Tag Archives: Liberal arts

Want a job? Major in what you enjoy.

The Seven liberal arts. Grammatic and Priscianus.

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Excellent blog post in the NY Times website this morning telling us that the choice of college major is not as important as we think. The author shares this research finding:

A University of Texas at Austin professor, Daniel Hamermesh, researched career earnings data sorted by choice of major and concluded that:

“Perceptions of the variations in economic success among graduates in different majors are exaggerated. Our results imply that given a student’s ability, achievement and effort, his or her earnings do not vary all that greatly with the choice of undergraduate major.”

A study conducted by PayScale Inc. found that history majors who pursued careers in business ended up earning, on average, just as much as business majors.

The author goes on to cite four reasons why a liberal arts major would be a fine choice for career-minded college students, including the development of transferable skills and the value — both personal and professional — of majoring in something you truly enjoy rather than something you don’t enjoy but think might be useful someday.

I’m reminded of this great post over at Cal Newport’s blog from last year in which he advises prospective business majors not to major in business but rather to choose a classical liberal arts major and then take 4-6 math courses on the side. That amounts to majoring in something like economics or history and then getting a math minor. The liberal arts major will show employers that you are broadly educated and have those transferable skills, such as the ability to do research and communicate clearly in oral and written forms. Then the math minor adds a significant amount of training to show that you can handle quantitative information — a skill sorely lacking among a huge portion of new job marketeers today — and that you’re not in the liberal arts major to avoid hard work, which is unfortunately a common public perception of liberal arts programs. (That perception is something that we who work in the liberal arts colleges are partially responsible for perpetuating by not communicating the value of the liberal arts clearly enough.)

This combination doesn’t always work — engineering, for instance, really does require a degree in engineering at some point — and the student who goes this route takes on a double responsibility for making sure his or her liberal arts degree is really academically rigorous and for being ready to explain to hard-headed employers that they have the skills that will make them viable in the long term as employees. But I think it’s right to tell students to first study what they love, and then worry about the career part a little later. I’m certainly advising my own students to that effect. And given that most jobs are going to require new employees to learn on the fly the things they need to know anyway, it makes sense to develop students’ passions for learning and abilities to learn on their own, which is IMO one of the major things a liberal arts education is good for.

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Filed under Education, Higher ed, Liberal arts, Student culture, Vocation

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?

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Filed under Education, Engineering, Engineering education, Higher ed, Liberal arts, Life in academia

Turning questions into learning

Attacking Difficult Questions
Image by CarbonNYC via Flickr

The hardest thing about teaching the MATLAB course — or any course — is responding to student questions. Notice I do not say “answering” student questions. Answers are not the issue; I’m no MATLAB genius, but I can answer 95% of student questions on the spot. The real issue is whether I should. If my primary task is to teach students habits of mind that translate into lifelong learning — and I earnestly believe that it is — then answers are not always the best thing for students.

I’ve noticed four types of questions that students tend to ask in the MATLAB course, and these carry over pretty seamlessly to my other courses:

  1. Informational questions that have nothing to do with the problem they’re working on or the material. Example: When are your office hours? When is this lab due? When is the final exam?
  2. Clarifying questions that seek to make sense of the specifications of a problem. Should we use a script M-file or a function M-file here? A FOR loop or a WHILE loop? Do I have to make this plot from the command line or can I use the Plot Tools window?
  3. Functional questions that are generally of the form, How do I [insert task here]?. How do I plot a function in MATLAB? How do I get the plot to be red instead of blue? How do I get this FOR loop to work?
  4. Interpretive questions that seek the meaning of syntax, a command, or an error. What does MATLAB mean when it says I should ‘pre-allocate’ this variable? Why are there all these different ways to call the MAX command? Why do I have to use num2str in some situations but not in others?

I’ve tried to list these question types in increasing order of cognitive complexity, although that ordering doesn’t always hold. (Some clarifying questions can get quite complicated, for instance.) How these types of questions are ranked in this way points me in the direction of how to respond to them.

Formal informational questions are easy to answer. I always give the same, direct answer to these: It’s (on the syllabus || in the calendar || printed on your assignment). Students learn pretty quickly that this is the same answer to this kind of question all the time, so they tend to stop asking and just look it up instead, which is precisely what they should be doing.

I’m happy to give straight answers to clarifying questions, although sometimes it’s better not to. For example, if a student team is working on a program that needs a loop, and they want to know if they should use a FOR or a WHILE loop, then the best way to respond is not to tell students what to do but rather to lay out the pros and cons of each approach and let them choose.

It gets very tricky when we get to the last two types.

I let the following basic philosophy guide me: I don’t answer functional questions on labs during lab sessions or on homework while the homework is still not yet turned in. Once the lab or homework is over, then I’ll usually answer directly. But otherwise, my goal is to guide students into turning their functional question into an interpretive question. I do this through a series of Polya-like questions to the students that flows a little something like this (click to enlarge):

This is less complicated than it looks. Basically, if a student asks a functional question, I first see if the student’s done what they’re asking before. If so, they go refresh their memories. If not, they look it up in an appropriate help file until they find something that looks like what they want. Then they play with it for a minute or two to get the basic idea. Then, by that point, they either know what they’re supposed to do, or else they have a deeper, more cognitively complex question to ask, not What do I type in to do this? but Why does this work the way it does? In a freshman-level class like this one, any time I can get students to elevate themselves from functional questions to interpretive/clarifying questions, I consider it a win.

What students get out of this process is the ability to move beyond needing the professor to tell them what to do. They become self-feeders. This is important because the professor is not going to be there when they really need this stuff, two or three courses down the line or when they’re out on the job (for which they were hired because they, and nobody else around them, has these kinds of computer skills). They are getting the ability to learn on their own, which is what I consider really to be the single, primary life skill.

Unfortunately students tend to resist this process. It is not what they are used to. They are used to teachers telling them the answers to their questions, regardless of what kind of question it was, and to them a failure of a teacher to give a straight answer to their questions is tantamount to either incompetence or indifference. So this process requires a constant P.R. effort and constant clarifying about why we do things this way. And that P.R. effort doesn’t always work. I still have students who complain that I don’t answer their questions; who feel belittled when they identify that they’ve seen a command before and are asked to go back and review it; who feel questions are pointless because I’m just going to ask them more questions in return.

These are freshmen, used to a transactional model of education predominant in American high schools. The fact that this model — the teacher tells the students what to do; students follow teacher’s directions; students get good grades — is the predominant one is a serious problem in our schools, but that’s another issue. Whatever the case may be, I am getting these folks in the final four years of their formal schooling (for the most part) and if I don’t get them thinking on their own, they will crash and burn in the real world.

And I think that even if these students go on never to use MATLAB again after graduation but have a well-practiced and fluid ability to learn new and complicated things on their own, I consider that the biggest win of all. And it’s a good reason to take the MATLAB course in the first place.

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ICTCM underway

It’s a beautiful day here on the shores of Lake Michigan as the ICTCM gets underway. It’s a busy day and — to my never-ending annoyance — there is no wireless internet in the hotel. So I won’t be blogging/tweeting as much as I’d like. But here’s my schedule for the day.

  • 8:30 – Keynote address.
  • 9:30 – Exhibits and final preparations for my 11:30 talk.
  • 10:30 – “Developing Online Video Lectures for Online and Hybrid Algebra Courses”, talk by Scott Franklin of Natural Blogarithms.
  • 11:10 – “Conjecturing with GeoGebra Animations”, talk by Garry Johns and Tom Zerger.
  • 11:30 – My talk on using spreadsheets, Winplot, and Wolfram|Alpha|Alpha in a liberal arts calculus class, with my colleague Justin Gash.
  • 12:30 – My “solo” talk on teaching MATLAB to a general audience.
  • 12:50 – “Programming for Understanding: A Case Study in Linear Algebra”, talk by Daniel Jordan.
  • 1:30 – “Over a Decade of of WeBWorK Use in Calculus and Precalculus in a Mathematics Department”, session by Mako Haruta.
  • 2:30 – Exhibit time.
  • 3:00 – “Student Projects that Assess Mathematical Critical-Thinking Skills”, session by David Graser.
  • 5:00 – “Visualizing Mathematics Concepts with User Interfaces in Maple and MATLAB”, session by David Szurley and William Richardson.

But first, breakfast and (especially) coffee.

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The suckage of being an engineering student

A blog post at Wired claims to give the Top 5 Reasons It Sucks to be an Engineering Student. Discussion is in the comments there and at this lively thread at Slashdot. The reasons given at the Wired blog are (in reverse order):

  1. Awful textbooks
  2. Professors are rarely encouraging
  3. Dearth of quality counseling
  4. Other disciplines have inflated grades
  5. Every assignment feels the same

It sounds to me like the blogger at Wired is stereotyping, based on what goes on at large research universities. A student could avoid #2, #3, and maybe #5 just by doing a 3+2 program where the first three years are done at a liberal arts college (…shameless plug alert…).

As for the grade inflation, I admit there’s no solution to this short of doing the right thing and forcing real academic standards on some of the touchiest-feeliest portions of the liberal arts world. But I think that would lead to mass chaos, as the stability of many liberal arts college depends on having some department on campus to be the “good cop” which offers refuge to students who just aren’t that interested in getting good at something difficult. All I can offer is some sympathy, that math and science professors are often eviscerated on course evaluations by those very students, who are shocked — SHOCKED — that deadlines would be enforced, hard material would be on tests, and so forth.

So to all engineering students out there, keep on keepin’ on. It might suck a little in the short term, but when it’s over you get to run our entire society!

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What is a classical education approach to mathematics?

Following up on his three posts on classical education yesterday, Gene Veith weighs in on mathematics instruction: 

I admit that classical education may be lagging in the math department. The new classical schools are doing little with the Quadrivium, the other four liberal arts (arithmetic, geometry, astronomy, and music). The Trivium, which is being implemented to great effect (grammar, logic, and rhetoric), has to do with mastering language and what you can do with it. The Quadrivium has to do with mathematics (yes, even in the way music was taught).

This, I think, is the new frontier for classical educators. Yes, there is Saxon math, but it seems traditional (which is better than the contemporary), rather than classical, as such.

Prof. Veith ends with a call for ideas about how mathematics instruction would look like in a classical education setting. I left this comment:

I think a “classical” approach to teaching math would, going along with the spirit of the other classical education posts yesterday, teach the hypostatic union of content and process — the facts and the methods, yes (and without cutesy gimmicks), but also the processes of logical deduction, analytic problem-solving heuristics, and argumentation. Geometry is a very good place to start and an essential to include in any such approach. But I’d also throw in more esoteric topics as number theory and discrete math (counting and graph theory) — in whatever dosage and level is age-appropriate.

At the university level, and maybe at the high school level for kids with a good basic arithmetic background, I’d love to be able to use the book “Essential College Mathematics” by Zwier and Nyhoff as a standard one-year course in mathematics (and in place of the usual year of calculus most such students take). It’s out of print, but the chapters are on sets; cardinal numbers; the integers; logic; axiomatic systems and the mathematical method; groups; rational numbers, real numbers, and fields; analytic geometry of the line and plane; and finally functions, derivatives, and applications. You have to see how the text is written to see why it does a good job with both content and process.

(I took out the mini-rant against the gosh-awful Saxon method.)

Any thoughts from the audience here?

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A trifecta on classical education

Gene Veith, one of my favorite religious writers and the proprietor of the terrific Cranach blog (and provost at Patrick Henry College), has three quick posts today on classical education. He touches briefly on teaching content rather than process, and how classical education teaches bothl; on critical thinking; and on learning styles and the teaching of “meaning”. Some clips: 

The key factor in learning is grasping meaning, a concept that evades any of these sensory approaches. (While cultivation of meaning is what classical education is all about.)

and:

More substantive scholars say that being able to think critically requires (again, see below) CONTENT. You have to think ABOUT SOMETHING. Whereas much of the critical thinking curriculum is all process, trying to provoke content-free thinking. (The classical solution: DIALECTIC, featuring questions AND answers, as in that great model of classical education, the catechism, which, properly used, helps the student answer the question, “what does this mean?”)

I am pretty sure that Prof. Veith has this overall definition of “classical education” in mind, but I am not sure exactly how he defines it. And I wonder if all of what he says still works if you replace “classical” with the more generic “liberal arts”.

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