This is a transcript of the interactive video Grow Up, Branch Out: Achieving and Assessing Quantitative Literacy for the 21st Century, produced for the Massachusetts Department of Higher Education in 2019.
Quantitative literacy – also known as quantitative reasoning or simply “numeracy” – is said to be an essential skill in the workplace and in the world of the 21st century. But just what IS quantitative literacy, anyway? In this video I hope to help you to answer that question well enough to help you locate these skills in your teaching, whatever your discipline, and to connect you with resources that can take your teaching and support for these skills to the next level. You can use the video links as they appear to interact.
“More Than a Math Problem”
MASSACHUSETTS’ 2009 SALES TAX INCREASE: 5% TO 6.25%
In 2009, Massachusetts legislators proposed to raise the state sales tax from a rate of 5 percent to 6.25 percent, just the second increase in the tax’s history. Needless to say, the proposal was divisive. In an April article, the Boston Globe called it a “1.25 percent increase.” Later in June, when the proposal was on the verge of passing, the Globe ran an Associated Press article that called it a “25 percent increase.” Both articles are referring to the same tax proposal. So: which one of them is correct?
The April article is correct! Here the author compared the new tax rate to the old tax rate by subtracting, measuring what we call the “absolute difference.” The tax rate was indeed set to be increased by adding an amount of 1.25 percentage points.
The June article is correct! Because the author is comparing the new tax rate to the old tax rate by dividing, measuring what we call the “relative difference” reported as a percent. Here, the amount of the proposed rate increase is exactly one-quarter, or 25 percent, of the existing rate.
In reality, BOTH of the articles are correct, each in its own way, because their authors just made different choices. The absolute difference does a good job of communicating the total amount of the increase itself. The relative difference compares that increase to the previous amount. Each provides one important form of context while obscuring another. And, you can imagine how supporters of the new tax might prefer one framing and opponents favor the other – even though they are both talking about the exactly the same thing.
So, we could subtract. Or, we could divide. That choice is meaningful. But wait a minute. Both of those math problems have exactly the same answer on my calculator. Why are they so different when they make it onto the page? What’s happening to MEANING on its trip out of and back into context?
BEYOND MATHEMATICS: WHAT IS QUANTITATIVE LITERACY?
Quantitative literacy is what happens when instead of asking “What math could we do?” we ask “What math should we do?” “Why do we think so?” and “What are the impacts of that choice?” Quantitative literacy therefore is a process of “sophisticated reasoning,” using mathematics that may itself be sophisticated, or as in this example, fairly elementary.
“The Case for Quantitative Literacy”
Quantitative literacy is more than mere mathematics. Both of them have their roots in simple number skills. But while the job of mathematics is to grow upward, building conceptual and technical sophistication as it goes, quantitative literacy is about growing outward, not just upward, finding more – and more various – opportunities to understand the world through a quantitative lens, at any level of our mathematical development. Just as a tree’s trunk carries water to its leaves, and in turn the leaves catch the sunlight to nourish the tree’s growth, in the same way, math skills are vital for quantitative literacy AND the practice of QL reinforces our math skills. The crucial difference is context.
We grow upward in a math class because we reason abstractly, thriving independently of context. But we grow outward in quantitative literacy by reasoning concretely, attending to number and quantity that are steeped in context that is authentic, meaningful, and yes, even messy.
We learn to read and write by reading and writing ABOUT things, and the more things we read and write about, the more our language skills can develop. We call QL a literacy for the same reason: it is not a skill that we learn but rather acquire through repeated use across many and various contexts. So math plays an essential role in building quantitative literacy but hardly a sufficient one. Mathematics alone cannot create a more numerate world. Mathematics needs partnership – conspiracy, even – from every discipline to do that.
WHY QUANTITATIVE LITERACY?
And we no longer have the luxury of opting out of numbers. In the information age, data pervades every aspect of our personal, professional, and public lives. Some 2.5 quintillion bytes of new data are being stored every single day. We end every year with more than triple the data as when we started it. Data girds our decisions, suffuses our rhetoric. It drives our cars. And with that power comes risk.
In mathematics, after all, numbers are perfect constructs – but quantitative reasoning is the HUMAN expression of a numerical thought. Numbers are NOT truth; they are tools. And while numbers cannot lie, humans? They can. In order to give voice to numbers, we have to make a lot of choices. Those choices can reflect our biases. They can disguise our agendas. They can perpetuate inequality. And yet, we are all too content to uncritically assign credibility to arguments that use numbers. That concentrates disproportionate power into the hands of number-users — the more skilled among whom are actually MORE likely to use numbers to confirm their biases.
To handle the burning numerical questions of our age, our students need more than a fire extinguisher on the wall. They need a smoke alarm. A vigilant sensibility, a habit of mind. We don’t just want our students to use numbers; we want them to WANT to use numbers, to see the world through a quantitative lens. Because the stakes for numeracy have never been higher.
WHY QUANTITATIVE LITERACY? U.S. VERSUS DEVELOPED NATIONS
And that’s a challenge we are not yet prepared to meet. While there have been recent gains in school mathematics skills in the United States, American adults’ basic numeracy skills lag behind most of the developed world. And among young adults, we’re actually dead last. If the U.S. workforce is to remain globally competitive – if our citizens are to remain informed in an increasingly data-driven political climate – and if our college graduates are to have every opportunity to advance in their skilled careers – we have a lot of work to do to create a more numerate world.
WHY QUANTITATIVE LITERACY? THE WORKFORCE MANDATE
As so often is the case, with that crisis comes opportunity. Our data economy needs everyone to be more conversant with numbers, yes, but it also creates demand for new kinds of experts. On the one hand, employers of all types agree that candidates with data skills make more attractive hires. (And, higher education leaders seem to agree that too many of our graduates don’t yet have those skills.) Meanwhile, the number of data professionals – statisticians, data scientists, and so forth – in the workforce is projected to increase dramatically in the next few years, and the hundreds of thousands of college graduates who fill these positions are going to command quite a salary to do so.
ANSWERING THE CALL: DESIGNING AUTHENTIC EXPERIENCES
Higher education can answer that call. We can answer it by designing authentic quantitative experiences for students in every program of our universities. Those experiences look different in different programs. Math, science, and engineering majors have to grow taller trees, that are supported by deeper roots. Meanwhile humanities and fine arts majors might be better served to focus on broadening their foliage. Defining the right tree shape for each program, and ensuring each student’s roots in basic skills are strong enough to support it: those are the goals of Massachusetts’ initiatives on Math Pathways and Developmental Mathematics, work that as of this recording is quite active both on and among our public institutions.
ANSWERING THE CALL: ESTABLISHING QL PROGRAMS
Higher education can also answer this call by building quantitative literacy programs that complement our successful writing programs. A QL program brings together both an early, focused opportunity for students to develop quantitative expertise, what I call a “Big-Q” experience, and also myriad opportunities for students to use that expertise across the full spectrum of the curriculum: what I call “small q” experiences. Establish a strong trunk in the first year, and students will bear fruit and flowers all the way through graduation.
Faculty in mathematics and statistics are the agents of Big-Q; but faculty in every discipline are needed to support all the small q’s. So yes – if you’re watching this video, that includes you. Welcome to the conspiracy.
So, what does it look like to support both Big-Q and the small q’s? How do we both nourish the trunk of the tree and encourage it to grow limbs, branches, leaves, and flowers? And, since these tasks have different tools and different casts of characters, how do we do both at the same time in a complex university?
Well, remember first that Big-Q and small-q — our math and statistics departments on the one hand, and faculty across the curriculum on the other — are serving a common goal. Whether it occurs in the quantitative hothouse of an introductory statistics class, or on the other side of campus in an art studio, quantitative literacy tends to always involve the same elements: retrieving information from an authentic context, processing it, and then returning it back into its context. That includes an opportunity to calculate, yes, using tools that are appropriate, from pen and paper to supercomputer and everything in between. It also includes the process of choosing which calculation is appropriate. Showing an awareness of the inherent assumptions behind, and the limitations of, that choice. An interpretation – in context – of the results of that calculation. And, the ability to communicate all of the above in multiple forms of expression, formulas, data tables, visuals and graphs, and yes, in written and spoken communication.
“Roots and Trunk: The Big Q”
In a “Big Q” setting, what we find are focused experiences designed to establish a foundation of transferrable quantitative skills. In these settings, numbers are the main course. The expectation that students reason quantitatively is pervasive and consistent. We can assess students’ skills analytically, based on that expectation. It is also here where we also find the highest degrees of student anxiety and avoidance, and higher rates of D, F, and W grades that impair student success and drive attrition. So we have to get this part right. We see in the Big-Q examples of institutions revising their approaches to developmental and first-year mathematics; and rethinking curriculum and delivery of research-methods courses in the social sciences; and developing entire undergraduate and graduate programs in data science.
QUANTWAY: REIMAGINING FRESHMAN MATH
One of the most widely-adopted Big-Q strategies represents a convergence of two needs: on the one hand, the need to build students’ foundational quantitative literacies in their first year; and on the other, the need to reform ineffective developmental math courses that did not appropriately match all students’ roots with their trees. This is the story of a two-semester sequence of courses that build strong developmental foundations for quantitative literacy, in both root and trunk – as well as a standardized assessment of those skills.
The Carnegie Foundation’s QUANTWAY project is an example of a widely-adopted curriculum for freshman-level, general-education quantitative reasoning, that includes both college-level modules teaching numeracy, algebraic modelling, and elementary statistical literacy in context, and also developmental skills modules to support these outcomes on either a prerequisite or on a corequisite basis. The Charles A. Dana Center at the University of Texas has also developed a similar curriculum and, through their New Mathways Project, also provides support for institutions and for state systems of higher education to bring reform to scale.
QLRA: A STANDARDIZED MEASURE OF QL SKILLS
Since these Big-Q experiences are aimed at a general audience, the skills themselves can be assessed analytically. One widely-used instrument for measuring broad-based quantitative reasoning skills is the quantitative literacy and reasoning assessment. The QLRA is a multiple-choice test that asks students to use numbers in meaningful communications, to provide interpretations of graphical and tabular data, and to reason critically about uses of quantitative evidence. The QLRA has been used to assess the effectiveness of Big-Q courses, but also as a placement exam for those courses. QLRA has also been found to correlate with important student success outcomes in the first two years, in a way that adds predictive power independently to students’ math and verbal SAT scores.
NEW APPROACHES FOR STATS & METHODS
From the very beginning, social science faculty have been key drivers in the movement for quantitative literacy. Recent enrollment booms in programs like psychology, criminal justice, and political science have created new populations of students who have to be prepared for success in both consuming and producing quantitative research and data analysis. This is a story of social science programs that have begun to re-scaffold those skills within their curriculum to provide their majors with foundational Big-Q experience early in their program – This is also the story of an analytic rubric for assessing those Big-Q skills using projects their students are already doing in their discipline.
Required courses in quantitative and qualitative research methods are common in social science programs. But in a lot of those programs, students do not encounter these courses until their senior year, and sometimes find – on the doorstep of graduation! – that their quantitative and statistical preparation is not up to the task.
In 2004, for example, the American Sociological Association recommended that programs require statistics and quantitative methods courses as appropriate “earlier rather than later in the major, so that advanced courses can be taught at a level that assumes students have had a foundation.” In other words, the longer students wait before Big-Q, the less time they have to USE those skills in their discipline. So by moving the introductory statistics course in the major to the freshman or sophomore level, and/or linking it with a statistical or quantitative course taken to fulfill an early math requirement, faculty teaching upper-division courses can be more successful engaging their students with quantitative research. And what social science faculty member wouldn’t want to do that?
LEAP RUBRIC: MEASURING BIG-Q IN CONTEXT
As part of their LEAP project, the Association of American Colleges and Universities developed what is probably the most influential rubric for assessing “Big-Q” quantitative literacy, in whichever discipline it is taught. The VALUE rubric sets an analytic scale for each of the components of quantitative literacy: the interpretations and the assumptions needed to retrieve a quantitative idea from its context; the calculations and choices needed to gain an insight; and the analysis and communication needed to place that insight back into its context.
BUILDING A DATA SCIENCE PIPELINE
While it’s true that every college student’s future career will benefit from more quantitative fluency, the information economy also needs experts to inhabit new career paths in which Big-Q skills are central, Careers in business intelligence, predictive analytics, machine learning, and information management. New academic programs have arisen to meet this opportunity, many of which organize under the new umbrella called “data science.” Their rapid development has led to incredible variety in these programs, and consensus on a curriculum is still emerging. But typically it involves both foundational coursework in mathematics, statistics, as well as computer science; and partnerships with key client disciplines such as business, biology, and engineering.
Some of these programs arise as subsets of existing majors in mathematics or statistics, such as the data science specialization in Bowling Green State University’s math major. Other programs are essentially multidisciplinary, such as the programs at Iowa State which offers data science credentials at the certificate, minor, and major program levels. The highly marketable nature of the data science skill set has also driven undergraduate capstone experiences and industry-partnered internships, as well as pathways to advanced credentials and accelerated bachelor’s/master’s programs such as the one offered at the University of Massachusetts at Dartmouth.
One key design criterion for these programs is how do they provide access for students at the introductory level. An emerging practice is to leverage existing general-education courses, such as statistics, as on-ramps to the major, integrating some basic elements of computing to prepare interested students to continue to a second “bridge” course into data science. As one math chair put it, data science is not a math degree. But it’s not NOT a math degree either. And so, some programs even eschew the traditional series of calculus-based mathematics prerequisites in favor of a deeper dive into linear and matrix algebra.
“Leaves and Flowers: The Little Q”
Once a student’s Big-Q foundation is laid, there’s no limit to the breadth of “small q” expressions of quantitative literacy possible in their college experience. In a “small q” setting, we find programs in general education, faculty development, and student support that help to instill students’ quantitative habits of mind through repeated encounters across the curriculum. In these settings, the numbers are not always the main course; they can be side plates. Even desserts. Students should discover that the opportunity to wrestle with numbers presents itself far more often than does the expectation. So the tools we use to assess students’ success are more holistic, they adjust for the choices that students make to seize on those opportunities — or, not.
Here, we find students more at ease in their own discipline, where the choice to attend to numbers may not always be necessary for their task but can elevate a project from good to great. We see in small-q examples of general education programs that integrate quantitative reasoning opportunities within writing courses; of instructors who make a point of ensuring data is always incorporated among primary sources; and “infusions” and overlays that provide modularized quantitative experiences faculty across the disciplines can borrow for their teaching.
NUMBERS INTO WORDS: QUANTITATIVE WRITING
Students’ writing can shine a bright light on any of their critical thinking faculties. In contrast to mathematical skill, which can be evident in a symbolic manipulation, quantitative reasoning is inextricably wrapped up in the ways that we communicate. In vernacular and language. Culturally informed, socially constructed. And nothing draws those out quite like writing. Owing to the recent successes of Writing Across the Curriculum programs, college faculty are now providing more opportunities than ever for students to evince their thinking in written form. So, wisely, some quantitative literacy programs use these opportunities to also prompt students to write about quantitative information, and can use student writing to assess numeracy.
So-called “quantitative writing,” in which students are expected and supported to include analyses of quantitative information in any writing assignment, has been shown to enhance student learning by bringing them face-to-face with the messy questions and mindful choices necessary to navigate numbers in their authentic contexts.
QUIRK PROJECT: HOLISTIC RUBRIC FOR WRITING
Assessing quantitative skills in written work is correspondingly messy. But an exemplar approach is Carleton College’s QuIRK project. Before this rubric assesses the success with which students incorporated and drew valid inferences from quantitative information in their writing, it first controls for the opportunity that the assignment presented for them to do so, and then controls for the importance of the quantitative reasoning for their argument. Was it a central argument (a main course)? Or a peripheral argument (a tasty side dish)? At Carleton, this rubric was first used to assess quantitative reasoning in longitudinal portfolios of student work; but it has been adapted to many contexts and is useful anywhere that sourced, rhetorical writing incorporating quantitative evidence is assigned.
ACCORDING TO SOURCES: DATA IN JOURNALISM
Achieving quantitative literacy across the curriculum means resisting the urge to sort disciplines, courses, and worst of all, people into “math” and “not math” categories. That’s a tendency to which math-anxious students and let’s be honest, even some faculty and advisers can be prone. But we cannot build a more numerate world from within our math and science classrooms; we must learn to assign value to using numbers in “not math” spaces as well. Such as in the humanities.
In an early workshop on my campus, I worked with a history professor who realized that in all the years that she’d scrutinized and assigned her students a particular source text, she’d never looked closely at the many data tables that were there. What stories, she realized, were those data telling that she, the author, and most importantly, her students, might have been missing out on? Just adding an explicit prompt to her existing assignment was all she needed to bring a data conversation into her classroom.
Likewise, two of the most math-anxious student populations on campus are also two populations that will have an outsized influence on the health of our democracy: future teachers, and future journalists. Because numbers can be used to obscure a story as easily as to reveal it, journalists especially have to cultivate skeptical habits around inferences drawn from quantitative information, and there are several high-profile initiatives to support quantitative literacies in journalism and mass communication programs.
In fact, news articles can be valuable conversation-starters for exercising quantitative reasoning with any audience – as the beginning of this same video illustrated. Including news articles that have data and charts among source material, without explicitly asking students to attend to the numbers, can be a valuable way to assess their numeracy habit of mind, to address that all-important question: Are students really going use these skills when there’s not a “math person” looking over their shoulder asking them to do so?
QUANTITATIVELY BREAKING COGNITIVE ILLUSIONS
The most successful conspiracies are those that reach out into every corner. And several programs for quantitative literacy across the curriculum have made themselves indispensable on their campus through an “infusion” into general education. In a typical infusion model, a small-q experience is incorporated into each of a wide variety of gen-ed courses that students typically take throughout their college experience. This can come as just a module, something larger than a single class period but smaller than an entire course. Students then must take a minimum number of courses that include one of those modules in fulfillment their general education requirement. Infusions succeed in general education in part because they help faculty “add value” to the existing content they’re already teaching, rather than displacing it.
One exciting way to weave quantitative skills into the fabric of general education is to lead students into and then out of cognitive illusions. The Numeracy Infusion Course in Higher Education, at CUNY, supports faculty to pose and to help students wrestle with what happens when your gut reaction tells you one thing, but then a careful analysis of the numbers reveals something else. This approach recognizes that the biggest challenge in getting students to think critically about the numbers that are in a text, sometimes, is just getting them to actually slow down and to read the numbers, considering not just the emotional, heuristic response they create but also the precise values and interrelationships those numbers represent. Building the habit of treating written numbers as questions rather than answers; treating numbers as rhetoric rather than authority; treating numbers as being inseparable from communication skills and information literacy. That’s well worth the time spent in any general-education course. And when it comes to cognitive illusion, nothing engages students like surprise.
NOW WHAT? RESOURCES TO SUPPORT QUANTITATIVE LITERACY
As the need for more quantitative literacy has blossomed, so too has the organizational infrastructure to support it. On a national level, the National Numeracy Network draws together faculty and administrators across all disciplines working on quantitative literacy, hosting an annual conference in the fall and compiling essential resources for this work through their website and through the open-access Journal Numeracy. The Mathematical Association of America likewise supports math and statistics faculty with its quantitative literacy special interest group. Regional networks and conferences, some of them loosely affiliated with NNN, have also arisen to build community. Around Massachusetts these include the annual conferences of the Northeast Consortium for Quantitative Literacy (NECQL) as well as the Southeastern Massachusetts Quantitative Engagement and Literacy meeting (SEQuEL).
NOW WHAT? THE NEXT EVOLUTION FOR YOUR CAMPUS
As important as this work is, though, progress has come more quickly on some campuses than others – because it truly does take a campus-wide commitment to meet this challenge. So let’s wrap up this video by thinking about what quantitative literacy looks like at your own college or university right now. Which of these sounds more like your institutional design and culture?
Do you see your quantitative curriculum through the keyhole of traditional school mathematics? Or do you engage faculty across disciplines to review the curriculum for these skills, and incorporate institutional research and assessment in doing so?
Do you rely solely on a math course for students’ quantitative skill development? Or do you intentionally and unavoidably incorporate that skill development across your curriculum?
Do faculty in your disciplines feel like they have to lower their expectations when they teach quantitative skills? Or are your faculty able to transparently articulate minimum standards for these skills from the beginning of their course to the end?
Do you assume that students’ quantitative skills can be adequately supported by your math tutoring center? Or do you cultivate and train academic support staff to support this specific skill set in whatever contexts it arises?
And, do your internal programs and assessments themselves model effective quantitative reasoning in their processes of continuous improvement? Or, do you have your own struggles with data-driven decision-making?
Choose the closest overall rating and don’t worry. I’m just a video recording; your secret is safe with me.
At Level 1, you are where I believe the majority of QL programs are right now: just getting started. So if you haven’t yet, try to get out among a wide variety of faculty, and ask the question, and listen. Where do students have the opportunity to use numbers in your classes? What else could you bring into your teaching if they were better equipped to do so? When we began this process at my institution, we were surprised at how much and how varied students’ opportunities to use quantitative reasoning really were in their senior-level projects in all the disciplines. But, faculty themselves often hadn’t been aware of the opportunity, and those that were either didn’t make that explicit for their students, or didn’t know how to connect students with the support needed to be successful. Creating space for those grassroots faculty conversations, for us, was an essential first step at getting out of that Level 1.
If you’re at Level 2, maybe you’ve built some awareness on your campus of what quantitative literacy is and why it’s important, but maybe not everybody is at the table yet. You might be waiting on a catalyst for change. At a lot of institutions, this comes in the form of a general education revision, or a reaccreditation. These are the moments to take a really good look at your program-level learning outcomes for quantitative literacy. Put them, and your assessment data on them, in front of stakeholders: faculty, administrators, support staff, partners from industry and in the community. Are those outcomes and results describing what we really want from our students when they graduate? Are our students still going to be able to do these things a decade fro now? How are those going to be different a decade from now? Are those skills what our partner universities, our employers, and our community really need from us? Having those conversations can get you to the next level of your program.
At Level 3, you’ve got a mature quantitative literacy program with broad faculty ownership, strong co-curricular support, and regular assessment for improvement. Great job! But if you’re like a lot of mature programs, you might feel short on institutional priority – meaning, short on resources. Be sure that you can demonstrate the causal relationship between your program’s work and your students’ quantitative skills, and therefore on their success in college and in careers more generally. You might marry your learning outcomes assessment data to workforce trends; you might seek funding opportunities to create new programs or centers on your campus that can create and sustain pathways into skilled quantitative careers; you might support student interest and visibility through participation in high-profile competitions like DataFest. Consistently tying your work on campus to students’ opportunities off campus can create the well-deserved buzz you need to take your already-established program to the next level.
And if you rated yourself at Level 4, congratulations on your robust program for quantitative literacy, and let me know when I can come and visit your campus to see how you did it. (Call me!)
Roots. Trunk. Leaves. Basic skills, a Big-Q experience, and small-q’s galore. However mature your quantitative literacy tree is, I hope that the resources in this video can help you to water it. Whatever your next steps are, I wish you the best in taking them. A more numerate world awaits.