teachinglearning

Learners largely left out of digital bill of rights (essay)

A bunch of educators, several of whom I know and respect quite a bit, got together last month to write a "bill of rights" for online learners. Viewable and editable here.

They included the rights to access, privacy, openness, to create public knowledge, to "pedagogical transparency" (to understand the ways you are being taught and the value of any credentials offered), "financial transparency" (Where is my tuition money going? How will this “free course” be paid for?), to have great teachers, and to become teachers.

I can’t find myself disagreeing with anything much that they had to say, except for one screaming contradiction that brings the whole thing down.

"All too often, during such wrenching transitions, the voice of the learner gets muffled," this group wrote in their introduction.

The problem is, this group didn't include any learners. Of the 12 signatories, I count 8 Ph.D.s or Ph.D. equivalents. They didn’t reach out to any learners on public forums. They didn’t ask any learners what they wanted to put in the document. The voice of learners is absolutely silent.

Sure, we’re all lifelong and informal learners in some sense, but let’s draw a real distinction here. Let’s talk about people who don’t have a bachelor’s degree and need one or the equivalent to make a decent living and participate in society on an equal footing.  I’m not asking why the group didn’t poll Udacity users in Pakistan or Colombia, or YouMedia high school students in Chicago, or middle schoolers around the globe making their way through Khan Academy math videos, and find out exactly what their concerns are and how they would prefer to have them represented in such a document. Although really, it wouldn’t have taken much time or many resources to do this kind of research. I’m asking why they wrote a “learners’ bill of rights” without including one actual learner in their little group of 12.

I’m not going to be tendentious and draw parallels with other bills of rights. I’m not going to ask about the advisability of men writing a feminist Bill of Rights on behalf of the women they care about so deeply. Or of the North writing a bill of rights for Southerners after the Civil War.  Or of employers writing a bill of rights for their employees.

Suffice it to say that educators are in a historical position of no small authority over learners. And when one group of people with authority over another makes up the rights for the second group, they tend to get some things wrong.

The fact is, this isn’t a bill of rights for learners at all. It’s a set of principles to support the interests of a group of educators, who share concern for learners, blended with concern for their own group. They tip their hand in the eighth principle, “The right to have great teachers.”

“Students should expect -- indeed demand -- that the people arranging, mentoring and facilitating their learning online be financially, intellectually and pedagogically valued and supported by institutions of higher learning and by society. Teachers’ know-how and working conditions are students’ learning conditions.”

I am in favor of all who work with learners being fairly paid, and I am definitely in favor of great teachers. But I am not in favor of students being drafted onto the metaphorical or actual picket lines. Students in state four-year institutions are paying more and more of the salaries of their instructors and going into sometimes-extreme debt to do it. There’s an uncomfortable moment where the interests of the learners actually diverge from the interests of the career academics, and it should be discussed openly.

But enough. The authors intended this to be a living document, and I respect that there’s time to revise and collect comments from the hundreds of thousands of online learners out there. It’s not going to be that difficult.

When I first found out about this bill of rights, I posted it to OpenStudy, the online learning community. I got this response from an undergraduate computer science major within 45 minutes, which reads in part:

“you deserve education BASED ON WHAT YOU WANT TO DO IN LIFE..

Teach kids real world problems, and have them enjoy it…

Teachers/professors who care. In my time I have met a lot of wonderful professors, mentors, teachers, coaches, and a ton of HORRIBLE ones…

The job market sucks, and with students being taught the same thing, and not really learning what they wish it's hard to distinguish someone from the rest of the pack. If we want to succeed we need to produce students who enjoy learning, and have the tools to learn what THEY WANT TO LEARN."

Another wrote: "The rights I want in the ever-growing digital era are not anything different than what I would want outside of it. We have to expand these rights to be applicable into the digital world."

That’s a good start. Now there’s time to come up with a set of amendments -- a real learners’ bill of rights.

Anya Kamenetz is a writer and author of DIY U.

Essay on what professors can learn from MOOCs

Educators create online courses for the same reasons that they became teachers to begin with: to educate students, broaden their awareness of the world and thereby improve the students’ lives. And with massive open online courses (MOOCs), educators can now reach many more students at a time. But MOOCs offer many other benefits to the education community, including providing valuable lessons to the instructors who teach them.

Online courses inherently allow students to create their own pathways through the material, which forces educators to think about the content in new ways. And MOOCs offer professors fresh opportunities to observe how their peers teach, learn from one another’s successes and failures and swap tactics to keep students engaged. This is, in turn, makes them better teachers.

MOOCs are still the wild west of higher education, and there is no “one size fits all” approach to building one. At Coursera, we’ve been working with educators as they experiment with designing courses for this new format, and for a student body of unprecedented proportions. (For example, Duke University’s Think Again: How to Reason and Argue by Walter Sinnott-Armstrong and Ram Neta has more than 180,000 enrolled students.) We’re reimagining many aspects of what it means to teach a course, ranging from lecture delivery, to assignments, to strategies for engaging the online community of students.

While there are many resources for teachers to learn from when approaching online education, we’ve become aware that there is still a need for a central space for professors to share successful practices, ask each other questions, and showcase examples of what’s worked and what hasn’t in their online classes. Recently, we launched a course called Teaching a MOOC, open to all of the professors on the Coursera platform (we’ll be launching a free, public version soon). It functions like any of the courses we offer, including video lectures that offer guidelines for developing an online course for the first time, discussion forums and a gallery where professors can see examples from other classes. And that’s just the tip of the iceberg.

An educator who’s been teaching in a traditional classroom format faces many challenges and unknowns when creating an online course. The lecture creation process is different. The peer-graded homework is different. The process for managing your “classroom” is different. Even the copyright law requirements are different. Jeremy Adelman, a Princeton University professor who teaches A History of the World Since 1300, explains, “When you lecture into a recording box, it’s different from lecturing to students in person. I have a teaching style that relies on energy from students, and I had to figure out strategies that would transcend [that style] for my class on Coursera.”

Adelman discovered that in putting his course online, he became more focused on what students are experiencing, even though he wasn’t in direct contact with them. “When I lectured, I had to ask myself at all times ‘What is it that I want my students to learn?’ In the old-fashioned lecture hall I was an entertainer, more self-focused rather than teaching-focused, but I was not conscious of this dynamic until I put a course online for the first time,” he says. “For me, the lectures alone were a source of continuous learning and adaptation.”

Throughout the entire MOOC creation process, educators must constantly be student-focused, figuring out what is the most useful content for their students to experience next. With no admissions office, online students are vastly more diverse than the students in a typical college classroom. They vary in educational background, learning ability, and culture. Students are also at different points in their life, and range from teenagers to working professionals to retirees, and may have different learning goals. Educators have to make classes accessible without underestimating student ability.

Stanford professor Scott Klemmer was pleasantly surprised by his experience teaching a Human-Computer Interaction course. His class was the first to use peer grading (in fact, he worked with Daphne Koller and me to design Coursera’s current peer assessment system). After using self-assessment for six years in his class at Stanford, he thought there was “no way” that he could expect students to handle self- and peer-assessment online.

“But it worked amazingly well,” Klemmer explains. “When we surveyed students at the end of class, one of the things they rated highest, in terms of what taught them the most, was the act of assessing peers -- they found it extremely valuable. I put a huge amount of time into designing course materials based on rubrics and assessment techniques that I taught in my Stanford class on campus; I had no idea what it would mean to translate that into the online world.”

There has always been a tendency in distance education to focus on the physical barriers -- the distance between the professors and the students, and between the students themselves. Many people, including those in academia, believe there to be a broadcast quality to online lectures, with one person delivering lectures to students behind screens, where they can’t engage directly with the professor. They wonder, “If the professors don’t see their students, how can it be teaching?”

But through today's technological advancements, online courses are very much alive. They are part of an ecosystem that, if nurtured through community discussion forums, meetups, e-mails, and social media (like Google+ hangouts), can flourish and grow. This allows each class’s community to take on a life of its own, with a distinct culture that’s defined at least as much by the students as the instructor, and which even skillful instructors can only guide, but not control.  Nearly every instructor that I’ve spoken to has been surprised by the  deep desire of students to connect with each other as well as with the teaching staff and professor. 

University of Michigan professor Eric S. Rabkin found his experience teaching Fantasy and Science Fiction: The Human Mind, Our Modern World incredibly enriching. “I had not anticipated the kindness and excitement I see in this large body of participants. Despite the potential for impersonality, I have received emails of thanks, of enthusiasm, of discovery. I have replied to some of those and some of my replies have been re-posted to the forums by the recipients. The community knows I care and, at first astonishingly to me, cares back. They care enough not only to spend time with each other but to share their experiences, some even through blogs of their own, with the wider world,” he says. “Amazingly, this feels somehow like a family. Not like a nuclear family, but like a suddenly discovered distant city brimming with eager cousins one had never known before.”

“I have been [teaching] the same way for years -- for decades and decades -- without being mindful of the changes in technology, the changes in our students. Online courses blow up the old conventions. But I think it will take us a while to figure out what works and what doesn’t work,” says Princeton professor Jeremy Adelman.

University of Pennsylvania professor Al Filreis, who teaches Modern & Contemporary American Poetry, says that teaching online has given him his “most extraordinary pedagogical experience” in 30 years of teaching. “The course is rigorous and fast-paced, and the material is difficult, but the spirit of curiosity and investigation among the students produced very good results,” he says. “Several eminent poetry critics joined the course to rate the quality of the students' critical writing and came away very impressed -- and surprised. We discovered that a qualitative, interactive humanities course can indeed work in the MOOC format."

With MOOCs, there is so much more potential for educators to go into each other’s classrooms and share resources with their peers.  We’re seeing this happen more and more, especially when it comes to professors adapting online course structures from other professors.

“Online education means that I have shared more stories with fellow professors about teaching than I had in the eight years I’ve spent teaching on campus,” says Stanford professor Scott Klemmer.

We might not have an answer to the question “What defines a high-impact MOOC?” just yet, but universities and professors who have taken the plunge are constantly learning and growing from their experiences. And what we’re seeing emerge from the trenches is an exciting new breed of education.

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Andrew Ng
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info@insidehighered.com

Andrew Ng is a co-founder of Coursera and a computer science faculty member at Stanford University. He is also director of the Stanford Artificial Intelligence Lab, the main AI research organization at Stanford. In 2011, he led the development of Stanford University's main MOOC platform, and also taught an online machine learning class that was offered to over 100,000 students, leading to the founding of Coursera. Ng's goal is to give everyone in the world access to a high quality education, for free. His Twitter handle is @AndrewYNg.

Texas A&M Will Push on Engineering Enrollments

Texas A&M University announced a major campaign to increase enrollment in engineering, with the goal of enrolling 25,000 students (more than double current levels) by 2025. The effort will involve both recruiting more students, but also looking for ways to improve the educational experience of engineering students.

 

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Group drafts bill of rights for digital learners

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12 scholars and experts on technology and education propose a "bill of rights" for those who study online -- a first draft, they quickly emphasize.

Essay on the flaws of distance education

One potentially positive result of the current fascination with online education is that universities and colleges may be forced to define and defend quality education. This analysis of what we value should help us to present to the public the importance of higher education in a high-tech world. However, the worst thing to do is to equate university education with its worst forms of instruction, which will in turn open the door for distance learning.

Perhaps the most destructive aspect of higher education is the use of large lecture classes. Not only does this type of learning environment tend to focus on students memorizing information for multiple-choice tests, but it also undermines any real distinction between in-person and online education. As one educational committee at the University of California at Los Angeles argued, we should just move most of our introductory courses online because they are already highly impersonal and ineffective. In opposition to this argument, we need to define and defend high-quality in-person classes.

Although some would argue that we should prepare students for the new high-tech world of self-instruction, we still need to teach students how to focus, concentrate, and sustain attention. In large classes, where the teacher often does not even know if the students are in attendance, it is hard to get students to stay on task, and many times, these potential learners are simply surfing the web or text messaging. In a small class, it is much harder for students to be invisible and to multitask, and while some may say that it is not the role of university educators to socialize these young adults, it is clear that the current generation of students does need some type of guidance in how they use technology and participate in their own education.

When people multitask, it often takes them twice as long to complete a task, and they do it half as well. For instance, my students tell me that when they try to write a paper, they are constantly text messaging and surfing the web: the result is that they spend hours writing their essays, and their writing is often disjointed and lacking in coherence. Since they are not focused on a single task, they do not notice that the ideas and sentences in their essays do not flow or cohere. Literally and figuratively, these multitasking students are only partially present when they are writing and thinking.

This lack of presence also shows up in the classroom. Students often act as if they are invisible in small classes because in their large lecture classes they are in many ways not present. Many students seem to lack any awareness of how they appear to others, and they are so used to sleeping in their large classes that they do not think about how their present absence appears to other students in a smaller class. Of course, it is much more difficult for students to be either literally or figuratively absent in a small class, but some students have been socialized by their large lecture classes to ignore the different expectations of more intimate learning environments.

As many higher education teachers have experienced, some students are able to participate in online discussion forums but have a hard time speaking in their small seminars. Once again, students may find it difficult being present in front of others and taking the risk of presenting their own ideas in the presence of others. Some distance educators argue that we can resolve this problem by just moving classes online, but do we really want to train a generation of students who do not know how to communicate to other people in a natural setting?

I worry that students are losing the ability to make eye contact and read body language, and that they are not being prepared to be effective citizens, workers, and family members. This disconnect from in-person communication also relates to a distance from the natural world, and a growing indifference to the destruction of our environment. In this alienation from nature and natural environments, people, also lose the ability to distinguish between true and false representations. Since on the web, everything is a virtual image or simulation generated by digital code, we live in a state of constant in-difference.

The web also creates the illusion that all information is available and accessible to anyone at any time. This common view represses the real disparities of access in our world and also undermines the need for educational experts. After all, if you can get all knowledge from Wikipedia or a Google search, why do you need teachers or even colleges? In response to this attitude, we should recenter higher education away from the learning of isolated facts and theories and concentrate on teaching students how to do things with information. In other words, students need to be taught by expert educators about how to access, analyze, criticize, synthesize, and communicate knowledge from multiple perspectives and disciplines.

While online educators argue that the traditional methods of instruction I have been discussing are outdated because they do not take into account the ways the new digital youth learn and think, I would counter that there is still a great need to teach students how to focus, concentrate, and discover how to make sense of the information that surrounds them. Too many online enthusiasts sell the new generation of students short by arguing that they can only learn if they are being entertained or if learning is an exciting, self-paced activity. Yet, we still need to teach people to concentrate and sustain their attention when things may get a little boring or difficult. Not all education should be fast-paced and visually stimulating; rather, people have to learn how to focus and stick with difficult and challenging tasks.

In this age of distracted living, where people crash their cars while text messaging and parents ignore their children while multitasking, do we really want a generation of students to take college classes on their laptops as they text, play games, and check their Facebook status updates? Isn’t there something to value about showing up to a class at the right time and the right place with the proper preparation and motivation? The idea of anytime, anyplace education defeats the purpose of having a community of scholars engaged in a shared learning experience. Furthermore, the stress on self-paced learning undermines the value of the social nature of education; the end result is that not only are students studying and bowling alone, but they are being seduced by a libertarian ideology that tells them that only the individual matters, and there is no such thing as a public space anymore.

When students have to be in a class and listen to their teacher and fellow learners, they are forced to turn off their cell phones and focus on a shared experience without the constant need to check their Facebook pages or latest texts. This experience represents one of the only reprieves young people will have from their constantly connected lives. In fact, students have told me that they would hate to take their classes online because they already feel addicted to their technologies. From their perspective, moving required classes online is like giving free crack to addicts and telling them that it will be good for them.

In order to help my students understand their dependence on technology and their alienation from nature and their own selves, I often bring them outside and tell them that they cannot do anything. This exercise often makes students very anxious, and when I later have students free-write about the experience, they write that they are not used to just doing nothing, and they felt an intense need to reach for their phones: this dependence on communication technologies will only be enhanced by moving to distance education.

Online education then not only adds to our culture of distracted multitasking, but it also often functions to undermine the values of university professors. In the rhetoric of student-centered education, the teacher is reduced to being a "guide on the side," and this downgraded position entails that there is no need to give this facilitator tenure or a stable position; instead, through peer grading and computer assisted assessment, the role of the teachers is being eliminated, and so it is little wonder that colleges operating only online employ most of their faculty off the tenure track.

These online colleges and universities have also separated teaching from research and have basically “unbundled” the traditional role of the faculty member. Like the undermining of newspapers by new media, we now have more sources of information but fewer people being paid to do the actual on the ground work of researching and reporting. Also as Wikipedia has turned every amateur into a potential expert, our society is losing the value of expert, credentialed educators. Although some see this as a democratization of instruction and research, it can also be read as a destruction of the academic business model and a move to make people work for free as traditional jobs are downsized and outsourced.

Many online programs proclaim that education is democratized by having students grade each other’s work, but isn’t this confusion between the roles of the student and the teachers just a way of rationalizing the elimination of the professor? Moreover, the use of computer programs to assess student learning is only possible if people think that education is solely about rote memorization and standardization. Yes we can use computers to grade students, but only if we think of students as standardized computer programs.

In contrast to massive open online courses, small, in-person classes often force students to encounter new and different perspectives, and the students cannot simply turn off the computer or switch the channel. Unfortunately, too many colleges and universities rely too much on large lecture courses that allow students to tune out during class and then teach themselves the material outside of class. While I am all for flipping the class and having students learn the course content outside of the classroom, we still need to use actual class time to help students to engage in research in a critical and creative fashion.

This push for small interactive classes will be resisted by the claim that it is simply too expensive to teach every student in this type of learning environment. However, my research shows that it is often more expensive to teach students in large lecture classes than in small seminars once you take into account the full cost of having graduate assistants teach the small sections attached to the large classes. Furthermore, the direct cost of hiring faculty to teach courses is often a fraction of the total cost of instruction, and massive savings could be generated if higher education institutions focused on their core missions and not the expensive areas of sponsored research, athletics, administration, and professional education. Being present at the university means that students and teachers are present in their classes and that education is the central presence of the institution.

(Illustration by Giulia Forsythe, licensed under Creative Commons Attribution-ShareAlike 2.5 agreement)

 

Bob Samuels is president of UC-AFT and teaches writing at the University of California at Santa Barbara. He is the author of the blog Changing Universities and the forthcoming book Why Public Higher Education Should Be Free (Rutgers University Press).
 

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Governors' Group Examines State Regulation of Online Learning

Governors should work together to undertake a review of states' policies on online education, given the fast-changing state of the industry and the cost to states and institutions of regulation, the National Governors Association said in a policy brief Thursday. The paper lays out the landscape of state regulation of distance learning and suggests areas that a study might examine, including whether states would consider joining a multistate compact or reciprocity agreement for authorizing online programs.

 

 

Essay on a combined writing and mathematics course

Everything would have been perfectly ordinary that October morning in my freshman writing course at Stanford University. Bright autumn light reflected up from the Main Quad to our third floor. Unfed, sleepy-eyed freshmen offered ideas about the assigned reading, which I tracked on the board.

As I often do, I drew a doodle to describe a concept in the reading. This doodle — so I thought — demanded less artistry and complexity than my usual sketches of Thomas Hobbes’s "arrant Wolfe," for which I hash out two mangy-looking wolves squinting at each other, or Immanuel Kant’s famous "crooked timber," for which a bent log suffices to get the idea across. Here, I simply tossed up a rectangle with a triangle inside.

My students gasped.

"What’s wrong?" I asked.

“Um … everything." They wagered cautiously.

"Well," I tried. "This is just like the one Lockhart shows in his essay." I was referring to a drawing in Paul Lockhart’s famous 2002 "Lament" about the state of mathematics education. Here it is, precisely as it appears in the essay, not the  version I drew in class.

 Paul Lockhart’s,

"Sorry … no … not really, well … it’s not even close," they ventured, as if not to hurt my feelings.

My students, mostly young aspiring mathematicians, found themselves so ill at ease here, because their teacher with a humanities doctorate had not bothered to notice that the triangle inside the rectangle touches both corners of the same length and thus forms several other triangles. My doodle — whatever it looked like, I can’t remember — was simply an approximation, a lonely triangloid adrift in a rectangular sea of lopsidedness.

My students had expected greater precision. After all, the course title "Rigorous and Precise Thinking" had suggested as much. Secondly, this was a college writing course, which, as the rumor goes, is supposed to be a smackdown of style, argument and organization, where freshmen quickly learn they must jettison comfortable high school formats and every illusion of their personal literary genius. Expectations for rigor and many other new adventures ran high in this new course, an experimental hybrid college writing/mathematical thinking and proof writing class, one of five liberal arts courses in a new program called Education as Self-Fashioning.

Like the other four ESF classes, this one intended to "engage actively in the types of thinking promoted through these different conceptions of education for life, so as to try those lives on for ourselves ..." and offer students a “chance to shape [their] educational aspirations in dialogue with fellow students and an exciting group of faculty from across a wide range of disciplines — from the humanities and social sciences through the natural sciences and mathematics." I was the writing instructor paired with Professor Ravi Vakil, an American-Canadian mathematician working in algebraic geometry.

Vakil invented the course concept as a rejoinder to C.P. Snow’s "Two Cultures" hypothesis with the hope of showing undergrads, and even the world, that writing in the humanities and writing in math gained force and excellence through similar structures of precise reasoning. Vakil more than delivered on the rigor and precision. His lectures introduced students to proof writing, number theory, set theory, and many other advanced forms of math most academics expect to address only with advanced university students. For my part, I was simply to help students elaborate the readings from Plato, Descartes, Douglas Hofstadter, Bertrand Russell, Paul Lockhart and many others, while teaching writing.

Tellingly, my imprecise doodle proved to be not my first, second, nor even third example of lack of rigor. In fact, the moment seem to demonstrate the deep divide between Snow’s "two cultures," since I evidently betrayed a lack of familiarity with the basic truths of measurement, "mass, or acceleration, pretty much the scientific equivalent of a humanist asking skeptically, Can you read?" Without a doubt, much of that difference proved disciplinary — the very limit this course hoped to transgress.

Yet, we experienced no ordinary rift between the two cultures. The class had read Snow’s famous 1959 Rede Lecture and chuckled at his description of subverbal grunting mathematicians ruining a young humanist’s dinner party experience. My students saw themselves as beyond what old Stanford lingo designates as the split between "fuzzies" and "techies." Interested equally in learning all things humanist and STEM, e.g., Shakespeare and thermodynamics and beyond, these students insisted that math and math culture far surpassed the cartoonish figures of Snow’s dinner party. Nor (my students believed) were humanists so incorrigibly "fuzzy" as to not be able to reproduce a mathematical doodle — or were they?

Had I inadvertently proven Snow’s point, right before the eyes of my epistemologically optimistic students? In fact, both the students and I discovered that many of the clichés about our respective fields proved instructive. I really do need to be more careful in my doodling — and thinking about my doodling — if I am drawing triangles (with mathematical aspirations) and not wolves (no matter how humanistically inclined).

The awkward doodle moment proved not the existence of two never-the-twain-shall-meet cultures, but rather a need for me to look more closely at the other side. Once I recovered from the initial jolt of difference, I began to realize the opportunity for me to reconsider my pedagogy. Not having seen a university math professor teach proof writing before, I witnessed several fascinating interactions while attending Vakil’s sections of our course. Most striking, when Vakil wrote a problem on the board, the room jumped to life with students calling out and frantically waving their arms. He would ask: "How can you prove the square root of 2 is irrational?" and it was as though Vakil were standing at the board waving a bloody steak at a group of famished tigers. Everyone wanted to offer some solution.

Seldom have I been bombarded with solutions or suggestions when I ask students to show me "textual proof" that Sigmund Freud has a Hobbesian view of nature … hint hint … homo homini … wolf sketch, ... Civilization and Its Discontents, try page number and reference…Freud 1930a [I929], SE 21:111. That special classroom enthusiasm surely arose from Vakil’s charisma and love of his subject, but the response was new to me because humanities courses that I know at least demand a very different kind of invention. Vakil asked a question and students racked their brains trying to imagine which set of mathematical tools or ideas they might use to solve the problem. Confident that they all share these tools, or at least know of such tools, the students seemed to feel much more at ease trying out different approaches.

In humanities courses, previous knowledge certainly helps, especially with literary references, but at the end of the day, a humanist’s tools remain much more contested and may not be applicable in different contexts. For example, students asked me why I requested they not use the third-person plural perspective "we." I told them writing in the humanities differs from math, where one can simply write in a proof “we assume that x=2.” Humanists can neither be sure who that “we” is, nor what to "assume" nor how one can know x. All such terms are permanently available for debate.

In contrast, the mathematicians’ particular disciplinary certainty also revealed a fierce loyalty and love of the subject, which produced a very different discourse than I traditionally hear from humanities students who feel a strong affinity with their work. These math students spoke a Russellian language of awe toward the "cold and austere" "supreme beauty" and "elegance" of math. Perhaps other humanists have encountered students who express an emphatic humility before their subjects, but that this for me was as new as the students’ shock at my imprecise drawing. For I learned that day, that my students had not yet adopted a humanistic skepticism toward mathematical precision. For them precision is very real, especially in a world of increasing complexity and Gödelian incompleteness.

For humanists, precision lies elsewhere, side by side with ambiguity, and we pursue it with nuance rather than with proofs. My task therefore became one of translation. I understood little of the doodles and equations that Vakil and the students so hotly debated in his sections, but I knew that I had helped my students articulate arguments within the very different confines of humanistic inquiry. Where they were convinced of certain mathematical truths in the landscape of defined terms, they nevertheless arrived in my class with the classic freshman enormity of themes.

Asked to find “precise” topics in math to write about for their research papers, nearly all 29 students first chose grandiose topics like "the definition of intuition," "the connections between art and math" or "math and humanistic knowledge." With such great ambitions in mind, they also fervently believed in math as a liberal art capable of teaching the exact same virtues of critical (self) reflection as any of the great classical texts I teach from Greek virtue ethics to Rawls.

Most provocatively, they claimed that by practicing mathematical reasoning they were indeed preparing themselves in the fashion of liberal arts education for ethical citizenship. They claimed with confidence their rigorous and precise thinking could lead them to ethical reasoning as equally well as a discussion of the Plato’s “Apology.” For my part, I could not see how debating a triangle or even practicing some form of applied math as statistics would help me lead the "examined life" in a qualitative fashion.

In class, Vakil often reflected on the limits of mathematical reasoning in a mode reminiscent of Greek virtue ethics; that is, perfecting one’s art whether mathematical or literary skill, is surely a virtue, but not one that can replace ethical action. When asked whether excellence in math could prevent one from doing evil, no one doubted the inadequacy of that proposition. History has no shortage of evil uses of math, and the students could quite easily number these. Yet, many of the students persisted in their strong claims for math.

One student asserted a mathematical imperative in times of emergency: "Just imagine it’s war or a crisis: you have a moral obligation to shut up and do the math." By which she meant one is ethically compelled to run a statistical analysis to develop a more concrete understanding of actual dangers. Another student expressed less certainty about quantitative methods. "Statistics aren’t bulletproof, you know; what matters ultimately is thinking clearly, and math trains the mind for such emergencies."

Vakil softened these strong claims for both applied and pure math:

I'm less certain that this [mathematical reasoning] in any way replaces the approach to the virtues of critical self-reflection through great philosophical texts. I hope that our students will better appreciate the importance of such texts, because of an appreciation of the problems that earlier thinkers were grappling with (and that we should grapple with today). Similarly, I doubt that this is sufficient to lead them to ethical reasoning, although I would make a milder claim that thinking clearly in this way can assist in carrying out ethical reasoning.

Vakil also elaborated ways in which math could serve ethics, both by providing empirical data and asking Socratic questions about knowledge and decision-making. In the end, we hoped the students finished the course knowing a bit more about practices of rigorous thinking in our respective disciplines, and that they would see these as equally essential and complementary. Could this sprawling, seven-unit course provide a model for future courses? We’re not sure, but are happy to share our data and materials.

 

Ruth Starkman writes on higher education and teaches college writing, biomedical ethics and social media at Stanford University.

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ACE to assess Udacity courses for credit

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ACE considers credit recommendations for a batch of Udacity courses.

Essay on teaching students who seem unengaged

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On the Fence

Eliza Woolf wonders what to make of students who seem disengaged from class and then give her great evaluations.

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Lynn University to require all new students to buy iPads

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As another step in the overhaul of its core curriculum, Lynn University will require every first-year student to purchase an iPad mini, and will use iTunes U as a content delivery method for those courses.

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