had hoped to launch the surveys early in the semester to capture student info before and after the course. Their item fell by the wayside as the majority of the effort was spent learning and developing lessons. This is an item that could be revisited in subsequent years.

There was a change in one of the teachers from semester 1 to semester 2. This required training for the new teacher which slowed the revision process from semester 1 to semester 2. At the same time, it provided opportunity for a fresh perspective and feedback on what had been done/deployed in semester 1.

Enhancing Student Learning and Development

It was observed that student engagement was high during the inquiry-based learning project and the critical challenges. There was more conversation collaboration among students and they took more ownership of learning.

It was clear through their conversations that students were vocalising their thinking and metacognition. The inquiry-based learning activities were also scaffolded to allow many points of entry so that weaker students could contribute to the discussions.

Habits of mind such as attention to detail, open mindedness, full mindedness and perseverance were constantly reinforced. It also encouraged students to learn from their mistakes in a safe environment.

Students were able to use multiple strategies for solving a common problem, which is a key goal in mathematics.

It is unclear if students improved/increased growth mindset as this is more difficult to measure, but students did gain more confidence in group discussions.

The Math Fair was a success allowing students the opportunity to investigate linear relations with actual data. It provided students a forum for collaboration, creativity, problem-solving and initiative. Proceeds from the Math Fair were donated to a charity of the students’ choosing.

Engagement was improved through the increased use of vertical space strategies in the classroom. Students were more willinging to engage in problem-solving exercises and work with each other.

It is unknown at this point to what extent student achievement was increased from a mark perspective. There was increased achievement in learning skills such as collaboration and initiative. Soft skills such as leadership communication and teamwork were fostered. It is important to be mindful that marks are not the only indicator of student achievement.


  • All lessons developed with the critical thinking framework have been shared amongst teachers in both semester 1 and 2 through formal/informal meetings and via email. Team members met almost daily to review unit plans and lesson activities. Updates to other members of the math department were provided at department meetings and informal discussions.
  • Other schools involved in developing critical thinking and sustaining inquiry were contacted. Ideas, lessons and pedagogical strategies were shared.
  • All resources developed will be put into a team drive and shared through GAPPS with all department members. In addition, any teachers teaching the course in the future will be coached in how to implement the new critical thinking strategies.

Project Evaluation

  • The project was a great success. About half of the Grade 9 course framework was revised to incorporate sustaining inquiry and critical thinking tasks. A Math Fair was implemented in both semesters which continues to be improved.
  • The majority of the teachers in the department received training in the critical thinking framework through additional support from admin
  • Teachers in other courses have also tried to incorporate critical thinking tasks and assessments
  • Continued work in this area is planned to improve the other units in the Grade 9 course and to deploy these strategies in the other courses.  Through this work, it is hoped and anticipated that students’ thinking and reasoning skills will be improved. As a byproduct, their disposition towards math and their math ability will be more positive and growth-minded.

Resources Used

The Critical Thinking Consortium website

Peter Liljedahl’s Building Thinking Classrooms website