Engagement in Math Learning
Phase 3

Where we stand on the Double Diamond

Selecting our problem of practice put us in the middle of the double-diamond process. At this point, we chose a grade level of math we wanted to focus on and mapped in the Alberta curriculum. For field IV, we are all returning to teach grade 5 math so this was an obvious focus for all of us. We then chose two design approaches to explore to help find a solution on how we might motivate students to be more engaged in the math discipline. We chose Universal Design for Learning (UDL) and Design-based Inquiry (DBI). Within the UDL approach we explored the Shape and Space Unit in grade 5 math and within the DBI approach, we explored an interdisciplinary project that involved Data Analysis (math) and Weather (science).

Design-based Inquiry

After selecting a topic to explore, Data Analysis and Weather, in this case, we begin by asking ourselves some core questions about the topic. These include;

  1. What matters about this topic?
  2. Who cares about this topic?
  3. What are the issues surrounding this topic?
  4. What are the problems that are unresolved?

Answers to these questions helped us choose possible directions we could take our topics of interest. By narrowing in on what these topics meant to us, we could begin to think of possible learning outcomes that would interest us and our students. The last questions specifically were insightful because answering that question about any topic would mean that the answer would be relevant and require critically thinking to answer.

Once we knew in which direction we were headed, we could begin to think of possible inquiry tasks students could do related to the topic. This allowed us to dream up amazing things students could do any sort of work backwards. Instead of thinking about how I would start teaching this topic, which is a very overwhelming thought, we instead thought of cool things students would love to create. In that dreamt up creation, we would then think of how to get students there but brainstorming subtasks and scaffolding steps. Collaborating with a peer was also very helpful during this step because they could provide other ideas from a different perspective.

This step went hand-in-hand with the step of thinking about disciplinary identities, related to the topic, within students could work and complete the tasks/projects we brainstormed. Essentially, if the tasks we dreamt up could somehow fit into real-life identities, then they would naturally be meaningful and relevant.

This is was a huge “aha” moment! A lot of students and teachers treat math exclusively and cannot see math problems existing outside the classroom walls. This makes math boring and gives it no purpose! The discipline-based inquiry approach forces the designer to insert those math topics into real-life tasks and identities, thereby giving them life outside the classroom. Giving students the opportunity to sample the math discipline in a way that transports them into a different identity is massively appealing for us as designers and will be much more engaging than completing worksheets with the aim of acing an exam.  

Universal Design for Learning

After selecting a topic to explore, Shape and Space in this case, we begin by analysing and interpreting the three UDL principles and the nine guidelines spread across within them. The guidelines read to us as if they were trying to answer our problem of practice. For example, if we could provide options for physical action (guideline 4), then we might motivate students to be more engaged in math. Reading the guidelines with this lens really made this approach easy for us.

All we had to do was brainstorm how these guidelines might fit in with the topic we selected. So we started selecting specific guidelines in which we could envision creating tasks related to shape and space. Some of the guidelines stood out more than others so we evidently focused on those more. With the general and specific outcomes of the shape and space unit in mind, we dreamt up a task that we would focus on. The task will ask students to create a structure using a given material that can support a given mass. Within this task, we could incorporate many of the specific outcomes within this math unit.

With this task in the forefront of our minds, matching the guideline indicators became easier and we could really envision how a unit plan or lesson plan might be designed to encompass many of the UDL guidelines. Exploring this design approach led us to realize that we could also incorporate the DBI approach. Instead of just creating a stand-alone task, lesson, or unit that fit in with UDL principles, we could take a step further and make that task, lesson, or unit design a life outside the classroom. Our task of creating a structure could exist within a unit design that asks students to think, design, and create as architects do in the real world. This was our “aha” moment!

Like the DBI approach, we really had to think of tasks that were meaningful but this task explicitly made us think of elements of the task itself that were not present in the DBI approach. For example, in which modes can we present our information as a designer is an explicit question we answer within the UDL approach. However, the UDL approach is made stronger by incorporating the foundational idea of a discipline-based inquiry. In the end, we ultimately decided that utilizing both Universal Design for Learning and Discipline-based Inquiry would give us the best support in finding a solution to our problem of practice.

Using two different topics in math to explore the different design processes allowed us to sample the elements of both. This was extremely helpful because each exploration process helped us generate solutions to how we might motivate students to be more engaged in math. However, we decided to focus on the Shapes & Space topic because teachers may not always have the opportunity or resources to do an interdisciplinary project. By focusing on the math discipline exclusively, we hoped to show that even when math exists alone it can be engaging for students. We began with our building structure idea which evolved into using playing cards as the building materials.

Card Structures Lesson

We wanted to create something that was aligned with the ideas we generated in the design process. Whatever we created had to involve some hands-on activity, permit the students to create as they desired, have a real purpose that they cared about, while all the time being connected to the curriculum. Building a structure using playing cards is what we came up with. This activity could fit within these criteria and therefore be engaging for students. With this in mind, we tested out how it might look and feel like in the classroom and set out on making a lesson or unit design that revolved around this task.

Phases of an Architect

The task was a great start and got the ball rolling but it was still lacking some greater real-world connection. We could draw connections to the architect discipline but we needed to make it more explicit. That’s why we decided to come up with a unit design skeleton. We asked ourselves, how might this task look if it existed within the Shape and Space unit. We mapped out a very rough sketch of our thought process modelling it on the real-world design process of an architect. Keeping true to the curriculum, we tried inserting as many elements of what might motivate students to be engaged with this design. In the end, our rough design became to be a discipline-based inquiry skeleton in which we could weave in hands-on activities, student autonomy, and have it all be student-centred.

Advice & Feedback From ‘Experts’

We shared our ideas with a couple of certified elementary teachers in Calgary to strengthen our prototype. Their insights are shared below and will be incorporated into our final deliverable in the last phase of the design thinking process.

Ms. Harmeet Kandola, Early Childhood Teacher


  • Extend the hook to apply restrictions and discuss how changes can affect the structural design.
  • Have students do an “expert study” as one of the assignments. Analyze an architect!
  • Cross-curricular elements – A writing component for ELA or an Arts component within the construction drawings/building.
  • Differentiation – Some students may need a range to work within. Define parameters and boundaries.
  • Incorporate a lot of self and peer reflections throughout the process. This should include self and peer assessments.
  • Student-led – Work with the students to create a rubric. Guide them into deciding what a good design should have.

Mr. Philip Tuck, Werklund School of Education Professor

  • Include a narrative that references pop culture that the students can relate to. This will get students more engaged and wanting to participate.
  • Work in real-life problems of an architect like availability of resources, budget, location, etc. These elements of the profession can mesh with the narrative you build as a class.
  • Implications for teaching. This design can exist exclusively in math but can also be extended to incorporate the science curriculum. This would require teacher collaboration and a great deal of planning but definitely possible
  • The hook (Card Structure Lesson) can act as a pre-assessment. It could inform the teacher about what skills the students have in building, what knowledge they have about measurement and shapes, and what sort of structures they are interested in building.

Phase 1

By using a peer interview method, we were able to collect as much data as possible on our teaching process and specific issues we face in our classrooms. Collaboratively, the information gathered from the interview was analyzed and used to generate as many potential problems as we can think of.

Phase 2

Looking at all the proposed problems from phase 1, we converged and isolated on the core problem. This core problem is put into the statement of “How might we…”

Phase 3

Using 2 design processes, we mapped out the solution and how it is connected to the curriculum through the Programs of Study.

Phase 4

The final product or an example of the solution is produced in this phase.


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