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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Monday GTD moment: Scholarship and GTD

This is the third installment of Monday GTD Moment, where I take a post to blog about Getting Things Done and how it applies in an academic setting. If you’re unfamiliar with GTD, here’s a good overview, and make sure to read David Allen’s book that started it all.

Last week I wrote about grading and GTD. I noted that grading is kind of a poor fit in traditional GTD. A prof can grade anywhere, so the idea of contexts fits awkwardly; and grading “tasks” are usually projects, although we think of them as tasks and although the next actions contained in those projects are usually nothing more than smaller projects. GTD wasn’t really made for the academic profession, and so the staple activities of academics don’t often fit well.

Another area similar to grading in its relatively poor fit within the canonical GTD philosophy is research, or more generally scholarship. By “scholarship” I am including not only the usual pure research that most profs do (at least while they are getting their terminal degrees) but also any significant creative activity based on one’s expertise that contributes to a discipline or the application of a discipline. This is Boyer’s model of scholarship, and it is finding increasing purchase at colleges and universities all over. So, for example, an applied mathematician who contributes her skill by consulting “on the side” for some external project is scholarship; so would be research that she does on the teaching of applied mathematics or using her expertise to  do a math workshop with a bunch of elementary school kids.

Scholarship is hard for many reasons, perhaps the main one being that original creative work is amorphous. When I was working on my dissertation, the hardest aspect of that work was that at any given point in the process, although I could always measure how much work I’d done, I had no way to tell how much more work I needed to do, what course of action was really the best next action, or even if my previous work was going to remain or be wiped out by the discovery of a mistake or a more elegant and general theorem. It wasn’t like reading a book, where you knew not only how far you’d read but also how far you had left to go and which page was next, and you had a reasonable assurance that the pages you’d read wouldn’t disappear from the book once you’d read them.

Even now, I have all these scholarly projects I want to finish (or start), and I struggle to GTD-ize them. For example, I’m currently working through this book on probability as a self-study course. Some parts of this project are pretty linear and predictable and therefore have clearly-defined next actions —  “Read and work through examples in section 1.2”, for instance. But then the nonlinearity hits. I will eventually read through all of Chapter 1 and will need to work through the exercises. Do I do them all in order, or do I skip around? Would it be fair to lump exercises 1-5 together as a single task, or is that another project? Is even a single exercise a task, or a project, and how can you know in advance? Academic or intellectual work is a black box — you have no idea how long it’s going to take, what resources you will need, whether it is properly thought of as a task or a project, or indeed even if David Allen’s idea of a “task” (a single physical action) is even appropriate at any level.

Scholarship is highly nonlinear, which makes it much different from the business tasks for which GTD was originally created. But it’s what also makes scholarship fun and rewarding, and it’s why most of us eggheads went and got PhD’s in the first place. So, what’s a scholarship-enthused, GTD-powered prof to do in order to bring this important aspect of his work under the GTD framework? Here are some thoughts.

1. Use the review process — all six levels — to craft a coherent and realistic scholarship plan. The heart of GTD is the weekly review, but don’t forget the other kinds of review that Allen talks about in the book. Specifically, Allen gives a six-level model for review in terms of altitude: 50000+, 40000, 30000, 20000, 10000 feet and “runway”. The weekly review often tends to stay on the runway — which, if your work looks like mine, resembles the runways at O’Hare around Christmas — but those higher-level reviews are important. Scholarly directions change rapidly and often at the discretion of the individual. In the business world, you don’t often get the opportunity to change the fundamental direction of your work on your own initiative. But in academia, every day has the potential for such change. If I decided tomorrow to stop studying cryptology and start doing mathematical finance, I could do that. That ability is liberating but also a recipe for stagnation. It’s important to see your scholarship, regularly, not only in terms of current projects and areas of responsibility but also in terms of where you want it all to head in the next year, the next two years, and so on. The tenure and promotion process at an institution, if that process is well-designed, will help profs to think in these terms, but only once a year or (post-tenure) every five years. GTD, done with these higher altitudes in mind, would say to think about the big picture a lot more regularly so that your overall plan is more coherent.

2. As much as possible, concretize your research agenda. Since scholarship is amorphous, once you get down to the level of 10000 feet and lower, some superimposition of structure on scholarship is necessary. It doesn’t always fit well, like a nice suit on an unruly young boy. But it’s still important to break the scholarship plan you’ve created down into manageable projects with a list of concrete next actions. Having “Write a paper” as a project will lead nowhere; most scholarly activities are projects within projects, and at bottom you find one project that can finally be broken down into discrete next actions, each of which has a well-defined context. The challenge is to get to that point. (This is a major similarity with grading.)

3. Don’t be bothered if the plan changes. The nature of research puts all scholarship-oriented action lists into an automatic state of flux. That nice, tidy list of actions under the “Prove the twin prime conjecture” project stands a good chance of being brutally rearranged if, say, you discover a journal article that shows your main theorem so far (which you thought you proved 3-4 next actions ago) to be false, or somebody proves it first, or if you get an unexpected opportunity to work on something else which requires dropping or postponing the project. We all know that research and scholarship are highly volatile areas. But one of the strengths of GTD as a workflow management system is that GTD assumes that tactical decisions will change fluidly and constantly, and that’s OK. The system doesn’t fall apart if things change; you just adjust your next actions and move on.

4. Subdivide your Read/Review folder and make it more like an inbox. Read/Review means something very different to an academic than it does to a business person. The entire life of an academic could be summed up by the term “Read/Review”. So I think Allen’s conception of the Read/Review file needs to be expanded for academics. In my system, I’ve got three Read/Review folders for physical stuff and three for electronic stuff — the three folders in each medium being Teaching/Service (articles about the profession, articles about GTD, articles about pedagogy, etc.), Research (traditional research papers from journals), and Popular (math-related but not from journals; sometimes ed tech items make it in here). I treat these folders like inboxes in the sense that I make them part of my weekly review. Sometimes I gather articles that look good at the time, and I do intend to read them, but they get crowded out by something more urgent. I find that I need to go through Read/Review at least 2-3 times a week to process stuff. Expanding on the Read/Review idea helps keep fresh ideas coming onto your radar screen and into your brain.

5. Stick to your guns with GTD on everything else besides scholarship. Being a prof involves wearing lots of hats — we teach, we serve on committees, we grade, we mentor and advise students and colleagues, and many other things. In order to have the time and flexibility to carry out these amorphous, nonlinear scholarship projects, we have to exercise discipline in getting things done that are “morphous” and linear — stuff like grading, prepping courses, working on committee proposals, and so on. If a person can use GTD to get those tasks and projects under strict discipline and control, then there will (for the most part) be time and space in our schedules to do scholarship. But if the manageable stuff is running all over us, then we can forget about research, unless you are one of the tiny minority of professors who do research and basically nothing else.

I think there’s a great deal of connection between being happy in your academic work and being balanced. The more we enable ourselves not only to be excellent teachers but also active scholars, the more we benefit and so do our students and institutions. I think GTD can help in that regard.

Have a productive week!

[Photo by Jay Lichtman; artwork by ynot2006]

What is a basic syllabus in educational technology?

So I’m plotting out my tactical plans for research and scholarship over the next year right now — my imagination being stoked by the completion of my Statement of Scholarship — and I’d like to go deeper into educational technology on a number of levels. I’d like not only to stay abreast of the rapidly-changing face of the technology being used in schools, but also the social implications of that technology, the legal issues behind it, and the technical nuts/bolts/bits of how this stuff works in the first place (including the computer network/programming side of things).

I’m just a user and a self-appointed pundit of ed tech, so I have no idea exactly where to start if I want really to go deeper on this subject. I do know that I’m going to swallow hard and read Digital Natives, Digital Immigrants by Prensky carefully (as opposed to skimmig it as I have done in the past) even though I disbelieve in nearly everything I’ve drawn out of that essay. And I have Friedman’s The World is Flat, which seems to be a seminal work among School 2.0 people, on my bookshelf at work waiting to be read. But what other suggestions would you readers have?

Remember, I’m looking not to become a mindless School 2.0 zombie (that takes no effort at all) but a person who is fluent with all the important aspects of ed tech, including the “tech”.

Letting teaching and research feed each other

Good article here at the Chronicle on balancing teaching with research, from a neuroscience professor who makes it work for him.

The reality of modern academe is that, no matter what your institutional affiliation, the time you can devote to research is being squeezed by multiple competing demands. No simple solution to that problem exists for any of us. But I have found that rethinking the nature of our professional commitments, such that teaching activities bleed into research ones (and vice versa), can be an effective way to reduce the time crunch. Academics describe their workload of scholarship, teaching, and service as if those were entirely separate entities. In reality, the line between teaching and research is usually much fuzzier.

Read the whole thing, in which Prof. Gendle writes at length about the potentially prosperous symbiosis between teaching and research. He points out three key scholarly skills which teaching reinforces: developing your presentation skills, responding appropriately to odd questions, and making connections across fields. He emphasizes his success in maintaining an active research agenda while keeping a “moderately heavy” teaching load, which for him is 5-6 courses per year. My teaching load is 8 courses (6 preps) per year, and to that situation Prof. Gendle says:

I am fortunate that my teaching load still allows some dedicated time for research. That may not be the case at institutions with teaching loads of seven or more courses in a single academic year. Teaching loads of that magnitude often pass a tipping point for most faculty members (myself included). With that many courses, there simply are not enough hours in the day to conduct classes, grade papers, etc., and still have time left for research.

Gendle is in the psychology department at Elon University, which is well-known for being an undergraduate institution with a reputation for engaging students in meaningful scholarly work.

Do any of you teach at institutions with a 7+ course-per-year teaching load, and still manage an active research program of some sort?

Fun with finite fields

For those of you interested, I have a review of Finite Fields and Applications by Gary Mullen and Carl Mummert now posted at MAA Reviews. You can get to it here, although you have to be an MAA member to view it, or else pay $25/year for a nonmember subscription.

If you aren’t an MAA member and don’t want to pay, the bottom line of the review is: It’s a pretty good book. Very good for mathematicians, grad students, and advanced undergrads. Normal undergrads will need patience and perhaps a lot of help with the initial chapter, which is a lot of serious algebra which unfortunately doesn’t appear to make that much of an appearance in later chapters when the applications show up. And what’s with the three-paragraph treatment of AES? On the other hand, lots of neat stuff about Latin squares, including a cryptosystem based on mutually orthogonal Latin squares which I’d never seen before. 

This review was one of the things I was trying to get done last week. It’s gratifying to see a publication process go this fast — I sat down on Tuesday and wrote the review; emailed it in on Wednesday; and it was put up at the MAA yesterday. 

A place for rejected math articles

If you’ve been submitting mathematics articles to refereed journals only to have them sent back to you every time, there’s hope. You can try submitting them to the new journal Rejecta Mathematica, which will consist only of papers which have been rejected from peer-reviewed journals. From their web site:

At Rejecta Mathematica, we believe that many previously rejected papers can nonetheless have a very real value to the academic community. This value may take many forms:

• “mapping the blind alleys of science”: papers containing negative results can warn others against futile directions; 
• “reinventing the wheel”: papers accidentally rederiving a known result may contain new insight or ideas; 
• “squaring the circle”: papers discovered to contain a serious technical flaw may nevertheless contain information or ideas of interest;
• “applications of cold fusion”: papers based on a controversial premise may contain ideas applicable in more traditional settings;
  
• “misunderstood genius”: other papers may simply have no natural home among existing journals.

Rejecta articles also allow the authors to speak out in defense of their rejected articles and include an open letter from the authors describing any known flaws in the paper.

And yes, although there’s no formal peer review process to get a paper into Rejecta, you can still have a paper submission rejected.

[ht Math-Blog]

Some ruminations on research

So I spent the entire day today up the road at Butler at an NSF workshop for people interested in writing grant proposals. It was very informative, and it was especially helpful to have most of the actual program directors there in person — all of whom were friendly, very down-to-earth and open to talking with faculty grunts like me. (One request for the NSF folks, though: Please, for the love of God, consider the 10/20/30 rule for your presentations. Four straight hours of 40+ slide Power Point presentations done in 20-point font almost (but not quite) drove me crazy. Thanks.)

What I wanted to blog about right now, though, isn’t the NSF stuff per se, but more about the feeling I always seem to take away from conferences or workshops like this where there are a lot of people who actually do research. The feeling is one of being on the outside looking in, of being past my prime.

To understand this, you need some context. It’s been 10 years now since I finished my PhD in mathematics, with a specialty in some very esoteric homology theories that I myself never fully understood, and the use of exotic category theory stuff to make the symbols associated with those homology theories do what I wanted them to do. At the end of the day, I had proven that Quinn homology was isomorphic to G-equivariant homology when G is a discrete group acting cellularly on a simplicial complex. I worked for another year following my dissertation to edit it down into publishable form, and got it published.

But that was the last real mathematical research I have touched since then, with the lone exception of a paper I got published in Cryptologia a couple of years ago. And that paper was so error-riddled in the original draft that it only barely was accepted at all, and  even then it was more of a curiosity than an actual result. But it was research. However, it took me a year to write it, and over a year to edit it since part of the editing process was interrupted by traveling to China to adopt our oldest daughter and stumbling into being a parent.

Getting that paper published, especially since it was in an area (cryptology) in which all my training has been self-teaching and in which I have no formal coursework, makes me believe that I still have the intellectual chops to do mathematical research. But the amount of time it takes to get anything done, and the number of times I’ve sat down to try and learn new things and get out to the frontiers of a subject where the research happens, makes me think that I’m too old or too involved with other things in life or carrying too heavy of a teaching load to make it happen.

Don’t get me wrong — my family is more important to me than research, and teaching is what drove me into being a college professor to begin with. But I also want to be a well-rounded professional, which means that not only am I teaching excellently and leading a fulfilling personal life, I am also learning — consuming and producing new knowledge both for the purposes of the world and my discipline at large but also for my colleagues and students. The more I look back on the last several years, the more I realize that my scholarship and the attempts to satisfy my hunger for learning have not gone anywhere.

And this is no more frustrating than when I am around a bunch of talented researchers, especially scholars who work at liberal arts colleges whose job is primarily teaching but still have the time and space to learn and be experts in their areas. I have been trying to reinvent myself as a scholar over the last few months in a different area — computational linguistics and data analytics — in hopes that I could succeed in scholarship here where I had not succeeded elsewhere. Things went well over the summer. But when the semester started,  everything ground to a halt as every moment of the week was taken up by grading, prepping for the next class, grading some more, etc. Then, today, I was walking from one meeting room to the next when a guy behind me starting talking about his research in computational linguistics. I turned around to introduce myself, thinking perhaps it was somebody from IU’s excellent linguistics department. But it turned out to be… someone from a neighboring liberal arts college. Where they have the same emphasis on teaching as we do. So, how is this guy able to get his research done where I can’t even find the time to open my Jurafsky and Martin?

So I am left with a question, which I wrote in large print at the bottom of my workshop notes today: How does somebody like me — holding a PhD but 10 years removed from any significant research, not anywhere close to the cutting edge of any discipline, and tenured in a position at a small, teaching-oriented liberal arts college — how does somebody like me get to the point where he can do research in his field or a closely related field? Is it possible? If so, how do I get there? If not, how do I come to terms with knowing that my math research days are over, even though intellectually I feel like I am still in the game, and want to be in the game?

[Photo by slight clutter]

Spider-sense and social networking

A researcher in Argentina has just published a paper entitled “How to Be a Superhero” in which he analyzes the social networks of superheroes in the Marvel Comics universe. Here’s the abstract:

We analyze a collaboration network based on the Marvel Universe comic books. First, we consider the system as a binary network, where two characters are connected if they appear in the same publication. The analysis of degree correlations reveals that, in contrast to most real social networks, the Marvel Universe presents a disassortative mixing on the degree. Then, we use a weight measure to study the system as a weighted network. This allows us to find and characterize well defined communities. Through the analysis of the community structure and the clustering as a function of the degree we show that the network presents a hierarchical structure. Finally, we comment on possible mechanisms responsible for the particular motifs observed.

If I had read this paper in high school, when I was knee-deep in X-Men and Avengers comics, I might have become a data analyst!

[Hat tip:  Data Mining: Text Mining, Visualization, and Social Media]

The 80/20 rule

Olivier Bousquet at Machine Learning Thoughts has an insightful observation about life in academia or a research setting: “No matter where you are, it is almost impossible to spend more than 20% of your time doing research.” He calls this the 80/20 rule, and goes on to make a very sensible proposition:

Instead of choosing a job based on the amount of time that you will be allowed to spend on research, rather choose it based on what exactly the 80% other activities are.

Indeed, you should rather pick a job whose 80% activities you find enjoyable (unless you really can stand doing things you do not like for the sake of the remaining 20%).

Good advice. It can be frustrating when you want to do scholarship but don’t have the time, thinking that you should have as much time as you’d like for such things. Read the whole thing as well as the articles before and after that one, which are on “The Happiness of a Scientist”. (The last update on his blog was February; I hope he continues the series.)

Weasel words in education: “-based”

Some of the worst abuses of the English language today occur in education, and one that I dislike particularly is the suffix “-based” when applied to pedagogical methods. In particular, the terms weasel-words academically-based and research-based make my muscles tense up and my skin crawl, and ought to be banished forever from any kind of discourse.

You hear the term “academically-based” applied to early childhood education. I know this because my 3-year old started her Montessori preschool program this morning after having gone to two different daycare centers previously. When we were looking for daycare centers, we chose the two that she eventually attended because they touted themselves as having “academically-based curricula”. But more often than not, this meant half-hearted attempts at leading the kids through counting from 1 to 5, and that’s about it, while the harried daycare worker instead spends most of her time trying to keep the kids from killing each other.

At the Montessori school, on the other hand, they learn numbers, words, counting, the planets, the seasons, the continents… it’s a curriculum. There’s a plan. And all curricula — all real curricula — are either academic, or they aren’t. You don’t start with something academic and then veer off into a different direction, and retain the academic quality of the curriculum. There’s no “-based” to it.

And you hear the term “research-based” used by those who have way-cool, whiz-bang new pedagogical ideas — and grant proposals for funding them — and who want to make their ideas sound like they have more credibility than they really do. More often than not, this term is used for compensation purposes. The person behind the pedagogy knows that there’s nothing but her or his opinion to suggest that their idea is any good. So instead of presenting actual research to support her/his claims, they say it’s “research-based”, meaning that there’s research out there — there must be — that supports my idea, and I could look it up if I really felt like it.

And the frequency of use of the term is usually inversely proportional to the actual scientific credibility of the idea. I mean, if you have to keep clubbing me over the head with how research-based your stuff is, then why don’t you just show me the data? Pedagogical techniques either arise from legitimate scholarship or they don’t. There’s no -based to it.

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