Grow Up, Branch Out: Quantitative Literacy for the 21st Century

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. 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? 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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? 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. 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. 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. 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. 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. 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? 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. 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). 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.

1 thought on “Grow Up, Branch Out: Quantitative Literacy for the 21st Century”

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