Tag Archives: Engineering

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?

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.

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.

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.

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Filed under Calculus, Education, Educational technology, Engineering, Engineering education, Higher ed, Math, Problem Solving, Teaching, Technology

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.

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Filed under Education, Engineering, Engineering education, Higher ed

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

Summer plans

I’m still in recovery mode from this past semester, which seemed somehow to be brutal for pretty much everyone I know in this business. But something that always helps me in this phase is thinking about what I get to do with the much lighter schedule that summertime affords. Here’s a rundown.

Mostly this summer I will be spending time with my family. On Mondays and Fridays, I’ll be home with my two daughters. On Wednesdays I’ll have them plus my 16-month old son, plus my wife will have that day off. On Tuesdays it’ll be just the boy and me. So I plan lots of trips to the zoo, the various parks around here, and so on.

I still have plenty of time to work, and I have a few projects for the summer.

First, I need to get ready for my Geometry class this fall. I am making the move from Geometer’s Sketchpad to Geogebra this fall, and although I took a minicourse at the ICTCM on Geogebra, I still need to work on my skills before I teach with it. Also, I need to figure out exactly what I am going to teach. I’m going to be using Euclid’s Elements as the textbook for the course, eschewing commercial textbooks for both monetary and educational reasons. But I’m not totally sure what I’m going to have students do, exactly. So I’ll be reading through the Elements and possibly thinking out loud here on the blog about how to incorporate a 2000-year old mathematical work with modern open-source dynamic geometry software in an engaged classroom. I’m calling it “ancient-future geometry”, whatever it turns out being.

Second, I’ll be working on our dual-degree Engineering program to try and make it a little easier to schedule and complete. This is hard-core administrative stuff, interesting to nobody but a select few geeks like me.

Third, I’ll be working to further my programming skills with MATLAB and Python. I picked up a lot of MATLAB programming to get ready for the course this past semester, but that seemed only to highlight how much more I needed to learn. And I watched enough of this MIT computing course over Christmas break that I want to do the whole thing now that I have some time.

Fourth, I’ll be attending the American Society for Engineering Education conference in Louisville next month. Part of that experience is a day-long minicourse titled “Getting Started in Engineering Education Research”. I’ll be taking my participation in that minicourse as the kickoff to a concerted effort to get into the scholarship of teaching and learning. Along with the minicourse I’ll be reading through some seminal SoTL articles this summer, and probably blogging what I’m thinking.

Fifth, and finally, I’ll be mapping out some incursions of the inverted classroom model in my Calculus course this fall. More on that later as well.

For now, my family and I are heading out to Tennessee on vacation to visit family and hang out. I’ll be off the grid for a week or so. Enjoy yourselves and stay tuned!

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Filed under Education, Geogebra, Geometers Sketchpad, Geometry, Higher ed, ictcm, Inverted classroom, Math, Teaching, Technology, Textbook-free

Active learning is essential, not optional, for STEM students

This article (1.2 MB, PDF)  by three computer science professors at Miami University (Ohio) is an excellent overview of the concept of the inverted classroom and why it could be the future of all classrooms given the techno-centric nature of Millenials. (I will not say “digital natives”.) The article focuses on using inverted classroom models in software engineering courses. This quote seemed particularly important:

Software engineering is, at its essence, an applied discipline that involves interaction with customers, collaboration with globally distributed developers, and hands-on production of software artifacts. The education of future software engineers is, by necessity, an endeavor that requires students to be active learners. That is, students must gain experience, not in isolation, but in the presence of other learners and under the mentorship of instructors and practitioners.  [my emphasis]

That is, in the case of training future software engineers, active learning is not an option or a fad; it is essential, and failure to train software engineers in an active learning setting is withholding from them the essential mindset they will need for survival in their careers. If a software engineer isn’t an active learner, they won’t make it — the field is too fast-moving, too global, too collaborative in its nature to support those who can only learn passively. Lectures and other passive teaching techniques may not be obsolete, but to center students’ education around this kind of teaching sets the students up for failure later on.

One could argue the same thing for any kind of engineer, or any of the STEM disciplines in general, since careers in those disciplines tend to adhere to the same description as software engineering — a tendency toward applications (many of which don’t even exist yet), centered on interaction and collaboration with people, and focused on the production of usable products.

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Filed under Critical thinking, Education, Engineering, Higher ed, Liberal arts, Teaching

MATLAB course details and update

We start classes this week, a bit later than most other folks thanks to our January term. That means the long-awaited MATLAB course will be formally kicking off. I’ve had a few people ask me about what we’re doing in this course, so here’s an update.

This has been a tricky course to plan, because the audience is definitely not the usual one for an introductory MATLAB course. Almost all the introductory textbooks and materials I reviewed for the course, and all the introductory MATLAB courses I looked at from other schools, have a particular student demographic in mind: they are all engineering majors; they are all freshmen or sophomores with either a semester of programming under their belts or at least a very high level of comfort with computers and the “guts” of programming; and they are all attending large universities in which the particular academic makeup of the institution plays little to no role in how the class is designed.

By contrast, of the 15 students enrolled right now in my course:

  • 9 are freshmen; 5 are sophomores. (At least that demographic fits the profile.)
  • 5 are Education majors; 3 of those are secondary education majors, the other 2 elementary education majors. There is one lone Pure Mathematics major. 9 have no declared major at all.
  • Of the 9 undeclareds, two of those are students who are pursuing our dual-degree program in Engineering and just haven’t gotten around to filling out the paperwork yet.
  • But that’s it: Two undocumented engineering majors; NO science majors. The plurality are Education majors, and once the undeclareds get around to declaring, this may become the majority.
  • I don’t have data for this, but I am pretty sure less than half of the students have ever had any exposure to programming whatsoever. I wouldn’t be surprised to find out it’s more like 1/5 of the class with no programming experience.
  • Again, no data, but I think a good portion of the students would not consider themselves comfortable around computers once we start talking about something besides basic office apps and web pages. For example, anything having to do with typing stuff into a command line. (Like much of MATLAB.)

So this is not the audience that is “supposed” to be taking a MATLAB course. They are not (for the most part) scientists and engineers, and if you start throwing the details of fprintf, memory addressing, floating point arithmetic, and so forth to them you will likely lose them.

And yet — and this has been the frustrating thing — almost all introductory MATLAB materials assume students are engineers and scientists who have no problem being thrown directly into learning about fprintf, memory addressing, and floating point arithmetic. I won’t name names or authors, and these are not bad books, but they are written with a particular assumption in mind about who is using them. And that assumption does not work for my class.

Therefore I have had to do a lot of remixing and retrofitting of existing materials in order to deliver what I think is a solid intro MATLAB course, one that I honestly think satisfies the same learning objectives as the course at our partner university (which uses one of those books I mentioned above, and it works for them because they have the “right” audience for those books), but also one that really works for the decidedly non-MATLAB-like group of students I will have.

I’ve tried to adhere to a few basic design principles when drawing up this course:

  • Get students comfortable with the software and how it works before throwing them into programming. But: Don’t wait too long to begin programming.
  • Connect use of the software back to the mathematics courses they know: namely Calculus I and Calculus II. (The course is a prerequisite for Calculus III and is usually taken alongside Calc II.) And take it very easy on any other kind of math in the course.
  • Get them doing plots and working with data from Excel files early and often. Pictures and data: Students dig these.
  • Make heavy use of the Symbolic Toolbox and get them using it early as well. And by “Symbolic Toolbox” I really mean MuPad, not the nearly-indecipherable symbolic manipulation done inside the MATLAB command line by calling the Symbolic Toolbox. This is actually quite different than how most intro MATLAB materials do it; if you see the Symbolic Toolbox at all, it’s the last chapter of the book and MuPad is never mentioned.
  • Take it easy on the science content of the course and instead emphasize use of MATLAB on topics with which the majority of the class is familiar and comfortable. In the canonical audience, that would mean precisely that a lot of science ought to show up. For us, not so much.
  • Have fun first, foremost, and throughout. Remember that many of the students in the course are not only unfamiliar with computers (aside from using them to check Facebook or use a word processor) but are actually scared of them — probably a greater portion of the class than will let on to it. Keep it light. If something looks more confusing than useful, it probably is; and unless there’s some compelling reason to hack through it, just drop it and cover something else.

I think that with these principles in mind, a lot of MATLAB purists would look at my course and sniff at it, thinking it’s not a “real” MATLAB course. It certainly will not walk or talk like the MATLAB course you’ll find at the typical Big Engineering School. But we’re not a big engineering school; we’re a liberal arts college, and the Liberal Arts informs what we do in every course, including a MATLAB course. I guess I am not trying to create a course that in turn creates more MATLAB purists. I am trying to create a course that shows students that programming is a great application and instantiation of critical thinking and problem solving. If they don’t know all the command line options to fprintf, but later on when confronted with a problem they first thing they think is to try out some MATLAB code to solve it, I think we’ve had a successful experience.

That’s an overview of the philosophy and design of the course. In another post, I’ll talk about the course schedule, assessments, and plans for what we’ll do in the class. This gets interesting because, as mentioned above, we’re not really using a book but rather just McGyvering a bunch of pre-existing resources to fit our particular needs.

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Filed under Computer algebra systems, MATLAB, Teaching, Technology

Links for Tuesday

  • What’s that smell? It could be the latest in biometrics.
  • At Slashdot, a discussion on combining computer science and philosophy. I think that, in general, there is a lot of really interesting yet uncharted territory in the liberal arts arising from combining computing with [fill in humanities subject here].
  • Circuit City hits Chapter 11. The only reason I’m sorry to hear about this is because I know people who work for Circuit City who might lose their jobs. But that’s the only reason. There used to be a time, when I was a teenager, when going to Circuit City to paw over all the tech stuff was fun and exciting. Now when I go, it’s a game of “dodge the irritating service rep”.
  • Some nice tips on getting the most out of Google Scholar. Especially useful if, like me, you’re in a place that doesn’t have access to a lot of technical journals.
  • Mike at Walking Randomly is finding symbolic integrals that the new version of MATLAB can’t do. This is a really important series he’s doing, and his articles are a great resource for MATLAB users.
  • Speaking of math, here’s Carnival of Mathematics #43.
  • The University of Cincinnati is trying out a market-based approach to its various schools that might levy budget cuts on programs that don’t produce. What a concept! Of course the anti-free market people are running wild in the comments.
  • Finally, make sure you thank an engineer today.

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