# Data Portraits: Visualizing Social Justice in Mathematics

Integrate social justice into mathematics
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This strategy provides instructions for teachers who are seeking opportunities to authentically integrate social justice in mathematics. This strategy may require application or problem solving involving both conceptual understanding and procedural skills. It is recommended that this strategy be situated at the middle or end of a statistics or a graphing stories lesson unit and can serve as a formative way to assess students’ ability to apply their learning to real-world, authentic situations.

## Implementation Steps

1. Introduce the concept of "Data Portraits" and share 1 to 3 examples with your students.

• Data Portraits depict an individual or a collective group of people's accumulated data rather than their faces. Portraits are visualizations of information about aspects of daily life (i.e., social networks, travel patterns, salaries, housing, education). In this strategy, Data Portraits will be designed to communicate mathematical information about an individual or sample of the population.

• The use of questions related to data and representations of data becomes increasingly important as more of our interactions occur online, where we exist as data not bodies.

2. Share information about a historical event and data portraits that pertain to it

• For example, you could share the history of W. E.B. Du Bois and the 1900 Paris Exposition.

3. Share information about a current event and data portraits that pertain to it and engage students in a discussion about what they notice and wonder about the data portrait or have the students engage in a math circle discussion

• For example, you could provide students with an opportunity to review the images of the Black Lives Matter murals.

4. Instruct students to journal a response that supports them to analyze both the historical and current event data portraits. Some questions to consider asking are:

• What is the impact of Du Bois' use of non-traditional information graphics to represent the data?

• What is the impact of the artistic representation of #BlackLivesMatter and #EndRacismNow painted in the streets?

• Select one of Du Bois' portraits for further investigation and respond to the five questions using a think-pair-share partner approach:

• What can you infer from this data portrait beyond what it shows directly?

• What do you notice? Share what you are noticing and what this may imply.

• What’s the deeper story that comes from this data portrait?

• What’s going on in this data portrait?

• What do you wonder? Where could you find the answers to what you wonder?

5. Identify a social justice issue within your school or community that you can assess statistical information about in order to create a data portrait.

6. Identify one or more relevant social justice standards from the "Learning for Social Justice Standards" guide included below.

7. Create a data portrait featuring the statistics of the social justice issue in a manner that is affirming similar to the message of #EndRacismNow and answer the following five questions using your data portrait.

• What can you infer from this data portrait beyond what it shows directly?

• What do you notice? Share what you are noticing and what this may imply.

• What’s the deeper story that comes from this data portrait?

• What’s going on in this data portrait?

• What do you wonder? Where could you find the answers to what you wonder?

## Algebra Lesson Example Using Desmos

This strategy can be used in the "Graphing Stories" activity from Desmos, in which students make the transition from one-variable representations (e.g., number lines) to the TWO-variable representation of the coordinate plane. Students will watch 15-second videos and translate them into graphs.

Implementation Steps:

1. Invite students to participate in the Desmos activity.

• In this lesson's activities, students are asked to interpret the actions of the person in the video and sketch a graph that represents their actions over time. The teacher's guide suggests highlighting unique answers for the class. The point of the first video is to help students orient themselves with the concept of storytelling using graphs and realize there are many variables they could graph.

• Encourage students to attend to precision. If they say "height," for example, ask them, "The height of what?" The person's height doesn't change. The person's height off the ground does change, but even then, students should specify from which point they're measuring height off ground. From the person's feet? From the person's head?

2. Encourage the use of the Desmos graphing calculator.

• The second activity in this lesson, encourages teachers to monitor student screens as students are working on these sketches individually or in groups, and ask them to interpret their sketches in words. If they're completely stuck, consider highlighting on the graph where t = 0 and asking, "Where is the person's waist at the start of the video?" Have students place a point there. Then do the same for t = 15.

• If you see a student who has a graph but it's incomplete or shows early thinking, consider telling the student with words what their graph says to do with math. For example, you could say, "Your graph tells me that at five seconds the person is both 1.2 meters above the ground and 2 meters above the ground. If that's what you meant to communicate, keep it. If not, change it." Then give the students time.

• When the entire class has had a chance to complete at least one draft of a sketch, bring the class together. Consider pointing out interesting and unique sketches, starting with examples of early thinking and moving towards more precise thinking.

• Ask students to describe a feature of each graph they like and another feature they want to modify. After several rounds of this conversation, offer every student the chance to modify their sketches before sharing the teacher's sketch.

3. Prioritize class discussion about how the graph relates to key concepts.

• Emphasize that this is only one answer sketch not the only answer sketch. Tell students the sketch was made by a teacher, and every person's sketch will be subject to model and measurement error.

• Once again, ask students to describe a feature of the graph they like and another feature they want to modify.

4. The Desmos activity concludes with providing opportunity for students to create their own challenges and solve challenges from their classmates.

• Encourage students to complete each other's challenges but also to take some time to review responses to their own. Use the teacher dashboard to look for unique challenges and unique solutions that may expand your students' understanding of mathematics. Highlight those for students and also ask them what they learned from the experience.