By studying Quantitative Reasoning, we can analyze and interpret mathematical information as a means to evaluate arguments and make informed choices.

Perspectives

As you begin your day and catch up on those news articles, you click on one about crime in your area. The author includes a graph that breaks down crime by racial group and then proceeds to analyze the data and present conclusions that seem a bit inconsistent. You have two choices: you can accept what the author is claiming or you can take a closer look at the data for yourself and apply Quantitative Reasoning skills, making your own conclusions or choosing to find other data to support or contradict it.

Concepts to Consider

On social media, you will often see memes with something along the lines of: “Another day has passed, and I didn’t use math once.” These may earn a bit of a laugh, but the truth is they are completely inaccurate. When we think of math as more than numbers or “getting a correct answer,” as Quantitative Reasoning, we can realize that it is really a set of skills for thinking and communicating that involves, according to the Mathematical Association of America’s report “Quantitative Reasoning for College Graduates: A Complement to the Standards” (originally published in 1994), “drawing inferences from data, interpreting models, estimating results, assessing risks, suggesting alternatives, and even making reasonable, testable guesses.” The report also talks about how Quantitative Reasoning complements and reinforces reasoning skills in general, particularly problem-solving (see Procedural and Logical Thinking in chapter 5). We rely on it regularly in our lives, and it enhances our lives to have effective skills in this area. Quantitative Reasoning helps us understand our relationship to the world from a mathematical perspective and be able to process numerical information and data, which comes to us in various forms, from the written to the visual such as graphs and charts. We use it to figure out finances and career moves, even to decide which school system is best for our children. Indeed, even hobbies – for example, as Bennet Attaway, et. al. (2023), “we would expect that fans of tabletop role-playing games should be well-acquainted with basic probability.” Math is everywhere!

A joint statement by the National Council of Supervisors of Mathematics and TODOS: Mathematics for ALL, “Mathematics Education Through the  Lens of Social Justice:  Acknowledgment, Actions, and Accountability” (2016), states that Quantitative Reasoning is “both a mirror and a lens to understand the world around us” and “an analytical tool to understand, critique, and transform the world” (p. 3). They continue that “[m]athematics can be used to problem-solve and model real-world phenomena, sociopolitical situations, community issues, and power relationships.” Mathematics for Social Justice: Focusing on Quantitative Reasoning and Statistics by Gizem Karaali and Lily S. Khadjavi (2021) discusses how Quantitative Reasoning can be applied to studying and finding solutions to issues such as poverty, gentrification, human rights, income gaps and the minimum wage, crime, racial profiling, nutrition, recycling, and gerrymandering, among others (see Diverse Perspectives in chapter 5).

The Mathematical Association of America’s “A Common Vision for Undergraduate Mathematical Sciences Programs in 2025” (Saxxe and Brady, 2015, p. 6) comments that “[s]ociety benefits from college graduates who are generally educated in higher mathematics, whose lives and social activities are influenced by their understanding of mathematics and, through it, of interesting aspects of history and culture.”  The “Quantitative Reasoning for College Graduates” report asserts that Quantitative Reasoning skills “enhance the quality of citizens” (see Civic Learning in chapter 5). Much of how our civic systems’ work relies on the analysis of numerical data. The decision of how much funding a certain educational district receives is often reliant upon data concerning demographics, test scores, and tax contributions. Crime laws emerge out of various statistics. Census data drives many choices, including the shape of voting districts. Being an informed citizen means being able to apply Quantitative Reasoning skills.

Besides civic life, Quantitative Reasoning is an essential part of many majors and careers. “A Common Vision” (p. 5) states, “Courses in the mathematical sciences have been taught as part of a classical education for thousands of years and continue to gain new meaning and relevance. There are now, perhaps more than ever, amazing career opportunities for people with training in mathematically-intensive fields.” They view general education Quantitative Reasoning courses as “pathways into many different STEM majors and also as key components in the preparation of scientifically-literate citizens” (p.6). Business, engineering, biology, chemistry, economics, math education, psychological science, sociology, and geography are among some of the most obvious and well-known majors that utilize Quantitative Reasoning, but they are also underlying skills in criminal justice, public health, journalism, political science, history, and exercise and sports science, just to name a few.

It is common for some people to believe that they are not “good” at math, and therefore are not a good fit for Quantitative Reasoning courses.  Due to societal pressures, women and historically marginalized groups in particular demonstrate this belief at higher rates (“Quantitative Reasoning for College Graduates”). Attaway, et. al. (2023), find that “[b]eyond anxiety, adults may have a range of affective responses toward math and quantification, and those who find math difficult may equally react with skepticism or with uncritical trust in numbers.” In fact, Quantitative Reasoning skills, like other general education skills, are not innate, but learned, and anyone can improve with practice (see chapter 2.3 on neuroplasticity).

Special note: check out the Lathisms website dedicated to “showcasing the contributions of Latinx and Hispanic mathematicians” and Spectra, the Association for LGBT Mathematicians.

Quantitative Reasoning and Good, Necessary Trouble

The way Evelyn Lamb, Omayra Ortega, and Robin Wilson (2023) describe mathematics’ role in racial justice highlights how learning a subject and the skills associated with it – in this case, Quantitative Reasoning – can be an act of “good, necessary trouble” unto itself. Just as John Lewis discusses how study and preparation are necessary, foundational skills can be applied to address and support a range of issues.

Racial profiling is the “practice by law enforcement officials of targeting individuals for suspicion of crime based on the individual’s race, ethnicity, religion or national origin,” such as using these characteristics to decide which drivers to stop for minor traffic violations” (“Racial Profiling: Definition,” 2005). It has been the subject of Black Lives Matter protests, in particular. Such police practices have been defended with a number of arguments. Jack Glaser (2006, p. 396) identifies the arguments that “targeting groups who have a higher criminality rate improves police efficiency and thereby increases public safety” (p. 396) and the more racist belief that there are “real behavioral differences across groups” (p. 395). Glaser, however, used a mathematical simulation to find that “profiling invariably has the effect of increasing differences in incarceration rates between groups” and “popular presumptions about its efficiency are probably overconfident” (p. 413). Camelia Simoiu, Sam Corbett-Davies, and Sharad Goel (2017) developed a statistical approach to detecting discrimination called the threshold test that builds on previous approaches – the benchmark and outcomes tests – and overcomes their limitations. They reached the conclusion that, in “a dataset of 4.5 million motor vehicle stops in North Carolina, [their] threshold test suggests that black and Hispanic motorists face discrimination in search decisions” (p. 1213).

Anecdotal or qualitative data of racial profiling is powerful, particularly when hearing the stories of Black or Latinx people who have been harmed or even killed for supposedly minor police stops. Quantitative data and analyses provide compelling evidence that disproves arguments for the continued use of racial profiling and can be used in court cases and calls for policy changes.

Activity 4.2

• Watch the following video: “A brief history of banned numbers – Alessandra King”

• Discuss what reasons are given for the banning of certain numbers.
• In light of these example of banned numbers, consider the significance of Quantitative Reasoning.

Discussion 4.2

• • If you have already taken a course with a primary focus on Quantitative Reasoning, think about what you were asked to do and what you learned. If you have not already taken a Quantitative Reasoning course, think about the types of courses you could take.
  • In what ways did or might the idea(s) or example(s) discussed above apply in such a course?
  • What other ideas or examples would you add to the discussion?