Community-Based Math Teacher Resources

Overview

Over the summer, I completed a mentored internship at MathTalk, a community-based mathematics education organization that makes math come alive for early learners and their families. ver the course of this mentored internship, I worked on two MathTalk projects: this one and the symmetry dot grid project.

For this project, I worked closely with MathTalk and a cohort of elementary school teachers to co-design a teacher resource prototype that supports teachers' capacity to "mathematize the community" for their students and aligns with a set of community-based math teacher professional development (PD) sessions.

"Mathematizing the community" refers to crafting math learning materials that are consistent with students' out-of-school experiences. It entails uncovering the math that students, their families, and their neighbors use in their daily lives and connecting it to classroom standards.

Design Challenge

Because the intention of the project was to co-design with the teacher cohort, my challenge was to:

Support co-design efforts with teachers by co-facilitating focus groups that elicited their ideas about mathematizing the community
Synthesize teachers' ideas with research from the learning sciences to develop an initial prototype of the teacher resource

When developing my prototype, I had to consider how to:

Show teachers what mathematizing the community looks like in the classroom
Guide teachers to mathematize the community in their own classrooms
Align with the MathTalk's PD sessions that the teachers accessing this resource will have experienced
Create a starting point for a set of community-based math resources that MathTalk can develop over time

Example of a Design Solution

I created a resource prototype for teachers who have participated in MathTalk's community-based math PD so that could draw upon the PD topics, discussions, and activities as they applied what they learned to the real-world.

The resource is built around a sorting activity developed by teachers involved in the project. This activity is used to illustrate what is involved in helping students to mathematize their community. The intention for this activity is to serve as an anchoring case study for use by new teachers as they are grappling with mathematizing the community for their own students. The resource has three parts:

An illustrative vignette that serves as an anchoring case study of how a group of teachers went about mathematizing the community for their students and aligns with PD topics and ideas
A set of planning questions to guide teachers through the process of creating their own community-based math activities that was shared during the PD
The set of equity-based practices shared during the PD as "best practices" to embody when creating community-based math activities for students

1. Illustrative Vignette

2. Set of Planning Questions

3. Set of Equity-Based Practices (Best Practices for Community-Based Math)

Learning Objectives

Teachers who access this resource will be able to:

Recognize what community-based math activities look like and what it takes to develop them
Create their own math activities that mathematize the community in ways that enable their students to make connections between their culture, their community, and the math they are learning in school
Value the role that community-based math activities have in strengthening students' math identities and will encourage other teachers to adopt it

Design Conjectures

Learning Conjecture

How I expect to achieve my learning objectives

As teachers access and return to the illustrative case study, complete the planning questions, and reference the equity-based practices, they will recognize, develop, and value community-based math and, over several years, they will gradually develop expertise in mathematizing the community for their students.

Engagement Conjecture

How I expect to invite and sustain participation

As teachers develop activities that make math standards come alive for their students and successfully mathematize their communities, they will experience the value of this approach and be motivated to continue to strengthen their mathematizing muscle and help other teachers do the same.

Impact Conjecture

How I expect to contribute to a better future

Through seeing the process that real teachers used to come up with a community-based math activity for their students, teachers accessing the resource will be inspired to apply what they learned from the PD to leverage their own community's unique assets to create their own authentic community-based math activities that allow more students to access and value math.

Initial Research

Design Lenses

The following areas of the learning sciences informed my ideas for designing the teacher resource.

Communities of Practice (CoPs)

CoPs are groups of people who engage in similar practices and share knowledge and ideas so that they can develop greater expertise and contribute to their field.

What I learned: Teachers need tools to communicate ideas with others and foster collaboration.

Islands of Expertise

Islands of expertise refer to the topics that people are naturally interested in, that they read books about, watch videos about, and share with others, and through this repeated exposure, they gradually develop a deep and rich knowledge of these topics.

What I learned: Teachers develop expertise through repeated interactions with resources, other teachers, and their students. These interactions will lead to go deeper into the process of mathematizing the community for their students as they continue to ask questions and make connections through by returning to the same example over time.

Anchored Instruction

Anchored instruction refers to learning experiences that provide a shared context, often in the form of a story, for learners to explore a problem-rich setting.

What I learned: An anchoring case (like the seed sorting example) can provide teachers with a model for how to adopt a new teaching process, like community-based math.

Educative Curriculum

Educative curriculum refers to learning resources that support students' and teachers' learning.

What I learned: Teachers need resources that support their own learning and support them in enacting a new approach to classroom learning, like community-based math.

MathTalk's Teacher PD

When I started working on this project, MathTalk had already developed a set of PD sessions for a cohort of teachers who would continue to be involved in the project. I attended these sessions and took field notes related to what the teachers did, said, and created.

The PD was part lecture and part activities. The lecture portions covered topics related to mathematizing the community (i.e., identity development, curiosity), and the activities included hands-on experiences, group discussions, and brainstorming initial ideas for community-based math activities.

What I learned: The teachers brainstormed an community-based math activity related to sorting seeds at a local greenhouse.

Teacher Resource Landscape Review

I also reviewed existing teacher resource kits and PD materials related to mathematics. I drew insights from this review to create guidelines around what works well and what should be avoided when creating this type of resource, much of what I noticed was in line with what I learned from the research on educative curricula.

What I learned:

Best Practices

Develop a simple, intuitive interface. Design for easy navigation that facilitates teacher decision making.

Integrate standards or competencies. Reduce the effort of aligning activities and teaching practices to a curriculum.

Practices to Avoid

Piecemeal supports. No pedagogical supports for implementing the activities or explanations for why a certain strategy works.

Lack of collaboration supports. Written for individual teachers to use in isolation.

Design Process

Task 1. Support co-design efforts with teachers

At the initial PD, teachers formed small groups and brainstormed a community-based math activity for their students. One of these ideas was the seed sorting activity. This group of teachers described their activity concept with the whole group. Based on their idea, I created a digital prototype for the activity. Later, when I co-led teacher focus groups, the participating teachers got to try the activity they imagined.

What I wanted to learn:

How do teachers come to value mathematizing the community?
What do teachers imagine needing to enact this type of activity in the classroom?

What I learned:

Teachers value mathematizing the community because it deepens students' connection to math and their identity as mathematicians.

"My hope is that students who are able to see an explicit connection between the real world context and the math of it will deepen their agency as a mathematician both outside and inside the classroom.” - Focus Group Attendee

Teachers imagined needing a range of resources to facilitate this activity in the classroom.

These included

Ways to build complexity gradually
Strategies for differentiating instruction
Prompts and questions that linked the activity to learning objectives
Situating this activity within the overall unit progression

Seed Sorting Activity Plan - Prototype 2.pdf

Task 2. Task 2. Synthesize teachers' ideas with research from the learning sciences

Based on the lenses listed above and what I heard from the teachers in the focus groups, I made my first pass at a teacher resource prototype (scroll through PDF on the left).

At this phase, research regarding CoPs, islands of expertise, and anchored instruction influenced my design: I added a range of scaffolds (e.g. ideas for learning objectives, suggested community connections) that fit together to support a teacher in enacting community-based math in their own classroom.

The design is formatted like an activity plan or lesson plan for the seed sorting activity. It illustrates the result of undergoing a community-based math activity development process.

What I wanted to learn: Does this capture the process of mathematizing the community?

What I learned: After presenting this prototype to the MathTalk team, I received feedback on how to improve the design. Their main concern was that it encourages teachers to use this activity as an "off-the-shelf product." The resource was the activity, not the process of creating the activity.

Per MathTalk's suggestions, I refined the prototype by integrating the story behind this particular activity (the vignette) to explain why it was contextually-appropriate for a specific community of students. I also added scaffolds to support teachers in developing their own community-based math activities, leading to the example solution shown above.

The MathTalk team will show this prototype to the teacher cohort to get additional feedback and ideas. Then, they will continue to refine and build upon it as they prepare to facilitate the PD with another teacher cohort.

Final Thoughts

Critiquing My Design Solution

Overall Strength: Design Justice

The ideas and contributions of the teacher cohort had a critical role in shaping the evolution of the development of teacher resources. Teachers' authority, expertise, and ideas were prioritized in developing the teacher resource prototype. The seed sorting idea and their conversations around it formed the basis of the community-based math resource. To this end, the co-design aspects of the project and the way teachers' ideas came through at all phases of the process made it a good example of design justice.

Needed Improvements: Inviting Learners to Engage

The current resource does not provide any background information around what community-based math is and why it's important. Without this backing, teachers may not be motivated to access the resource. If I were to develop the resource further, I would add introductory information about why mathematizing the community for elementary school-aged students is a worthy endeavor to get teachers' initial buy-in.

Insights that Emerged

It's challenging but rewarding to wait until you know enough about what learners need before designing and prototyping.

I spent the bulk of my time in this internship establishing a foundation for the teacher resource I developed. As a result, I created the first prototype only in the last few days of my internship, which was much later than I initially imagined. However, I didn't have a solid understanding of what teachers truly needed until I watched them complete the community-based math activity and listened to their thoughts about it during the focus group. This information, paired with the baseline research I completed, allowed me to rapidly prototype. This experience helped me see that there is a right time to start prototyping.

Starting with the student experience as the basis for co-designing materials for teachers was a very useful technique to elicit how they would go about mathematizing their community for their students.

In designing teacher resources, I had to design for a learner population (teachers) who were designing for their own learners (their students). Figuring out how to go about this was hard to wrap my mind around at first. By starting with the student experience, I was able to access teachers' strengths: their expertise about their students and what they need to learn math. Then, I was able to work on what they would need to help students get there.

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