MHF4U: Spiralling in the Vertical Classroom

Area(s) of Focus: technology, math
Division(s): Senior
Level(s): Grade 12

We designed an activity-based, student-centred course plan for MHF4U for our classrooms with vertical non-permanent surfaces. The lessons and activities do not follow a unit/chapter plan, they spiral through the curriculum.

At Glebe Collegiate Institute in Ottawa, a core group of teachers has been teaching the Advanced Functions MHF4U course together for several years. Over the years, we came to realize that the students were spending way too much time watching us do math instead of the reverse and we wanted to make a change. We do most of our planning together and have developed the curriculum in such a way that students spiral through the course.

Spiralling allows the students to frequently review all strands of the course. They are evaluated on all strands through rich questions several times throughout the semester. Last year, we started to shift to more student-centred, activity-based classrooms. Our classrooms have whiteboards on all boards and the students do their activities in groups at the boards. This vertical classroom has changed the way our students think about math class. Our project this year was to have all lessons be activity-based. We used release time to meet as a team to develop the activities and, if possible, do some moderated marking as well. Our main focus was on the design and implementation of the activity-based lessons.

Team Members

  • Janice Bernstein


  • Alexander Overwijk


  • Mike Phillips


  • Barry Needham


  • Thach-Thao Phan


Professional Learning Goals

Our math department at Glebe has been actively sharing current research in math education among its members and teachers across the province. We are inspired by Jo Boaler’s ideas in the Stanford course on “How to Learn Math,” Carol Dweck’s book on growth vs. fixed mindset, Sandra Herbst and Anne Davies’ work on co-creating criteria and finally Peter Liljedahl’s ideas on how to create a learning environment which promotes critical thinking. Our professional learning goals are to facilitate sharing of rich activities, increase student engagement, and continue to improve our assessment and evaluation strategies for the MHF4U course.

Activities and Resources

First we started with activities we had already created or gotten from other teachers.

We met as a team to create activities. One teacher tried the activities in her classes and reported back to the team. Modifications to the lessons were done as needed.

We created a website to share the course plan with activities and references to borrowed activities. The website can be found at:

Unexpected Challenges

One challenge was timing. We expected to receive the funding earlier in the year when the four initial team members were all teaching MHF4U. We only started meeting at the end of first semester. It would have been nice to get the funding earlier so that we had more time to meet. A second challenge related to timing lies with the fact that only one of the four teachers taught MHF4U in second semester. The other three teachers had less time to dedicate to the course as they had other ones to consider for the new semester.

Enhancing Student Learning and Development

The idea of spiralling in a course is very important to student learning.  Traditional unit/chapter-based course plans require students to learn and be evaluated on one topic then put that one aside and move onto the next topic. In spiralling, evaluations touch on multiple strands and overall expectations from the course.  Students do not forget material from one strand because it comes back several times throughout the course. This also allows students multiple opportunities to show their understanding in a strand.

Activity-based learning is much more engaging for the students. With specific ties to curriculum content, rich activities can drive student learning. Using non-permanent vertical surfaces also increases student engagement as they have no choice but to participate at the whiteboard. They cannot sit passively and watch someone else do the math for them.


We shared our project in five ways:

1. We invited another teacher from Glebe to join us as she expressed interest in being involved.

2. We created a Google site to share the whole course plan including the activities and lessons. We shared the link to the Google site on Twitter.  Here is the link:

3. We presented our project at the annual Ontario Association of Mathematics Educators in Toronto.

4. Two other teachers from different schools in our board asked to join the project as well so we will be expanding our collaboration with them.

5. We have received requests from teachers in other boards to find out more about our project. Next year, we will be hosting teachers and math consultants from different parts of the province as they visit our classes and share in our discussions.


Project Evaluation

Our project was successful in that we created a course plan which we shared with teachers from across Ontario. We have implemented many of the activities already. For next year, we will be using this new course plan from the very first day.

We would have like to spend more time on assessment and evaluation.

Resources Used

Peter Liljedahl’s research on Vertical Non-Permanent Surfaces with Random Groups.

Twitter – #MTBoS – which is the Math Twitter Blog-o-Sphere

Carol Dweck’s research on Growth Mindset vs. Fixed Mindset

Massive online course taught by Jo Boaler of Stanford on how to learn math – it is still offered and highly recommended for teachers, parents and students.

John Hattie:

Professor John Hattie is a researcher in education. His research interests include performance indicators, models of measurement, and evaluation of teaching and learning. John Hattie became known to a wider public with his two books Visible Learning and Visible Learning for Teachers. Visible Learning is a synthesis of more than 800 meta-studies covering more than 80 million students. According to John Hattie, “Visible Learning is the result of 15 years of research about what works best for learning in schools.” TES once called him “possibly the world’s most influential education academic.”

Dan Meyer’s work on getting rid of textbook-like questions

Our google site which includes the course plan with activities and resources.

It can be found at:

Resources Created

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