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Scaffolding an Open-Ended Social Justice Statistics Inquiry Project in Introductory Statistics

Joint Mathematics Meeting 2023

Dr. Laura Kyser Callis, Curry College, Milton, Massachusetts

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Mathematics is a gatekeeper

Mathematics helps us understand the world

Mathematics is a language of power – people listen when you speak with mathematics

Curry College, Milton, MA

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SOCIAL JUSTICE STATISTICS

It’s the right thing to do: The history of statistics has a racist history – we have a moral duty to use the power of statistics to make the world a more just place
Student motivation, engagement, and recruitment: We can demonstrate to students that statistics can be used to address real-world issues

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THE PROJECT

DEATHS THAT OCCUR IN POLICE INTERACTIONS

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THE PROJECT: THE DATA

https://fatalencounters.org/
30,000+ cases of deaths that occurred in police interactions since 2000.

Freedom of Information Act Requests
Media Stories
Individual Reports with follow up
Volunteers & Paid researchers
Google Sheet

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STEPS OF A STATISTICAL INVESTIGATION

Ask a research question that can be answered by collecting data
Design a study and collect data
Explore the data
Draw inferences beyond the data
Formulate conclusions
Look back and ahead

Tintle, Chance, Cobb, Rossman, Roy, Swanson, 2021

Most of our textbook investigations already have the research question determined, so this is an opportunity for them to engage in creating research questions. They do not design the study or collect data; the data is provided. This is a controlled research project so that I can support them; they must use the provided data set. This allows me to help them with technology, but it also helps me to know whether they’ve gotten “correct-ish” answers, since I have access to the data. Also, finding and cleaning data is a lot of work and could take an entire semester.

For inferences, we have only done hypothesis testing for 1 proportion. A few students do the hypothesis testing if their research question calls for it, but it is not required. When they draw inferences, instead they talk about how the data is collected, does there seem to be a sizable difference, recognizing, for instance, that police departments will only categorize by gender assigned at birth and so the transgender group is likely an underestimate and drawing conclusion about that group may be difficult, etc.

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THE PROJECT: SETTING

Week 6 of a 15-week semester
Simulation Based Curriculum
Have only done hypothesis testing for 1 proportion
25-ish person classes, 2-3 sections per semester, 3 years
Taken by majority of students to satisfy college quant requirement.
Non-selective 4-year college
Mostly first year students, some second-year
In lieu of midterm exam
Working in groups optional

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THE PROJECT: PRE-WORK

Week 2. �In-class time, ~20 min

Written intro question about their thoughts on deaths in police interactions
Orientation to the data (spreadsheet),
Small Group Brief Brainstorm of Potential Research Questions

Out-of-class

Discussion Board Post: 3 Potential research questions
I comment on:

Is this a research question, or just a fact question? (E.g., how many people died in 2000?)
Can this research question be answered with the given data?

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THE PROJECT: PRE-WORK

Week 4. In Class time <10 min

In-Class Small Group Brief Brainstorm of Analysis Plan. What numbers? What graphs?
Discussion Board Post: Analysis Plan (What numbers? What graphs?)
I comment. Will this method actually help, or should it be something else?

Week 5.

Watch how-to videos for Google sheets that build on their research questions – especially pivot/cross-tabs tables
Students try some techniques ahead of time

Week 6.

In-Class time (2 x 1.25 hours) to work with spreadsheets, trouble shoot, with instructor circulating

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THEIR RESEARCH QUESTIONS

What are students interested in finding out?

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RESEARCH QUESTIONS

Topic	# student projects Fall ‘22	# student projects Spring ‘22
Race*	11 (37%)	17 (53%)
Age*	8 (27%)	6 (19%)
Gender*	5 (17%)	9 (28%)
Geography	2 (7%)	8 (25%)
Time	1 (3%)	0
Mental Health	1 (3%)	1 (3%)
Other	1 (3%)	1 (3%)
Total	29	32

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EXAMPLES OF �FINAL RESEARCH QUESTIONS: �RACE

Are African Americans disproportionately likely to die in a police interaction?

Are the rates of the levels of force different for different racial groups?

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EXAMPLES OF �FINAL RESEARCH QUESTIONS: �GENDER

Are different levels of force used among different gender groups?

Is the gender make up of people who die in police interactions different among different racial groups?

Do men die in police interactions due to “suicide” more often than women?

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EXAMPLES OF �FINAL RESEARCH QUESTIONS: �AGE

How many minors/young adults/children are killed in police interactions? Is there a difference in the level of force used compared to older adults who die in police presence?
Is the age distribution different for different racial groups who die in police interactions?
Is the number of young women dying in police interactions increasing or decreasing over time?

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EXAMPLES OF �FINAL RESEARCH QUESTIONS: GEOGRAPHY

How do the states compare in rates of deaths in police presence?

Some go further: Is that related to crime rate? Gun laws? History of segregation? Police cameras?

Are urban areas more likely to have a higher rate of deaths in police presence?
Are different uses of force (gun, taser, asphyxiation, vehicle pursuit) more common in deaths that occur in police interactions in different states?

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EXAMPLES OF OTHER STUDENT RESEARCH QUESTIONS

How does gunshot as the highest level of force compare among those who were fleeing compared to those who were not fleeing?
How many of the instances where people died in police interactions was there foreknowledge of mental health issues?
Is the number of deaths that occur in police interactions going down after George Floyd’s murder?
Is there a relationship between intended use of force and actual highest level of force?

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CHALLENGES

What do students need support on in order to be successful in this project?

A look through my comments & �reflections on my in-class and office-hours support

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CHALLENGES WORTH FACING: BENEFITS, NOT DRAWBACKS

These are reasons to do the project, not reasons to skip it. They address the learning outcomes, in particular:

Engage in regular discussion of quantitative information or results, with special emphasis on the context of the problem and general, real-world knowledge.

Communicate quantitative information effectively, incorporating symbolic, numeric, and/or graphical representations and appropriate syntax within verbal and written communication.�

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CHALLENGES: �WRITING RESEARCH QUESTIONS

Is it a statistical question? Does it anticipate variability? Or, could it be answered with just a single number?

For example, these are not research questions:

“How many victims have been shot by police?”
“Is there a mean age of those who have died?”

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CHALLENGES: �WRITING MEASURABLE RESEARCH QUESTIONS

Does the research question give you a plan of action?

For example: “Does the location of these shootings matter?”

We could instead ask,

Are large cities in Massachusetts more likely to have police interactions that end in death than smaller towns?
Are some neighborhoods in Boston disproportionately likely to have police interactions that end in death?
Which states have the highest rates of deaths that occur in police interactions?

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CHALLENGE: WRITING RESEARCH QUESTIONS WE CAN ANSWER

We do not have data on:

The race or gender of the police officer involved
Whether the deceased had prior convictions
The total number of interactions or the number of interactions that don’t end in death.
“Why” the person was killed – that might require qualitative analysis

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CHALLENGES: �PRECISE LANGUAGE

While exploring data:
The individuals in the data set are not necessarily suspects or criminals.
How can a 0.25-year-old (a baby) be a suspect?

While writing conclusions:
It’s not “Latinos live on average a year longer than African Americans,” it’s “The mean age of Latinos who die in a police interaction is a year more than the mean age of African Americans who die in a police interaction.”

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CHALLENGES: �USING TECHNOLOGY

Basics students may need help with:

Copying a file for editing
Inserting columns and rows
Sorting. Adding filters.
Formulas – concepts and syntax
Creating Pivot tables
Creating histograms and circle graphs

BUT, problems with “technology” are often really problems with an analysis plan, knowing what numbers or graphs would help answer the question – or are even reasonable

Some students will say something like, “I will use a bar graph” just to get the assignment of an analysis plan done, even if a bar graph doesn’t really make sense. Or they say that they’ll calculate the “mean” – of a categorical variable. Some students may not know or don’t pause to consider what graph would make sense. Discussion Board comments can help, but it doesn’t seem to always do the trick. If they are at this stage in their thinking about the project, figuring out what to do with a pivot table might not make a lot of sense. I’ve tried to survey students ahead of time, but that still doesn’t identify the issue completely – because they may think they know what graph or number would help; they may not realize that it is nonsensical to find the “average number of African Americans killed in a police interaction.”

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MATHEMATICAL CHALLENGES WORTH HAVING & SHARING

Choosing the right way to compare groups

Yes, there are more White/European-Americans who die in police interactions… because there are more White people in the US
We need to compare to the demographic make up of the US

The state with the most deaths is California…

But California has the most people
We need a percent of the population – but that’s a tiny decimal; maybe a rate of per 100,000?

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MATHEMATICAL CHALLENGES WORTH HAVING & SHARING

Choosing the denominator: E.g., highest level of force & gender

Women are a very small minority
If you look at the gender breakdown by level of force it is hard to see a pattern – all you see is that women are the smaller group for each level of force
If you look at the level of force breakdown by gender, then you can see the percent of women who died for each level of force – and you can see a difference.

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STATISTICAL CHALLENGES �WORTH HAVING & SHARING

How do we group? How do we filter?
What methods give us too much detail to process? Too little detail?

Does comparing mean age help? Median?
Do boxplots show more than histograms?
Should we use individual ages, or should we group them by decade? Or by under 18 and 18+?

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LEARNING OUTCOMES

Scaffolded group project in an introductory course

Did it introduce these outcomes?

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LEARNING OUTCOMES

Learning Outcome	Level
Engage in regular discussion of quantitative information or results, with special emphasis on the context of the problem and general, real-world knowledge.	Achieved by all who submitted paper
Utilize statistics software to perform data analyses to interpret and compare multiple representations of quantitative information and draw inferences from them.	With support
Organize, summarize, interpret, and compare single-variable data using descriptive methods of statistics.	With support
Recognize and apply the different representations of quantitative information (e.g. symbolic, visual, numerical, verbal) when describing relationships between two variables	With support
Communicate quantitative information effectively, incorporating symbolic, numeric, and/or graphical representations and appropriate syntax within verbal and written communication.	Varies; majority met with support & feedback

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COMMUNICATING RESULTS �FALL 2022

Communicate quantitative information effectively, incorporating symbolic, numeric, and/or graphical representations and appropriate syntax within verbal and written communication.

21 students communicated clearly about the meaning of the quantitative information and connected the numbers with the context
22 students communicated and made connections, but required clarification on some points
Students’ questions varied in complexity, as did their spreadsheet methods, graphs, and conclusions, so it may not be fair to compare them to each other.

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CONCLUDING THOUGHTS

Social Justice statistics projects have the potential to demonstrate to students that statistics can be used to address real-world issues.
Allowing students to choose their own research question based on a common set of data provides an opportunity to experience the authentic, messy nature of statistics with support
Conjecture: Breaking the project into small parts throughout the semester with regular feedback can make the project more feasible for students and the instructor and can result in richer final products.

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REFERENCES

Burghart, D. (2022). Fatal Encounters. https://fatalencounters.org/
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York, NY Routledge.
Larnell, G., Bullock, E., & Jett, C. (2016). Rethinking teaching and learning mathematics for social justice from a critical race perspective. Journal of Education, 196(1), 19-29. 10.1177/002205741619600104

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ABSTRACT

Mathematics and statistics are often portrayed as neutral and objective, yet mathematics and statistics have been used to maintain oppressive systems and preserve privilege (Larnell & Jett, 2016). Fortunately, statistics can also be used to identify and communicate the impact of oppressive systems and create positive change. Indeed, using social justice topics to teach statistics has the potential to help students appreciate the power of statistics to understand and change the world, rather than see statistics as a disconnected, esoteric discipline to be suffered through to complete formal schooling (Gutstein & Peterson, 2013). Using real data sets that address critical issues of inequity makes it possible for students to learn more about the world, in addition to learning statistics.
For three academic years, at a small, less-selective liberal art college, introductory statistics students completed projects using data from Fatal Encounters, an organization that complies data on deaths that occur in police interactions (Burghart, 2022). Fatal Encounters makes the raw data of over 30,0000 cases publicly available on a Google Sheet. Students developed their own research questions that could be addressed with the data, chose methods that could answer their research questions, used spreadsheet commands to analyze data, and wrote their results, following the statistical inquiry cycle (Wild & Pfannkuch, 1999). I retroactively analyzed subsets of the discussion board posts, student emails, final papers, and supplemental support materials I created to identify the challenges and scaffolds needed to support my students in the statistical inquiry cycle for this topic and the skills they showed evidence of learning through the experience. In this session, I describe the project, the scaffolds and challenges, the types of questions students typically investigated, and the student learning outcomes, in order to support other instructors interested in investigating social justice topics in introductory statistics courses.