Reclaiming the “Third R”

Algebra skills make a difference in college — but arithmetic skills make a bigger and broader difference in life.

Look, algebra skills are important. Not only does a mastery of algebra give a student among the most powerful tools ever developed to model and predict quantitative phenomena, it also develops key logical and analytical skills. But algebra is a major obstacle to success in college-level math courses (and hence success in college in general), and it may be the biggest “dropped stitch” in students’ mathematical development. Peter Bahr ( Res High Educ (2012) 53:661–693 ), in a study of retention within college remedial math sequences, writes that

beginning algebra is a ‘‘low point’’ in the math sequence in terms of the likelihood of success on the first attempt among students who progress up to this course from a lower level.

Indeed, a study by the Community College Research Council shows that scoring in the highest quartile versus the lowest quartile on the Accuplacer algebra placement exam has an effect size in predicting students’ college credit attainment comparable to that of reading and writing placement exams (a 10-credit advantage for algebra vs. 10.6 for reading and 11 for writing). But all three of these tests were less predictive than a fourth placement exam: arithmetic, which conferred a 12.7-credit advantage to its top-quartile scores. The authors write:

the predictive power of these [algebra, reading, writing] placement tests on college credits earned was very low; the best-predicting test (ACCUPLACER Arithmetic) explained 6 percent of the variation in college credits.

So while efforts to improve students’ algebra skills will likely improve their chances at college success, it may be that improving their arithmetic skills would have an even bigger effect — and given algebra’s rarity in the public sphere and arithmetic’s pervasiveness, strong arithmetic skills are likely to provide the most benefit to the most people. To me, the single most crucial of these arithmetic skills is the arithmetic of ratios, proportions, and percentages.

As I wrote in the article Disenfractioned, one of the most important number skills for daily life, is the ability to attend to fractions conceptually. That is, to conceive of a number that does not represent an absolute quantity but rather a comparison between two quantities. This is one of the largest cognitive shifts in arithmetic, and is probably second only to the shift into algebra in the extent to which students’ success in high school and college mathematics depends upon it. But a lot of effort and time is devoted to calculating with, rather than conceptualizing, fractions. I put it this way:

Rather than treating fractions as a necessary annoyance of arithmetic on our way to algebra, geometry, and calculus […] slow down and explore how fractions and fractional reasoning help us make sense of real-world problems. Rather than reaching up toward higher levels of abstraction, reach out toward more diverse contexts of application. Contemplate before you calculate.

It’s not just math instructors who are stymied by students’ weaknesses with fractions and percentages. Others are starting to take notice. My colleagues who teach upper-level college accounting and management courses have told me that, more than algebra and calculus skills, at the top of their wish list for their students is stronger understanding of basic fractions and percents.

Outside of higher education, the trend is no less evident. New England meteorologist Dave Epstein tweeted his frustration this week:

So where do we begin rebuilding these skills? As I’ll suggest in the upcoming workshop “Seven Habits of Highly Numerate People (And So Can You!),” the first step is to catch yourself already using this reasoning in everyday life. How do you find a 20% tip? Most people aren’t fastidious enough to find an exact answer with a calculator, so typically they estimate — another undervalued numeracy skill — by rounding the bill to the nearest $10, casting aside the zero, and doubling what’s left. While it’s possible that many people do this without knowing “why it works,” at the least it is one slice of life where successful dealings with percents are more common than not. (Waitstaff can feel free to disagree with me on that last point.)

The more I learn about the upcoming Common Core State Standards for math, the more encouraged I am that the elementary school curriculum in these topics is moving in a positive direction. And that direction, according to the standards, is “early,” dwelling on fractions beginning with the third grade, including this standard (3.NF. a.3d) that I particularly appreciate (emphasis mine):

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

This standard is a direct assault on what may be the biggest “bad habit” that students pick up in making the shift from numbers as quantity to numbers as comparison: denominator neglect. Proper fractions represent relationships of parts to wholes; likewise with percentages between 0% and 100%. But too often, the role of the whole is lost, and this is especially true of percentages everywhere they are reported, from popular media to academic journals to federal budget bills. One of the most useful habits to build context-aware numeracy skills is to pause at each percentage you encounter and ask yourself: “Percent of what?” Forcing the lazy side of your brain to hold two numbers, both part and whole, in your memory is the most fundamental prerequisite to a better understanding of fractions and percents.

The front lines of the battle for numeracy, then, begins in elementary school — but continues into and throughout adult life. Innumeracy preys on weak arithmetic skills. But fortunately, these skills may be the easiest to rebuild, and everyday life provides plenty of opportunities to practice them.

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Innumeracy: An American Crisis

Tags

innumeracy, oecd, roots, timss

The numbers are out, and they don’t look good. But unfortunately, many U.S. adults might not be able to tell.

The Organization for Economic Cooperation and Development (OECD) has just released the results of a 24-country survey of adult basic skills, testing literacy, numeracy, and problem-solving. Its takeaways for the United States are grim:

Literacy: Japan ranked #1 overall; the United States 16th out of 22. Among 16- to 24-year-olds, the U.S. ranked 20th out of 24.

Numeracy: Japan ranked #1 overall; the United States 20th out of 22. Among 16- to 24-year-olds, the U.S. ranked 24th out of 24.

You read that right: not only do rates of adult numeracy in the U.S. lag far behind our first-world partners, they are especially poor among our young people of high school and college age — dead last in the study. The Washington Post writes:

Americans are “decidedly weaker in numeracy and problem-solving skills than in literacy, and average U.S. scores for all three are below the international average…

And the problem with numeracy persists even among the highly educated. WaPo again:

Among the most educated test-takers — those with graduate or professional degrees — U.S. citizens scored higher than average in literacy, but lower than average in math and digital skills.

When this news came out, I was struck by its juxtaposition with the recent good news regarding U.S. eighth-graders’ math skills in the updated TIMSS (Trends in International Math & Science Study). TIMSS’ findings ranked math skills in the U.S. well above average, and in some states — notably Massachusetts — stronger even than leading countries like Japan.

Is this hopeful news for the future of numeracy? Will today’s excellent eighth-graders grow up into more quantitatively literate adults? Or does it suggest an even bigger problem, namely, that somewhere between middle school and college our students’ number skills are being not only lost but dramatically so?

Given what we know about how students’ attitudes about math change as they transition from middle school through high school and into college, I fear it may be more of the latter. After all, strong math skills are necessary but not sufficient for strong numeracy skills: a mastery of the quadratic formula may look good on TIMSS, but it’s not enough for a student to make informed decisions about financing their first car. Committing area and volume formulas to memory will make a college calculus course slightly easier, but it won’t help students to interpret a presidential poll in the newspaper.

The social constructivist educator in me — and recalcitrant math students everywhere — suspects that what “math” courses need to do better is reach value claims, that is, engage in problem solving that students will find actually valuable to their courses, their careers, and their civic lives. D. Bob Gowin’s famous V-model even suggests that a basis in values should be the first consideration in how an educational experience is designed: before we invite students into a course, we have to answer the question “why will this be worth their time?” 

This is historically much easier to do for students in arithmetic and pre-algebra courses, and even beginning algebra. Maybe it is no surprise, then, that students through the eighth grade remain more engaged in their mathematics learning. But further along in the algebra-geometry-calculus sequence, the value basis begins to erode for many students. Why is trigonometry worth their time, for example? As the courses become more specialized, some students — chiefly those already interested in or planning for science, engineering, or technical careers — will see the value for their future education. Other students will not, and it is therefore no surprise that they disengage.

Don’t get me wrong: I don’t want to blame the high school curriculum for this predicament. Part of the solution may lie there, insofar as only part of the solution lies in education altogether. The remainder of the solution is a matter of public values and cultural values, and in a country like the U.S., capitalist values. U.S. Secretary of Education and former Chicago Public Schools chief Arne Duncan is quoted in the Post as saying of the OECD’s findings:

They show our education system hasn’t done enough to help Americans compete — or position our country to lead — in a global economy that demands increasingly higher skills.

That last claim — that the global economy demands increasingly higher skills, such as numeracy — is taken as an article of faith by many of us in education. But that message has yet to take cultural root, even in these difficult economic times. Until the value of basic skills, and the unspoken but very real stigma that comes with their absence, is felt in dining rooms across the country, the will to change is likely to remain scarce.

Whatever the cause, and whatever the solution, numeracy in the U.S. is indisputably a problem. Here’s hoping that that admission is the first in a collective twelve-step program to reclaim our numerate potential.

Do the Right Math

Tags

critical reasoning, roots

Numeracy is not just about doing the math right. It’s about doing the right math.

Nate Silver, the head of FiveThirtyEight.com and perhaps the country’s most visible practicing statistician, put his finger on this issue recently. In a critique of Public Policy Polling’s methodology, he tweeted:

For example, you might have the skill to compute the mean price of houses sold in a neighborhood. But even if you perform that computation flawlessly, the result is not necessarily meaningful if your goal is to quantify the “average” value of housing. Before you computed, you chose what to compute – and in this case unwisely. (Median is the more useful measure of central tendency here, since housing prices are prone to outliers.)

Put simply, no one will care what answers you arrive at if you ask the wrong questions.

Real, authentic numeracy is not just a critical reasoning skill, it’s a flexible skill. While the answers to its questions are convergent, the questions themselves can be divergent. To be a numerate individual, you must possess not only the (convergent) ability to do math right, but also the (divergent) ability to do the right math, choosing the right tool before taking it to hand. As Nate Silver said, this is a matter of good judgment.

Yet the traditional secondary math curriculum rarely encourages judgment, since it does not usually make room for divergent thinking. My favorite quote on this dilemma is from math education expert Barbara Rose, who wrote (emphasis mine) that

The standardized curriculum expects students to do mathematics, not to think about its nature or raise questions about its existence.

And indeed, the standardized algebra-geometry-calculus curriculum is so content-dense that it is legitimately difficult to invest the time necessary to develop critical reasoning and judgment. As anyone who has taught in this sequence can attest, it’s hard enough to bring students to a point of proficiency with each individual skill, let alone call upon them to recall and choose skills from their previous courses. In other words, “they have enough trouble with Section 4.3, I don’t want to frustrate them with unrelated, open-ended problems!”

So teachers do what they must to build skill proficiency in their course: introduce, develop, test — and move on. Taught in this way, it is not surprising that many students develop math skills in a series of unmotivated, disconnected, and often ineffectual “tricks,” rather than as integrative critical reasoning. As Robert Leamnson says in his book Thinking About Teaching and Learning, many high-achieving high school students are successful because they have learned how to play the school “game,” a strategic kind of learning in which they are able to quickly discern what their teachers expect of them, provide just that on exams, and receive high marks without doing much critical thinking.

For these students, it is as though their high school experience is like learning a foreign language one word at a time. They are excellent mimics and are lauded for their word pronunciation and inflection — but are unable to compose a coherent sentence in the language, and college is about ideas, sentences, not words. They excelled at the high school game, but the college game has a different set of rules.

But life is not a game, and the real world is not “chunked” according to topic or technique. What’s needed, then, are real, authentic number problems that require real, authentic problem solving, which begins not with an instructor telling you which tool is appropriate, but with you assessing for yourself which approach to use. That’s what separates relevant, transferable skills from isolated, task-specific skills. The latter skills, while necessary for the former, are by no means sufficient.

Choose your approach wisely, and your problem is already halfway solved. The rest, as my freshman physics professor used to say, is just details.

Do the right math.

New Approaches, New Attitudes in Statistics Courses

Tags

article, leaves, statistics

Negative attitudes toward numbers are a significant barrier to student success — but the right course can help turn them around.

Anxiety about numbers and mathematics is so common in Western culture as to be a cliche. Sheila Tobias’ landmark 1994 book Overcoming Math Anxiety explored the roots of, and strategies for reducing, math anxiety, and because females are more prone to adult math anxiety than males, the book was (rightly) hailed as a feminist triumph.

Yet a significant proportion of college students experience math avoidance strongly enough to affect their course-taking behavior. A 2012 study by Peter Bahr found that remedial math students – who we can expect experience math anxiety disproportionately – frequently delay taking required math courses. Not only did 50% of incoming remedial students in the study choose to delay their first math course for a semester or longer, among those that started math right away and passed, more than half delayed their next math course in the sequence by a semester or more. In short, this is an illustration of what my faculty colleagues – especially those who teach upper-level quantitative or statistics courses in their discipline – already know. When it comes to taking number-heavy courses, students delay, delay, and delay, to their peril.

This trend is particularly evident with statistics courses, even (perhaps especially) applied statistics courses in social science disciplines. These courses often are placed toward the end of the curriculum, carrying 300- or 400-level course numbers, which students interpret to mean that they are “advanced statistics” courses. Indeed, this perception seems to be common to all college statistics courses regardless of level: because of students’ limited exposure to statistics content in their secondary education, they tend to see all statistics as high-level mathematics.

This only serves to mystify the subject and amplify students’ anxiety. Perney and Ravid’s 1991 study of statistics students in an education graduate program at Northwestern found that their initial self-concepts toward the subject were generally low, and especially low among students with less background in math and statistics. While these attitudes did not significantly correlate with course achievement in the study, attitudes did significantly improve for all students regardless of their background throughout the course. (This improvement was seen in attitudes as measured by the Attitudes Toward Statistics and Math Self-Concept inventories. Interestingly, no movement was seen in the Test Attitude Inventory – suggesting that students grew more confident in the subject but still were no more thrilled to be tested on it as when they started.)

Gal and Ginsburg’s helpful 1994 survey of attitudinal effects in statistics education makes the case for attending to students’ perceptions explicitly, since they can pose significant barriers to achieving course outcomes – to say nothing of carrying statistical reasoning beyond one semester, whether into a next course, into the workforce, or into the world. In addition to calling for more variety in assessment scales to measure students’ attitudes toward statistics, they point to the then-emerging cognitive psychology research on how attitudes, attribution, and beliefs about the nature of intelligence inform students’ motivation in math and statistics content courses.

All of which leads me to pivot, as Gal and Ginsburg do, to a hopeful note by pointing at the redoubtable Carol Dweck’s work. I particularly enjoy both her 1986 study on how motivational processes help or hinder learning and her excellent 2006 book Mindset: The New Psychology of Success. Number-oriented work, as a colleague of mine in the humanities observed to me recently, requires one to persevere through several wrong attempts to find the right. To work with numbers is to discover success through an iterated process of failures.

How a student responds to numbers, Dweck theorizes, is ultimately a reflection of how they respond to challenge and failure, which is in turn affected by their self-conception of intelligence. Those who belief intelligence comes in fixed quantities, meted out to each individual at birth, perceive a challenge as a threat to their self-worth. When the going is easy, these students remain motivated by a desire to “prove themselves.” But when the going gets tough, they fall into helplessness: if I got it wrong, it’s because I’m not capable of getting it right. Their iterated failure process often stops after one iteration, so their success is elusive.

By contrast, those who believe intelligence – no matter how “much” one has – is malleable, that anyone can learn, develop, and expand their cognitive capacity, perceive a challenge as an opportunity to grow. These students believe that each iterated failure carries with it a valuable lesson, and remain motivated to see their challenges through whether the load is light or heavy. If I got it wrong, they say, then next time I’ll get it less wrong. This approach to challenge and development is captured by Samuel Beckett’s famous quote:

Try again. Fail again. Fail better.

Dweck’s work not only points to the difference that students’ intelligence mindset can make in their education, but also looks for ways to shift students’ mindsets to make motivation and perseverance possible. It begins by creating a classroom environment in which failure is not stigmatized, but indeed expected and even encouraged. Collaboration between students helps to deflect the damaging personal self-judgments that sometimes accompany failures. Presentations and activities that highlight to students what cognitive scientists have discovered about neuroplasticity – the ability of the brain to change in response to experience – have also been shown to result in shifts in mindset from a static to a more malleable viewpoint. The testimonials from students in Dweck’s book should be affirming to any educator, and are a fantastic antidote to the all-too-common teacher’s cynicism.

The best solution to changing students’ course-taking behavior to decrease their avoidance of quantitative courses, then, seems to be to make those courses more emotionally intelligent. At least in the beginning of the course, Rosenthal in an infamous editorial in the UMAP Journal implores instructors (emphasis mine)

to acknowledge and legitimize students’ perceptions of the quality of life in the course we create for them…[and] reflect the reality that unintended human suffering takes place under our watch.

In addition to overtly affective exercises, this also speaks to me of a need for more engaged pedagogy in these courses. Active learning, inquiry- and project-based techniques, low-stakes formative assessments, and team-based learning all seem to me to be ways to lower the barrier to success by encouraging more, more frequent, and less stigmatized failure.

Perhaps most hopefully, instructors have a considerable amount of leverage to affect their students’ perceptions. In the Northwestern study, students whose attitudes toward statistics improved over the semester overwhelmingly credited their professor for that positive change. What’s more, a positive experience with statistics also contributed to a positive change in these students’ overall math self-concept, leading Perney and Ravid to recommend that

instructors in statistics courses should focus not only on the course content, but also on providing a nurturing, supportive learning environment.

Well put, I say.

Context Matters, Even in “Basic Skills” Courses

Tags

article, developmental math, roots

“Basic skills” math taught contextually is rare – but more effective, finds this study.

Wiseley, W. C. (2011) Effective basic skills instruction: The case for contextualized developmental math. Policy Brief, 11-1.

College-going rates in the U.S. are higher than ever. In response to the needs of a more highly credentialed workforce, nearly half of all 18- to 24-year-olds who complete high school enroll in a degree-granting postsecondary institution, up from only about one-third in 1967. However, the increased importance of postsecondary education comes at a price: not only is higher education tuition expensive, the increased access to it has led to a wider population of entering college students whose high school education has left them deficient in basic reading, writing, or math skills.

These students typically play catchup in non-credit "developmental" (or "remedial") courses, having been assigned to these courses by a skills test. Developmental education is a massive undertaking: nationwide, roughly 2.5 million students per year, and almost 30% of incoming college students, enroll in developmental education courses. A 2008 study amusingly titled Diploma to Nowhere estimates the cost of developmental education at about $2 billion per year in community colleges and an additional $500 million in 4-year universities. Worse yet, students who take these non-credit courses in college are less likely to graduate: Massachusetts 4-year colleges have the highest graduation rate in the nation for remedial students, but it’s only 51%. The graduation rate for developmental students at community colleges, where more students are assigned to sequences of non-credit courses spanning two or more semesters, is much lower still: in Massachusetts only 10.3% have earned their associate’s degree after three years.

Basic skills math courses are frequently taught as just that: basic math, devoid of context and nearly identical in form and pedagogy to the middle- and high-school math courses whose content they mimic. One can hardly blame the instructors that teach them, as many of them have long experience as K-12 math teachers. But developmental math students owe their circumstances to an unproductive experience with the same kind of teaching. For many students, the developmental math experience in college amounts to the worst kind of high school déjà vu. The stigma of feeling “sent back to high school” is for some students insurmountable.

But that trend may be changing as more basic skills math classes are finding new life in context. A joint statement issued by Complete College America, The Charles A. Dana Center, and others makes the assertion that

With its one-size-fits-all curriculum, remedial education does not provide solid academic preparation for the programs of study most students pursue. As a result, remedial education too often serves as a filter — which sorts students out of college — rather than as a funnel — guiding them into a program of study.

The report cites a 2012 working paper by the National Bureau on Economic Research which finds that on the whole, students are not picking up the skills they truly need for college success in their developmental courses, because those courses tend to focus on isolated skills rather than connective reasoning.

This brings us (at last) to W. Charles Wiseley’s policy brief, written for Policy Analysis for California Education (PACE) at Stanford University. In it, Wiseley analyzes developmental math course offerings across California’s 110-school community college system, and carefully classifies each as being either a traditional, narrowly focused course (e.g. Beginning Algebra) or a contextual course (e.g. Business Math). Both tracks of developmental courses address the same mathematical reasoning outcomes, from pre-algebra through intermediate algebra content, and should therefore be considered preparatory for college-level mathematics.

The results are striking. The contextual students passed their developmental course at much higher rates (86% vs 59%) and passed credit-bearing college courses that same semester at higher rates (93% vs 75%). Students who passed contextual basic skills math were 70% more likely to pass credit-bearing courses in the following semester. While they were substantially less likely to attempt transfer-level courses in the following semester – likely because many were enrolled in terminal vocational certificate programs – those that did were more than twice as likely to pass that course as their traditionally-trained counterparts.

Success in contextual courses is also more inclusive. Compared to their counterparts and controlling for other demographic and socioeconomic factors, black students were 2.6 times as likely to pass contextual basic skills math than traditional; Native American and other nonwhite students 33% more likely; and Hispanic students 27% more likely. (Interestingly, there is a small negative effect among Asian students, who are 12% less likely to pass the contextual version than the traditional. White students saw no significant difference.) Given that students in racial and ethnic minority groups enroll in developmental coursework at disproportionately high rates, contextualization of these courses seems to be a socially just pedagogy.

This tells me that context has two effects. Tying math skills to vocational contexts supplies a necessity for learning that increases student engagement and receptivity to learning. It also enfranchises students’ informal quantitative reasoning abilities: especially when it comes to pre- and beginning-algebra content, students are more successful at solving contextual story problems than the equivalent context-free algebra problem. Not only does context give students a reason to learn and to care, it also permits them to access problem-solving abilities from their rich contextual lives.

Unfortunately, the study sample is fairly small since contextual pre-algebra level courses were (and are) incredibly scarce. Students in traditional courses outnumbered students in contextual courses 40 to 1. Furthermore, there was no ability in the study to correlate student success in common successor courses: for instance, it is not clear whether contextually trained students and traditionally trained students would perform differently in the same college-level course (e.g. College Algebra or Calculus for Business). The overall pass rates in the credit-bearing and transfer-level courses these students took were not contrasted, but it is in my opinion likely that some of the contextual students’ higher success is owed to higher overall pass rates in the credit-bearing courses their contextualized programs offer compared to traditional credit-bearing courses like precalculus.

Still, the study is eye-opening for all the reasons listed above. The more contextual a student’s development of basic skills, the more likely they are to succeed in developing and retaining those skills through the context important to their field. Contextual basic-skills training may be, for students beginning college at a math skill disadvantage, the best hope for (inclusively!) building their numeracy.

What is Digital Humanities?

Tags

branches, digital, humanities

 

 

Digital Humanities is a trend. I know, because it told me so. After the jump, we’ll talk about how digital humanities can give us new insights about literature, art, and music — all through the art and science of data.

Above, a Google Ngram graph shows how the phrase “digital humanities” has grown in the English language over time.

Scientists have long accepted the notion that observations and data provide fundamental insight into the physical world. But what can numbers tell us about ourselves? Can they shine a light past our individual selves and our societies, and illuminate the human condition? Do numbers have a place in the capital-H “humanities?”

A little skepticism about numbers is expected, and arguably healthy, among humanists. Met with their complaint that numbers are cold, incapable of capturing shades of meaning, and de-humanizing, mathematicians have long reached for fatuous examples of how quantitative reasoning can bear upon fields such as literature. Statistical analyses of word choice can give us clues to who wrote texts of disputed authorship, I’ve sometimes said by way of example; but these examples are often superficial and, in many cases, don’t work. (They can’t even distinguish between the different authors of the Federalist papers, for example – Martingale & McKenzie 1995.)

But armed with a new umbrella term – Digital Humanities – and advances in both computing and statistical technique, quantitative methods for extracting information from corpuses of literature, art, and music are seeing new energy. A glance at the (appropriately, online) Journal of Digital Humanities provides evidence of the field’s technical sophistication. Increasingly, historical works are being converted into digital, searchable archives. The social media sphere is flooded with human data, and researchers such as Deb Roy at MIT’s Media Lab have developed powerful algorithms to track sociolinguistic trends as they emerge in the Twitterverse. In short, more and more of the human experience is either being digitized or already takes place in the digital realm, and some aspects of it may only be captured by analyzing it where it lives, in bits and bytes. Digital Humanities is more legitimate than ever.

Implications for teaching: While the field has rapidly become highly technically and statistically sophisticated, digital humanities can begin with free online tools for content analysis. Google’s NGram generates graphs showing the prevalence of phrases over time in various corpuses of public-domain literature in several languages. (What does this graph of the usage of the words “gay,” “lesbian,” and “homosexual” over time tell you about the usage of these words?) The NGram at the top of this post suggests how the phrase “digital humanities” itself only emerged in the mid-1990s and was not very widely used until about the last ten years.

Even more simply, word cloud apps like Wordle generate spiffy diagrams calibrating by their size the frequency with which words are used in a body of text, such as this cloud for the U.S. Constitution. These tools employ simple statistical methods and display the results in a way that any student should be able to interpret, without specific background in statistics; other, more sophisticated tools might be appropriate to use within statistical methods courses where topics such as correlation are developed.

A Bridgewater State University reference librarian maintains an annotated list of “Cool Tools and Gadgets” that can be used for visualizing data, most of which are free online apps. More generally, BSU’s Digital Humanities MaxGuide is a guide to digital humanities research projects going on around the web and around the region.

A successful digital humanities project thrives on collaboration between humanists, statisticians, and technology specialists. If ever a literature professor needed an excuse to collaborate with a computer scientist, or a historian with a mathematician, the types of questions that can be posed in the digital humanities necessitate this kind of interdisciplinary work.

And me? Having used digital tools to analyze the mathematical features of some of M.C. Escher’s artworks (appeared in the Journal of Humanistic Mathematics), I can testify to the versatility of digital tools in humanistic investigation. What projects do digital tools make possible for you and your students? Tell us about it in the comments section below.

The “Tree” Curriculum

Tags

curriculum, theory, tree

I often think of a strong quantitative curriculum in higher education as taking on a tree shape. Students’ numeracy skills sprout from their diverse ROOTS in basic math skills, grow through a TRUNK of fundamental critical reasoning, then sprout BRANCHES into their various disciplines, and finally LEAVES as they bring their skills out of the academy into the world.

Launching The Third R Blog

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quac

Welcome to The Third R.

The purpose of this blog is to share news, articles, and thoughts surrounding issues of numeracy and quantitative reasoning in higher education. The Third R will share content with the website of Bridgewater State University‘s Quantity Across the Curriculum (QuAC) faculty development project.

QuAC’s mission is to increase faculty and student engagement with quantitative reasoning in their discipline. We support the development of numeracy skills at all levels of higher education, from remedial mathematics courses through upper-division, research methods, and capstone courses in all fields of study. 

Updates will be sent weekly, or as news breaks.