Mathematics for Social Justice

Class Overview

This class is essentially a traditional quantitative literacy class with a theme of social justice. When asked what "mathematics" means to them, students said:

"Being able to quantify the world."
"Perspectives of understanding."
"Critical thinking and problem solving."

When asked what "social justice" means to them, students said:

"Advocating for those around you, especially marginalized people."
"Having awareness and understanding of diversity."
"Listening and using power to create change."

With these definitions in mind, the relationship between mathematics and social justice becomes clear. I view this relationship as a two way street that we found ourselves going back and forth down.

Math education through social justice: using examples related to social justice issues that students care about to illustrate mathematical ideas. For example, the activity below titled Probability, Binomial Distribution, and Hypothesis Testing introduces students to the basic ideas of hypothesis testing using police traffic stop data.
Social justice through math education: using basic mathematical concepts to illustrate otherwise subtle issues that students might not understand otherwise. For example, the activity below titled Gentrification uses percentages and averaging to illustrate the basic economic mechanisms of gentrification.

Class Structure

Students were placed into groups of 4 for the duration of the term. Each day we would open class with discussion of current events, and then we would either transition into Discussion Day or Activity Day.

On Discussion Days, students went over discussion questions for the reading in their small groups, followed by a brief large group summary. We read two books: The Data Detective and Weapons of Math Destruction (WMD). The Data Detective is a list of 10 rules for reading and interpreting statistics in the news. Weapons of Math Destruction details how statistics and algorithms have inserted themselves into the lives of average Americans from cradle to grave. Each book was connected with project; the details of which are included in this ZIP file. For homework on Discussion Days, students would be asked to reflect on their reading on a shared document outside of class.

On Activity Days, students were given one of the mathematical activities below. Students were not given any instruction, but invited to struggle together under instructor supervision. The activities are included roughly in order of how they were introduced. LaTeX files can be found in this ZIP file. For homework on Activity Days, students would be asked to do some further reading and discuss it on Moodle.

List of Activities

Percentages

Fractions, Rates, and Percentages

Checking the Math in an Article

Simulating a Free Market

Histograms, Mean and Median, and Wealth Distributions

Measures of Inequality

Statistics

Probabilities, p-Values, and Hypothesis Testing

Red Lining, Environmental Racism, and Chi-Squared Test

Percentages

Fractions, Rates, and Percentages

Fractions Proportions and Percenteges.pdf

Mathematical Content: fractions, simplifying fractions, rates, inverse rates, percent, and other ways to communicate rates.

Social Justice Content: examples pull from common numbers present in news and daily life.

Discussion: Ask students to identify a rate or percentage in the news. Have them identify the meaning of the numerator, denominator, and if those numbers are provided in the news.

Comments: This has not been tested in class.

Checking the Math in an Article

Checking the math in an Article.pdf

Mathematical Content: average rate, compound units, estimation.

Social Justice Content: invites students to question the incentives of businesses when publishing their own statistics. Also invites students to check accuracy of numbers presented in the news.

Discussion: have students identify a more recent article about tech companies and ask them to critically check the statistics presented.

Comments: This activity was inspired by Common Sense Mathematics. This version of the activity has been revised to help students progress with less guidance, and has not been tested.

Gentrification

Gentrification.pdf

Mathematical Content: averages and percent.

Social Justice Content: introduce students to idea of property tax and basic budgeting for cost of housing. Students act out the role of county tax assessor, landlord, and tenant in the scenario of a rental unit in a gentrifying neighborhood.

Discussion: Have students read this article and discuss which historical trends have created the necessary economic conditions for gentrification to take place today. Also invite students to identify people from the article with the people in the activity and discuss how they might behave differently. As this activity was catered to Indianapolis, I also had my students read this article and compare/contrast the situation in Indy with Raleigh.

Comments: This activity was inspired by an activity in Mathematics for Social Justice about NYC. Students were able to complete activity easily, and the discussion was extremely in depth. We discussed red lining, eminent domain, the Highway Act, school funding, and segregation. Students also came to the conclusion that the individuals within the marketplace were not able to prevent harm without opting out of the system. Essentially students came to the conclusion that capitalism itself is responsible for racist outcomes in housing. I recommend adapting this activity using local taxes and housing prices.

Is That a Big Number

Is this a big number.pdf

Mathematical content: rates and estimation.

Social Justice Content: Students contextualizes large numbers related to contentious social issues.

Discussion: Invite students to find a large number in the news and to contextualize it in a similar manner.

Comments: This activity was inspired by a passage in The Data Detective where the author discusses the cost of the border wall. Students had lots of interesting ways to contextualize these numbers, but reported after the fact that they did not appreciate this activity. Perhaps it needs a more focused conclusion.

Contingency Tables

Contigency Tables.pdf

Mathematical Content: contingency tables, relative risk, quantitative variable, and atributable fraction.

Social Justice Context: Environmental determinants of health and police racial bias.

Discussion: have students read this article and discuss the methodology and conclusion of the study. Can also talk about other environomental factors of health like lead paint and proximity to highways, and the racial/economic disparities in exposure.

Comments: This activity was inspired by an activity in Mathematics for Social Justice about racial bias in policing. The asthma study was added because it was in the news cycle when the class was first taught. This activity was originally much more complicated and has been essentially rewritten for simplicity. It has not been tested.

Playing with Rates

Playing with Rates.pdf

Mathematical Content: rates and solving proportions.

Social Justice Content: Illustrates how people can "spin" numbers for different purposes. Also discusses the official definition of unemployment rate.

Discussion: Have students identify some other quantity and provide different ways it can be measured.

Comments: This activity was inspired by Common Sense Mathematics. This activity has not been tested.

Percent Change

Percent Increase

Percent Increase.pdf

Mathematical Content: percent increase, percent decrease, and the 1+ trick.

Social Justice Content: examples pull from common numbers present in news and daily life.

Discussion: have students identify an example of percent increase in the news and see if the initial and final quantity are included in the article. Discuss the meaning of each of these along with the meaning of the percent change.

Comments: This activity is inspired by Common Sense Mathematics. Students found the distinction between percentage point change and percentage change confusing, and so this section likely requires more guidance.

Inflation

Inflation.pdf

Mathematical Content: percent increase.

Social Justice Content: this activity introduces how inflation measures changing prices as a percent increase, how the Consumer Price Index is measured, how inflation effects workers, how it needs to be figured into discussions of government budgets, and how to use an online inflation calculator.

Discussion: have students read a recent news article about recent CPI numbers and discuss what is currently driving inflation.

Comments: Originally the activity simply began by inviting students to research CPI themselves. This was too confusing, so the first two sections were added to introduce students to what inflation is and how it is measured in the US. The first two sections have not been tested.

Finance

Finance.pdf

Mathematical content: percent change and compound interest.

Social Justice Content: teaches students the basics behind credit card payments, student loan payments, and mortgages.

Discussion: Have students research starting salary for a job they are qualified for and have them budget that salary with student loans and rent.

Comments: This activity was created upon the students' request.

Compartment Models

Mathematical Content: Excel

Social Justice Content: explores how the parameters of infectious diseases impacts the spread and mortality of the disease.

Discussion: have students read about early COVID models and discuss why drastic intervention was warrented.

Comment: This activity has not been tested. It is likely to be very challenging for students. One of the main goals is to explore how a disease with low mortality rate can actually result in significant deaths.

Data Analysis

Simulating a Free Market

Simulating a Free Market.pdf

Mathematical Content: average, median, and probability.

Social Justice Content: students get to experience the highs and lows of participating in a competitive market with equal resources.

Discussion: have students read this article and do further research into the proposed wealth tax and its public support.

Comment: This activity was inspired by The Pudding article on the yard-sale model. The bulk of the time in this activity is dedicated to simulating the model in the classroom. Be sure to invite students to opt out of playing if gambling is against their faith. You can see the outcome of our simulation in the Excel file on the next activity and the bar chart of individual's final balance is the cover image. Through random chance 2/3 of the class ended up losing money and the top 5 people ended up with half of all of the money. Students again came to the conclusion that inequality is inherent to a free market.

Histograms, Mean and Median, and Wealth Distributions

Mathematical Context: histograms, mean, median, and skewed distributions.

Social Justice Context: discusses commute times and builds on the data generated from the previous activity. Gives students experience accessing and working with governmental data.

Discussion: have students identify other distributions that are right skewed and discuss the significance of mean and median in that setting.

Comment: This activity was inspired by an activity from Mathematics for Social Justice. This activity has not been tested.

Measures of Inequality

Mathematical Content: deciles, Lorenz curve, Gini Index, and area.

Social Justice Content: builds of previous activity to measure how unequal different distributions are.

Discussion: have students identify other quantities that are unequally distributed and use one of the tools discussed to measure this inequality.

Comment: This activity was inspired by an activity from Mathematics for Social Justice. This activity has not been tested.

Statistics

Probabilities, p-Values, and Hypothesis Testing

Probability, P-values, and Hypothesis testing.pdf

Mathematical content: probability, binomial distribution, and hypothesis testing.

Social Justice Content: revisits police racial bias and addresses how we can judge whether racial disparities happened "by random chance."

Discussion: Have students read the executive summary of this study commissioned by the Carmel, IN police department and discuss whether it is a fair summary of the data.

Comments: This activity came out of discovering the Carmel report when looking for examples of racial bias amongst police in Indiana. This report is rife with errors and is extremely misleading. The binomial test is simple enough to explain to students in a few lectures, and they end up confident in their ability to criticize the report.

Red Lining, Environmental Racism, and Chi-Squared Test

Chi Squared Redlining and Environmental Racism.pdf

Mathematical Content: Chi-squared test.

Social Justice Content: Environmental racism and red lining.

Discussion: Have students read about red-lining as well as the health outcomes related to exposure to industrial sites.

Comments: This activity has not been tested.

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