In defense of big universities

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I’d like to take back something that I said in my post last week on the UCF cheating scandal (my emphasis):

[T]he more this situation unfolds, the more unhealthy it makes the whole educational environment surrounding it seem. Class sizes in the multiple hundreds: Check. Courses taught mainly through lecture: Check. Professor at a remove from the students: Check. Exams taken off the rack rather than tuned to the specific student population: Check. And on it goes. I know this is how it works at many large universities and there’s little that one can do to change things; but with all due respect to my colleagues at such places, I just can’t see what students find appealing about these places, and I wonder if students at UCF are thinking the same thing nowadays.

I’m coming at that statement as somebody who’s spent the last 14 years in small liberal arts colleges. The idea of 600-student lecture classes, using prefabricated tests from a test bank, and so on is completely alien to how I conceive of teaching and learning in higher education. The larger the university, the easier it is to adopt such depersonalized (even dehumanizing) “teaching” techniques. But I think I painted with too broad of a brush here. Because the fact is, there are going to be faculty who employ depersonalized approaches to education no matter how big or small the institution is. There are small colleges who willfully, even readily, employ such approaches to teaching on an institutional scale even though they are small enough to do better. And on the other side, there are large universities that, despite their largeness, still manage to treat undergraduate education with the care and skill it deserves.

I’d like to point out a couple of such large research universities with which I’ve had direct experience who, to me, really get undergraduate education right, or are at least trying to do so.

First is Vanderbilt University, where I did my graduate studies and got my first taste of teaching. Vanderbilt has a real culture of teaching and learning that pervades the entire academic structure of the university. It has a fabulous Center for Teaching where I was privileged to spend a year as a Master Teaching Fellow during my last year of grad school, working with other graduate teaching scholars and university faculty to help them get better at their craft. And what always impressed me at Vandy was that a lot of professors were interested in getting better. It’s a great research university, but the profs there — at least the ones I knew, with the exception of a few entrenched math people — all took teaching seriously and really wanted to work at getting better. And it shows in the quality of undergraduates Vanderbilt produces. I can definitely see why a high school kid would want to go there.

The other example is The College of Engineering at the University of Wisconsin – Madison. I spoke there recently to a group of faculty and support staff who are involved with a program called Engineering Beyond Boundaries, an ambitious program to transform the teaching, learning, and practice of engineering in response to key shifts in the discipline and the culture around it. The people involved with that program are embarking on an all-out effort to push the culture in the engineering school toward one that adopts a more modern approach to teaching and learning, including the renovation of learning spaces, work with innovative instructional techniques, and creating opportunities for cross-disciplinary work. They’re just getting started with this program, but I think some interesting things are ahead for them as they proceed in terms of teaching and learning.

Do you have other examples of big universities that are doing a good job with undergraduate education? Brag on them in the comments.

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Why change how we teach?

Sometimes when I read or hear discussions of innovation or change in teaching mathematics or other STEM disciplines, whether it’s me or somebody else doing the discussing, inevitably there’s the following response:

What do we need all that change for? After all, calculus [or whatever] hasn’t changed that much in 400 years, has it?

I’m not a historian of mathematics, so I can’t say how much calculus has or hasn’t changed since the times of Newton and Leibniz or even Euler. But I can say that the context in which calculus is situated has changed — utterly. And it’s those changes that surround calculus that are forcing the teaching of calculus (any many other STEM subjects) to change –radically.

What are those changes?

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First, the practical problems that need to be solved and the methods used to solve them have changed. Not too long ago, practical problems could be neatly compartmentalized and solved using a very small palette of methods. I know some things about those problems from my Dad, who was an electrical engineer for 40 years and was with NASA during the Gemini and Apollo projects. The kinds of problems he’d get were: Design a circuit board for use in the navigational system of the space capsule. While this was a difficult problem that needed trained specialists, it was unambiguous and could be solved with more or less a subset of the average undergraduate electrical engineering curriculum content, plus human ingenuity. And for the most part, the math was done by hand and on slide rules (with a smattering of newfangled mechanical calculators) and the design was done with stuff from a lab — in other words, standard methods and tools for engineers.

Now, however, problems are completely different and cannot be so easily encapsulated. I can again pull an example from my Dad’s work history. During the last decade of his career, the Houston Oilers NFL franchise moved to Tennessee. Dad was employed by the Nashville Electric Service and the problem he was handed was: Design the power grid for the new Oilers stadium. This problem has some similarities with designing the navigational circuitry for a space capsule, but there are major differences as well because this was a civic project as well as a technical one. How do we make the power supply lines work with the existing road and building configurations? What about surrounding businesses and the impact that the design will have on them? How do we make Bud Adams happy with what we’ve done? The problem quickly overruns any simple categorization, and it required that Dad not only use skills other than those he learned in his (very rigorous!) EE curriculum at Texas Tech University, but also to learn new skills on the fly and to work with other non-engineers who have more in the way of those skills than he had. Also, the methods use to solve the problem were radically different. You can’t design a power grid that large using hand tools; you have to use computers, and computers need alternative representations of the models underlying the design. And the methods themselves lead to new problems.

So it is with calculus or almost any STEM discipline these days. Students today will not go on to work with simple, cleanly-defined, well-posed problems that fit neatly into a box. Nor will they be always doing things by hand; they will be using technology to solve problems, and this requires both a different way of representing the models (for calculus, think “functions”) they use and the flexibility to anticipate the problems that the methods themselves create. This is not what Newton or Leibniz had in mind, but it is the way things are. Our teaching must therefore change to give students a fighting chance at solving these problems, by emphasizing multiple representations of functions, multiple methods for solution of problems, and attention to the problems created by the methods. And of course, we also must focus on teaching problem-solving itself and on the ability to acquire new skills and information independently, because if so much has changed between 1965 and 1995, we can expect about the same amount of change in progressively shorter time spans in the future.

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Also, the people who solve these problems, and what we know about how those people learn, have changed. It seems undeniable that college students are different than they were even 20 years ago, much less 200 years ago. Although they may not be natively fluent in the use of technology, they are certainly steeped in technology, and technology is a primary means for how they interact with the rest of the world. Students in college today bring a different set of values, a different cultural context, and a different outlook to their lives and how they learn. This executive summary of research done by the Pew Research Foundation goes into detail on the characteristics of the Millenial generation, and the full report (PDF, 1.3 Mb) — in addition to our own experiences — highlights the differences in this generation versus previous ones. These folks are not the same people we taught in 1995; we therefore cannot expect to teach them in the same way and expect equal or better results.

We also know a lot more now about how people in general, and Millenials in particular, learn things than we did just a few years ago. We are gradually, but also rapidly, realizing through rigorous education research that there are other methods of teaching out there besides lecture and that these methods work better than lecture does in many situations. Instructors are honing the research findings into usable tools through innovative classroom practices that yield statistically verifiable improvements over more traditional ways of teaching. Even traditional modes of teaching are finding willing and helpful partners in various technological tools that lend themselves well to classroom use and student learning. And that technology is improving in cost, accessibility, and performance at an exponential pace, to the point where it just doesn’t make sense not to use it or think about ways teaching can be improved through its use.

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Finally, and perhaps at the root of the first two, the culture in which these problems, methods, people, and even the mathematics itself is situated has changed. Technology drives much of this culture. Millenials are highly connected to each other and the world around them and have little patience — for better or worse — for the usual linear, abstracted, and (let’s face it) slow ways in which calculus and other STEM subjects are usually presented. The countercultural force that tends to discourage kids from getting into STEM disciplines early on is probably stronger today than it has ever been, and it seems foolish to try to fight that force with the way STEM disciplines have been presented to students in the past.

Millenials are interested to a (perhaps) surprising degree in making the world a better place, which means they are a lot more interested in solving problems and helping people than they are with epsilon-delta definitions and deriving integrals from summation rules. The globalized economy and highly-connected world in which we all live has made almost every problem worth solving multidisciplinary. There is a much higher premium now placed on getting a list of viable solutions to a problem within a brief time span, as opposed to a single, perfectly right answer within an unlimited time span (or in the time span of a timed exam).

Even mathematics itself has a different sort of culture now than it did even just ten years ago. We are seeing the emergence of massively collaborative mathematical research via social media, the rise of computational proofs from controversy to standard practice, and computational science taking a central role among the important scientific questions of our time. Calculus may not have changed much but its role in the larger mathematical enterprise has evolved, just in the last 10-15 years.

In short, everything that lends itself to the creation of meaning in the world today — that is, today’s culture — has changed from what it used to be. Even the things that remain essentially unchanged from their previous states, like calculus, must fit into a context that has changed.

All this change presents challenges and opportunities for STEM educators. It’s challenging to go back to calculus, and other STEM disciplines, and think about things like: What are the essential elements of this subject that really need to be taught, as opposed to just the topics we really like? What new facets or topics need to be factored in? What’s the best way to factor those in, so that students are really prepared to function in the world past college? And, maybe most importantly, How do we know our students are really prepared? There’s a temptation to burrow back in to what worked for us, when faced with such daunting challenges, but that really doesn’t help students much — nor does it tap into the possibilities of making our subjects, and our students, richer.

Funniest remark of the ASEE so far

…goes to Robert Grondin of Arizona State University Polytechnic Campus, who made this remark in his talk in the Liberal Education for 21st Century Engineering session:

We do projects at the beginning of the course, because projects are fun, and we want to fool students into thinking that engineering is fun.

This was apropos of how engineering curricula usually incorporate projects — either at the beginning of the curricula via a freshman design course, or at the end via a senior design course, or both. But you can pretty much substitute any discipline and get the way we often think about how projects fit into the curriculum, right?

Prof. Grondin, on the other hand, has designed a generic Engineering degree — not Mechanical Engineering, Electrical Engineering, or whatnot… just Engineering — for ASU Polytechnic that requires only 20 hours of engineering coursework beyond the freshman core and in which there’s a design project course in every semester. That’s what you call taking project-based learning seriously, and I’d daresay that these general Engineering students are better prepared for real engineering work than many students with specialized engineering degrees.

Partying like it’s 1995

Yesterday at the ASEE conference, I attended mostly sessions run by the Liberal Education Division. Today I gravitated toward the Mathematics Division, which is sort of an MAA-within-the-ASEE. In fact, I recognized several faces from past MAA meetings. I would like to say that the outcome of attending these talks has been all positive. Unfortunately it’s not. I should probably explain.

The general impression from the talks I attended is that the discussions, arguments, and crises that the engineering math community is dealing with are exactly the ones that the college mathematics community in general, and the MAA in particular, were having — in 1995. Back then, mathematics instructors were asking questions such as:

• Now that there’s relatively inexpensive technology that will do things like plot graphs and take derivatives, what are we supposed to teach now?
• Won’t all that technology make our students dumb?
• Won’t the calculus reform movement dumb down our curricula with all this nonsense about graphs and multiple representations and so on?
• How can you seriously call a person a mathematician/engineer if they can’t [insert calculation here] by hand? What if they are in a situation where they don’t have access to technology?

And yet, I actually heard all of these questions almost verbatim from mathematics and engineering professors this morning, multiple times. (To the great credit of the speaker who was asked the last question, he replied: If an engineer is ever in a situation where he is without access even to a calculator, we have a lot bigger problems on our hands than just bad education. TRUTH.)  I was having serious third-year-of-grad-school flashbacks.

These questions aren’t bad; they’re moot. In 1995, mathematical technology was just at the level of expense, accessibility, and functionality that these questions needed to be dealt with. Students could conceivably purchase calculators for a couple hundred dollars that were small enough to slip into a backpack and could calculate symbolically. Should we ban the technology, embrace it, regulate it, or what? Should we change what and how we teach? The technology could be controlled, so the question was whether we should, and to what extent, and these were important questions at the time.

But that was 1995. What the TI-92 could do in 1995 can now be done in 2010 using Wolfram|Alpha at no expense, using any device with an internet connection, and with functionality that is already vast and expands every other week. (This says nothing about W|A’s use of natural language input.) The technology is all around us; students are using it; there is no argument against expense, accessibility, or functionality that can reasonably be made. It’s going to affect what our students do and how they accept what we present to them regardless of what we think about it.  So I’d suggest that questions such as What do students need to know how to do in an engineering calculus course? and How do we ensure they can do those things? are better questions for now (and might even have been better then).

Some of the conceptions of innovative teaching and learning strategies I saw also seemed stuck in 1995. I won’t name names or give specific descriptions in order not to offend people who probably simply don’t know the full scope of what’s gone on in mathematics education in the last 15 years. (Although I must call out the one talk that highlighted the use of MS Excel, and claimed that there were no other tools available for hands-on work in mathematics. Augh! You should know better than that!)

I will simply say that people who concern themselves with the mathematical preparation of engineers simply must look around them and get up to speed with what is happening in technology, in the cultures and lives of our students, and in what we know now about student learning that we didn’t know then. Read some seminal MAA articles about active learning. Talk to other people. Read some blogs. Something! We can’t stay stuck in time forever.

What (some) engineers think about liberal education

I’m currently at the American Society for Engineering Education conference and symposium in Louisville. There is a lot to process as I attend sessions on student learning, technological literacy, liberal education, and so on, all from the perspective of engineers and engineering educators. There is an entire division (a sort of special interest group) within the ASEE for Liberal Education, and I attended one of their paper sessions this afternoon.

Engineers have a quite different perspective on liberal education than those in “liberal arts” disciplines (by which we usually mean social sciences, arts, humanities) and those of us math/science people working in liberal arts colleges, but surprisingly — at least for the engineers I hung out with in the session — the two conceptions largely agree. We all conceive of liberal education as education that integrates multiple perspectives into understanding what we study and do. We believe in the importance and relevance of disciplines other than our own and seek to learn about other disciplines, connect with practitioners and colleagues in other disciplines, and incorporate other disciplines in meaningful ways into our courses. We believe in teaching students metacognitive skills and preparing them to be human beings, not just workers.

Of course there are engineers who don’t think this way and in fact look down on other disciplines in direct proportion to their methodological distance from engineering (the less data and design involved, the greater the disdain). But consider too that there are also poets, philosophers, historians, mathematicians, sociologists, and so on who feel the same way about their own disciplines. The departmental silos exist all over campus.

Particularly enlightening was a parallel given in a talk by Cherrice Traver and Doug Klein of Union College (a liberal arts college known for its strong and historically-rooted engineering programs) between the criteria for ABET accreditation of engineering programs on the one hand, and the learning outcomes of Liberal Education and America’s Promise (or LEAP; a prospectus from the American Association of Colleges and Universities) on the other. Here are ABET’s Program Outcomes and Assessment criteria:

Engineering programs must demonstrate that their students attain the following outcomes:
(a) an ability to apply knowledge of mathematics, science, and engineering
(b) an ability to design and conduct experiments, as well as to analyze and interpret data
(c) an ability to design a system, component, or process to meet desired needs within realistic
constraints such as economic, environmental, social, political, ethical, health and safety,
manufacturability, and sustainability
(d) an ability to function on multidisciplinary teams
(e) an ability to identify, formulate, and solve engineering problems
(f) an understanding of professional and ethical responsibility
(g) an ability to communicate effectively
(h) the broad education necessary to understand the impact of engineering solutions in a global,
economic, environmental, and societal context
(i) a recognition of the need for, and an ability to engage in life-long learning
(j) a knowledge of contemporary issues
(k) an ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice.

The entire accreditation document is here (PDF).

Compare those with the LEAP outcomes:

Beginning in school, and continuing at successively higher levels across their college studies, students should prepare for twenty-first-century challenges by gaining:

Knowledge of Human Cultures and the Physical and Natural World

Through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts

Focused by engagement with big questions, both contemporary and enduring

Intellectual and Practical Skills, Including

Inquiry and analysis
Critical and creative thinking
Written and oral communication
Quantitative literacy
Information literacy
Teamwork and problem solving
Practiced extensively, across the curriculum, in the context of progressively more challenging problems, projects, and standards for performance

Personal and Social Responsibility, Including

Civic knowledge and engagement—local and global
Intercultural knowledge and competence
Ethical reasoning and action
Foundations and skills for lifelong learning
Anchored through active involvement with diverse communities and real-world challenges

Integrative and Applied Learning, Including

Synthesis and advanced accomplishment across general and specialized studies
Demonstrated through the application of knowledge, skills, and responsibilities to new settings and complex problems

As the presenters mentioned, you can make an exercise of lining these two lists of learning outcomes side by side (in fact, they gave us a handout where this was done) and draw lines connecting learning outcomes in LEAP with corresponding, or even identical, criteria from ABET’s list.

What this means, I think, is that there is a strong base of support for liberal education among engineers. One might even say that those in charge of accrediting engineering programs want engineers to be liberally educated. Some engineers, like the ones in the session I attended, will even say that themselves.

What nobody seems able to explain just yet is the implicit and sometimes explicit resistance to liberal education among many engineers and engineering programs. For example, why do most engineering programs require monumental depth in a single engineering discipline — as undergraduates — with only token amounts of university-required coursework outside of engineering? The electrical engineering degree at one university, for example, requires 68 credit hours just in freshman and electrical engineering courses. Then 33 hours in math and science, and a 3-hour mechanical engineering course. Eighteen hours total are left over for electives outside math, science, or engineering — and six of those are prescribed courses (composition and communication), leaving just 12 hours to be chosen from General Education elective blocks.

That’s just four courses the student gets to pick out of sheer curiosity and personal interest for his or her entire college education! Can that possibly be in line with what ABET — or for that matter, the engineering community and its clients — really want?