Symmetry Dot Grid

Overview

I completed this project during my mentored internship with MathTalk. MathTalk is a community-based mathematics education organization that utilizes technology, public art, and public spaces to make math come alive for early learners and their families. Over the course of this mentored internship, I worked on two MathTalk projects: this one and the community-based math teacher resources project.

For this project, I focused on one of MathTalk's primary offerings, math installations. These installations are place-based learning experiences that promote conversation and positive math interactions, transforming public spaces into playful early math learning resources.

My Challenge

The MathTalk team selects a set of math installations to revamp every summer. For this project, I supported the user testing and prototyping process related to improving this summer's installations, particularly the symmetry dot grid. User testing took place during a series of community pop-up events.

My Contribution

The MathTalk team started with an initial community math installation prototype to test with local children. My role was to observe the way children engaged with this prototype, collecting data related to their interactions. Then I analyzed these observation data to identify pain points and successes of the prototype. I shared my findings with the team, gathered their input, and made recommendations for improving the prototype. This process resulted in a second iteration to test, and I completed this collect-analyze-recommend cycle again. My final contribution was mocking up a third version of the installation that the team could continue testing with in the future.

My Analysis Goals

Observe the natural engagement patterns of children between about 4- and 10-years-old engaging with the installation.
Identify how and the extent to which each prototype builds child and caregiver capacity to notice, explore, and share the symmetry around them
Ground my analysis and design suggestions in findings from the learning sciences

My Personal Goal

Expand my imagination for connecting math topics to the wider community in culturally responsive and relevant ways.

The Prototypes

INITIAL PROTOTYPE

Sketch of prototype #1

To the left is a sketch of the initial prototype that MathTalk developed to test first. It was created to accomplish the learning objectives below.

Learning objectives:

Children engaging with this dot grid will be able to....

Identify lines of symmetry in the objects on the grid
Draw a symmetrical shape

So they can...

Increase their math play and awareness of symmetry in their everyday lives
Develop confidence in their ability to do (and enjoy) math
Set a foundation for developing a positive math identity

Expected interactions: Young children will examine the example objects in the dot grid and identify their lines of symmetry. Then, they can use the provided chalk to add their own symmetrical drawing to the grid. The dot grid will be large enough so multiple children can interact with it at once. The hope is that the installation will spark a discussion about symmetry between caregivers and children.

Supports: At the top and bottom of the grid are two questions that the children can answer as they engage with the grid, helping them get started and focus on the specific learning goals. A short explanation of symmetry is also available for reference.

TESTING

This prototype was tested during a "Family Math Night" at a local public elementary school in Cambridge, MA.

What we wanted to learn:

Whether/how the prototype enabled children to have fun (Fun-Factor)
Whether/how the prototype enabled children to demonstrate their math learning their the questions they asked and ideas they shared (Learning-Factor)

Photo from testing prototype #1

ANALYSIS

I observed 9 children interact with the prototype. I summarized the engagement patterns across these observations in consideration of the prototype's fun- and learning-factor. These findings were shared with the MathTalk team for their reactions and input and are in the table below.

SUGGESTIONS FOR THE NEXT PROTOTYPE

Theoretical lenses:

As I synthesized my findings with the input I received from the MathTeam, I also used these two areas of the learning sciences as lenses to shape my suggestions for the next prototype:

1. Playful and Embodied Learning

Playful and embodied learning suggests that learning is rooted in the actions of the human body in the physical world.

Design implications: Interactions with this installation should be fun by emphasizing exploration and providing opportunities to engage the whole body. Opportunities for hands-on, open-ended exploration that promotes curiosity and conversations among children and caregivers should be prioritized.

2. Sociocultural Learning Theory

Sociocultural learning theory considers learning to be inseparable from the contexts, practices, and histories in which it takes place.

Design implications: Interactions with this installation should be meaningful by making the connections between math concepts and children’s lived experiences apparent. Additionally, conversations between children and caregivers and/or among children who engage with the installation will deepen the math learning experience.

Other Suggestions:

Add more variability in the symmetry represented in sample drawings could support the development of more sophisticated mental models around symmetry.
Determine how to set up this installation in a way that doesn't rely on access to chalk so that it can be suitable for more settings and the space available becomes less of a limitation.

SECOND PROTOTYPE

Sketch of prototype #2

Based on my and others' suggestions, the MathTalk team developed the next prototype, a sketch of which is to the left. This one had similar, but modified, objectives, listed below (modifications are underlined)

Learning objectives:

Children engaging with this dot grid will be able to....

Recognize instances of both symmetry and asymmetry
Discuss ideas and ask questions with the people around them in ways that deepen their understanding of symmetry

So they can...

Increase their math play and awareness of symmetry in their everyday lives
Develop confidence in their ability to do (and enjoy) math
Set a foundation for developing a positive math identity

Expected interactions: Before engaging with the grid, young children will be provided with a "math passport" (more on this below) that gives a short introduction to the installation: their friend is going on a picnic and only wants to bring symmetrical objects with her. The picnic theme will serve as a realistic premise for looking at this set of objects and learning about symmetry.

With this in mind, young children will then examine each object in the dot grid and identify which are symmetrical. The dot grid will be large enough so that a child can walk across it and so multiple children can interact with it at once. The hope is that the installation will spark a discussion about symmetry among children using it and between children and their caregivers.

Supports: At the top and bottom of the installation there are questions/prompts for children to answer as they engage with the grid, helping them get started and focus on the specific learning goals. Unlike the first prototype, this one does not include any explanation of symmetry because we were curious how caregivers would step in and explain.

TESTING

Testing: This Symmetry Dot Grid was tested at an annual community arts event in Cambridge, MA. This prototype was part of a series of math-based activities that children could complete while completing their "math passport." When children completed all the activities in the passport, they received a "MathBuck," a coupon that they could exchange for a free slush from a vendor at the event. In addition to the "math passport" and the "MathBuck" incentive, this iteration had a couple of other new features that distinguished it from the previous iteration.

What we wanted to learn:

Whether and to what degree the modifications enabled children to recognize symmetry (Symmetry-Factor)
How discussions among children and their caregivers supported learning (Discussion-Factor)

Photos from testing prototype #2

ANALYSIS

I observed 50+ children interact with this prototype. I summarized the engagement patterns across these observations in consideration of the prototype's symmetry-and discussion-factor. These findings were shared with the MathTalk team for their reactions and input and are in the table below.

SUGGESTIONS FOR THE NEXT PROTOTYPE

As I did with the initial prototype, I synthesized my findings with the input I received from the MathTeam and continued to use playful, embodied, and sociocultural learning as lenses to shape my suggestions for the next prototype.

Suggestions:

Make (a)symmetry more apparent for some objects (e.g., if the pizza is included in the 11 items, it needs to have symmetrical toppings).
Feature a simple, image-based explanation of symmetry (like the one pictured right) alongside the installation to support independent engagement.

My Critique of the Initial and Second Prototypes

Overall Strength: Invitations to engage

Observations that the chalk grid filled up quickly in the first version and that there was a consistent stream of learners engaging the second iteration serve as evidence that these designs were successful at inviting learners to engage. In both cases, they were drawn into the design, but for different reasons. In the first, they wanted to add their own chalk drawings to the grid, whereas in the second, they wanted to complete the passport-based mission. Lastly, the design assets themselves were fun, colorful, and interesting to the children engaging with the installation.

Needed Improvements: Addressing the learning objectives

The initial prototype included an explanation of symmetry, but some children had difficulty accessing it. In both prototypes, children who were already familiar with the topic or had an adult (caregiver or facilitator) available who could explain the concept were better able to recognize symmetrical objects and their lines of symmetry. For this reason, I recommend that the next prototype include a simple, image-based explanation of symmetry so all children have access to the same baseline information necessary to successfully engage with the installation.

Suggested Final Design

Based on what I learned from the first two prototypes, I created the mock-up (pictured left) that the MathTalk team could continue testing with in the future. This one had similar, but modified, objectives, listed below (modifications are underlined)

Learning objectives:

Children engaging with the dot grid will be able to....

Define symmetry
Recognize instances of (a)symmetry
Discuss ideas and ask questions with the people around them in ways that deepen their understanding of symmetry

So they can...

Increase their math play and awareness of symmetry in their everyday lives
Develop confidence in their ability to do (and enjoy) math
Set a foundation for developing a positive math identity

Expected interactions: At the bottom of the grid, young children will be provided with a short introduction to the installation: their friend is going on a picnic and only wants to bring symmetrical objects with her. The picnic theme will serve as a realistic premise for looking at this set of objects and learning about symmetry.

Young children will examine each object in the dot grid and identify which are symmetrical. The dot grid will be large enough so that a child can walk across it and so multiple children can interact with it at once. The hope is that the installation will spark a discussion about symmetry among children using it and between children and their caregivers.

Supports: The text at the bottom includes a prompt and a question that children can answer as they engage with the grid, helping them get started and focus on the specific learning goals. A diagram is also available as a resource to explain what symmetry is. These supports are intended to guide children toward success in their interactions with the installation so that they have a positive math experience.

My Insights

Making relatively small changes to a design can profoundly change the way children engage with it and their learning experience.

Both prototypes had the same basic elements: a grid, objects, and prompts intended to develop confidence in recognizing symmetry. They also were in similar settings (playgrounds) and created using the same materials (chalk and spray paint).
Whereas, the first prototype was a more open-ended, stand-alone activity that focused on identifying lines of symmetry and drawing symmetrical objects, the second prototype was more close-ended, part of a series of other math activities, and focused on identifying positive and negative instances of symmetry.
In addition to these differences in format, framing, and learning goals, each instance had its own affordances (opportunities for creativity/story-based math learning) and constraints (needing chalk/needing to identify a certain number of objects) that affected children's engagement and learning experiences.

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