Celebrating Math With Demonstrations of Learning

As math teachers, how can we help students reflect on and celebrate their learning from the year, while ensuring that they are set up for success in future learning? I have relied on demonstrations of learning that allow my students to create something and see the culminating learning experience as a core memory.

What Are Demonstrations of Learning?

Demonstrations of learning, or DoL, are less than five minutes long and demonstrate a student’s (mathematical) learning through four communication competencies: content knowledge, clarity, cohesiveness, and captivation. Students are given an option to provide an in-class presentation or create a video (most students choose to create a video, since contemporary learners like creating content). The videos that my students create are either live-action videos like this fantastical drama or animations like this one, shared with a lens on sustainability.

Beginning with the end in mind, student demonstrations of learning should be luminous, delivered with clear and cohesive communication of content knowledge in a captivating way. In order for a DoL to be luminous, the four communication competencies must work in harmony with each other. 

When mathematical content knowledge is shared with

• clarity, a student demonstrates mathematical literacy;
• cohesiveness, a student demonstrates nuanced reasoning or problem-solving process;
• captivation, a student demonstrates mathematical rigor.

When clarity is shared with the other communication competencies of

• cohesiveness, a student demonstrates articulateness;
• captivation, a student demonstrates something fascinating.

When cohesiveness is shared with the other communication competency of

• captivation, a student demonstrates gripping storytelling, interactivity, and/or musical elements.

If one communication competency is missing, it all falls apart. Without content knowledge, one is delivering misinformation. Missing clarity? The DoL will be incomprehensible. Not cohesive? It’s scattered. What if it lacks captivation? Boring.

To help students visualize their interconnectedness, I’ve created explicit slides for how each of the communication competencies harmonize to create a luminous DoL.

DoL Instructional Sequence

Once it is time to create their DoL, students go through five key stages:

1. The elevator pitch. Students find their real-world application and share their hook. To spark creativity, students come up with as many ideas as possible. Simon Sinek’s Starting With Why helps inform our pitch delivery.

2. Storyboarding. At this stage, students first learn the importance of a meticulous backstory (Michael Jr.’s “Know Your Why” portrays this brilliantly). Then, students receive storytelling tips and begin storyboarding, informed with Matt Stone and Trey Parker’s guidance on using but and therefore to make and keep stories interesting. 

3. Content building. Equipped with their storyboard, students (1) record videos using my guidance on clear and captivating content and (2) create slides using Google or Canva to show their mathematical work.

4. First draft. To complete their first draft, my students mainly use iMovie or CapCut as their video-editing software. Then, the formative work begins.

I advise students to “be quick to finish, slow to revise,” with wisdom from Jeff Bezos’s “one-way versus two-way door decisions.” Students learn that it’s important to get to their first draft quickly because in its infancy, their DoL is still a “two-way door” with major edits. However, later on it becomes a “one-way door” for minor edits of meticulous revision.

After students share their first draft, feedback is provided for major edits to restructure their DoL (in alignment with the rubric). The following is common feedback during major edits:

• Content knowledge: Back to the drawing board to ensure that the mathematics used is grade level or up and incorporates sufficient elements of the lesson.
• Clarity: “Show what you say.” Word problems tell, videos show. My students and I discuss how a video is better than pictures. 
• Captivation: “Why do we care?” Why do we care that we saved 41 cents on the better deal? That helped us purchase the Shrek napkin holder we were saving up for. Videos are more captivating when they tell the audience why they should care.
• Cohesiveness: The student creating the DoL will always understand it more than their audience. It’s important to ensure that the audience doesn’t get lost, wondering “Where did that number come from?” or “What does that result mean for the situation?” For example, this student explicitly shares what each value means in their problem-solving, and brings closure by telling us exactly when Mr. Manfre will listen to the same amount of Encanto music as Frozen music.

Once major revisions are complete, students go through iterations of minor edits. The following is common feedback:

• Content knowledge: Ensure that appropriate math language is used.
• Clarity: Incorporate subtitles to compensate for any lack of comprehension (visual or auditory), using explicit animations to direct the audience’s “eye traffic” to where you want them to look in the video or labeling aspects of the mathematical work being done.
• Captivation: Use background music to set the tone/mood, like how the music in this video captures the despair of not being able to attend a Taylor Swift concert.
• Cohesiveness: Animate in one visual the continuum of mathematical work to make it digestible.

5. Final draft. When are students done creating a DoL? When is it turn-in worthy? The success criteria of a rubric are a great tool to ensure that communication competencies are met, though in the end, it all relies on the user experience. We want the audience’s experience to be immersive. If there are deficiencies in the DoL, the audience will shift from immersing (thinking about what is being shared) to critiquing (thinking about how it is being shared).

Earlier this year, my school leader, the Punahou School president, Mike Latham, shared in an after-school meeting, “We don’t teach students what to think, we teach them how to think.” This concise statement represents one profound product of education’s evolution through the Information Age: that as information accessibility grows exponentially, we must support students’ information literacy—how they synthesize information and communicate their understandings.

This evolution equitably emphasizes interweaving skill development in current instructional practices, like cultivating communication competencies in a math class through demonstrations of learning—teaching students how to think, not what to think.