Oct 29, 2016 Elisa Romeo & Angelica Mendaglio


The Fields Math Education Forum October meeting focussed on a single project called the Grade 9 Applied Mathematics Collaborative Inquiry Project. The project was a joint effort from the Ministry of Education, OAME, OMCA, and researchers at the University of Ottawa to document and support different teacher strategies in grade 9 applied math classes to improve student success.

The project involved teams from different schools across the province - teams included administrators, math department heads, 2-3 grade 9 applied teachers, special education teachers, and student success teachers. The teams met for 1 full day monthly to determine a focus for their classroom work for the next month. Different teams chose different focuses - the role of the project was to support with resources, research ideas, or other elements that the teachers may find helpful to their pursuits.

At the forum, we heard from many sides of the project - a ministry representative, a school board representative, researchers, and a team of grade 9 teachers who were involved with the project. Hearing from many different perspectives helped to give a clearer picture of each facet of the project.

Why Grade 9 Applied?

Alison Macaulay from the Ministry explained that grade 9 applied students have been consistently performing lower than students in Grade 9 academic students on the EQAO tests


Slide from Alison Macaulay's presentation

The College Math Project 2008 also found that students who enrolled in applied math in grade 9 or 10 are more likely to be at risk when they reach a college program. icme

Slide from Alison Macaulay's presentation

The grade 9 teachers who spoke at the Forum also said that students in their grade 9 applied classes often have negative attitudes towards math and their own abilities in math.

Benefits to Teachers

The principal benefit of involvement with the project that we heard from teachers is the time and support they were given to focus on their teaching strategies. Teachers found that having a team of like-minded colleagues working together made their experience much richer than it would have been otherwise. Teachers would often visit each other’s classrooms to observe how the lesson plans were working. We also heard that working in a group helped teachers to keep their work in perspective - if an idea did not work well, the teachers were less likely to take it as a personal failure and use it instead to critically assess the lesson. The involvement of school administrators in the project also seemed to give teachers a feeling of security when trying new things in their classroom, because they were confident that the administration understood and was on board with the project.

Underlying Theories of Project Based Learning

Growth Mindset

In her research, Carol Dweck explored ideas of Growth and Fixed Mindsets which play a major role in student success. The teachers involved in this project wanted their students to overcome the idea that their abilities are fixed (Fixed Mindset). For example, students believing they are or are not born “good at math.” Fixed Mindsets are dangerous because they prevent students from learning before they are even presented with course content. On the other hand, students who adopt Growth Mindsets understand that they can develop any skill as long as they believe they can and put in the needed time and effort. Students who show Growth Mindsets are mindful about the language they use when describing their abilities. Phrases like, “I can’t do this” are replaced with “I can’t do this YET.”

In order to help students understand that mistakes aren’t “bad,” but rather learning opportunities, the teachers in this project created an activity called Famous Failures. This activity allowed students the opportunity to understand what mistakes had to happen in order for them to get to get where they needed to be.

Spiral Curriculum

The spiral curriculum explored by Jerome Bruner was also embedded in this project through the use of rich-tasks. The spiral curriculum allows students to revisit the same material but in more and more detail as they progress in school. Thus, given the same rich-task, a student could approach the problem differently depending on their grade level. A fundamental idea to the spiral curriculum that follows suit with Growth Mindset is that anyone can learn anything as long as the material is well presented and structured. For example, if a kindergarten student can share their blocks, they are able to grasp the idea of equality.

Vertical Non-Permanent Surfaces (Whiteboards)

Students often worked on math problems in groups and standing at a whiteboard. Whiteboards are (almost) risk-free as you can always erase what you wrote. Paper isn’t as forgiving. In these situations the teacher takes on the role of facilitator rather than course expert. This allows students the opportunity to learn from each other and understand mathematics to be collaborative and socially constructed. A strategy that was adopted by one of the teachers is that that the person who writes on the board can’t do the talking. As the teacher, you are able to see what your students are thinking and address any misconceptions as they come up.


Teacher team's presentation - Students working in a "vertical classroom"

Rich-Tasks/Activity Based Learning

Rich-tasks are tasks that have multiple entry points. The more open-ended they are, the more they can be used across grade levels and diverse learners. In this project some of the rich-tasks that were used include: a Mini-putt course, algebraic structures (Crazy Forks), The Border Problem, The Painted Cube and Dan Meyer’s Gummy Bear.


Dan Meyer Gummy Bear Problem - How many regular bears would you need to eat to match the super-bear?

The benefit to using open-ended tasks is that they are cross-disciplinary. Students may approach the problem using knowledge from art, science, music, etc. Moreover, open-ended tasks develop student’s number fluency since students work with concrete manipulatives first and then develop strategies that make sense to them rather than memorizing an arbitrary sequence of steps. Drawbacks to rich-tasks include the time needed to create, implement and assess them, a noisy classroom, resistance from parents who are comfortable with rote math and a lack of support from administration. Considering that time and teacher training are the biggest roadblocks, it’s important to think about how you can effectively embed rich tasks into the classroom. Set a goal for yourself to try it out with a colleague. It might be planning a rich-task for a unit, month or big idea. What’s important is that as educators we take risks, just like we ask our students to do everyday!

Since this project was aimed at students in grade nine applied math, a question was raised about its relevancy and effectiveness in teaching students in academic math classes. Does Activity Based Learning work for students in the academic stream?

Before answering this, we have to remember why Activity Based Learning was implemented in the first place. The goal of this initiative was to increase student success by providing concrete opportunities for students to think on their own, make mistakes, develop strategies to solve math problems and collaborate. We can’t forget that these skills are not exclusive to Project Based Learning. In fact, these are fundamental to learning any skill. Even if a student in academic math scores well on their tests and is able to follow along in class, we shouldn’t make the assumption that these Project Based Learning experiences are unnecessary or not valuable to their learning.

Passing on the knowledge

Many teams extended their strategies to their classes in other grades and academic classes. We also heard that some teachers involved the grade 10 teachers from their school, as well as grade 7 and 8 teachers at their feeder schools. The feeling was that the strategies that were proving to be effective would also be effective in other classrooms.

Gap Day

Another strategy that was incorporated by the teacher team during the project was used to review material before tests. The teacher finds experts before a test to lead students in small groups through practice test questions. The student might be an expert for one question and need support in another. The benefit to this is that students learn from each other, and that some students who are weak overall are still able to take on a leadership role and improve their Growth Mindset.


Assessment for rich-tasks can be a challenge for many reasons. A big one is how to assess the solution for a question when there are multiple approaches. What does the student need to do to show their thinking? A strategy used by the teachers is to co-construct Success Criteria with their students.

For homework and tests, teachers implemented the Four Block Problem to help their students work through their thinking. If a student could use it for homework, why not a test? The Four Block Problem forced students to read the problem, decide and record what they know and need, create and carry out a plan, and explain their reasoning. Through the Four Block Problem, teachers went from seeing blank pages to attempted solutions.


Key Reminders

The main take-aways from the Forum for us were:

  1. It’s the lesson that failed, not you!
  2. Everything doesn’t have to be a rich task - use them to get across a big ideas.
  3. Mathematical thinking tools are for everyone, not just “struggling learners.”
  4. A task itself isn’t rich - it's how you use it.
  5. A good rich-task has multiple entry-points.

You can find the videos of the presentations here. The next Fields Math Education Forum will meet on Saturday November 26.


- Five Practices(Smith and Stein, 2011)

- Connecting Mathematical Ideas (Boaler and Humphreys, 2005)

Elisa Romeo and Angelica Mendaglio

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