Content theft

This blog used to have two different URL’s — castingoutnines.wordpress.com as well as castingoutnines.net. The latter was a holdover from the days I self-hosted this blog, and when the domain name registration period drew to a close in December of last year, I opted not to renew, since I think most people come here from an RSS feed or otherwise use the WordPress.com domain.

Well, that might have turned out to be a mistake, because as JackieB on Twitter informed me earlier this evening, someone has purchased the castingoutnines.net domain name and is using it to plagiarize content from here. I’ve spent about 90 minutes just now going through the “fake” CO9’s site, and all totalled, there were 53 blog posts copied in their entirety from here, and the “About” and “What is Casting Out Nines?” pages. Of course I was not given attribution for any of this.

WordPress.com has this helpful page on what steps to take if your content gets stolen. I’m in the process of putting together a DMCA infringement notice to send to Hostmonster, the service hosting the fake blog. In the meanwhile, I’ve also changed the RSS settings so that only post summaries are put into the feed; I hate these partial RSS feeds, but unfortunately this seems like a necessary anti-scraping measure. I’ve also posted a Creative Commons license over in the sidebar to make the terms of using my posts unambiguous.

Unfortunately there’s nothing I can do to wrest the castingoutnines.net domain name from the registrant (who, according to a whois search, is somebody in Israel), so if you are still using that URL to get here, switch to castingoutnines.wordpress.com. Thanks, and sorry for the inconvenience.

You can’t become an expert in college

Cover of Outliers: The Story of Success

Here’s something of an epiphany I had at the ICTCM while listening to Dave Pritchard’s keynote, which had a lot to do with the differences between novice and expert behaviors in problem-solving.

Malcolm Gladwell, in his book Outliers, puts forth a now-famous theory that it takes at least 10,000 hours to become a true expert in a particular area, at the top of one’s game in a particular pursuit. That’s 10,000 hours of concentrated work in studying, practicing, and performing in some particular area. When we talk about “expert behavior”, we mean the kinds of behaviors that people who have put in their 10,000 hours exercise as second nature.

Clearly high school or college students who are in an introductory course — even Dave Pritchard’s physics students at MIT, who are likely several levels above the typical college undergrad — are not there yet, and so there’s not a uniform showing of expert behavior. There are more hours to be put in. But: How many more?

On the one hand, if a person spends 40 hours a week working at this activity, for 50 weeks out of the year, then it will take 5 years to reach this level of expertise:

(10000 hours) x (1 week/40 hours) x (1 year/50 weeks) = 5 years

But on the other hand, a typical college student will carry a 16 credit hour load, which means 16 hours of courses per week. If the student does this over a 14-week semester, and if the student takes the standard advice of spending 2 hours outside of class for every hour inside of class, and if the student undergoes two semesters of classes every calendar year, how long does it take to get to 10000 hours?

10000 hours x (1 week/48 hours) x (1 semester/14 weeks) x (1 year/2 semesters) = 7.44 years

That’s fairly close to double the usual time it takes for people to earn a bachelor’s degree. And it assumes that all that coursework is concentrated into one area, which of course it isn’t.

So there’s an important truth here: Nobody can become an expert on something just by going to college. College might add the finishing touches on expertise that was begun in childhood — for example, with kids who start playing music or programming computers at age 6 — but there’s just not enough time in college to start from zero and become an expert.

This has implications for college coursework. Many of us profs have “expertise” in mind as the primary instructional objective of our courses, but this is quite possibly an unreachable goal for most students. Instead, along with reasonable levels of mastery on core subject content, college courses should focus on what students need for the remaining hours they need to get to 10,000. We should be teaching not only content in the here and now, but also processing skills and broad intellectual tools that set students up for success in continuing towards expertise after college is over.

We can’t make students experts in the time we have with them, probably, but we can put them in position to become experts later. Ironically, the harder we try to make experts out of everyone, the less we stress broad intellectual skills, and the less likely they are to become experts later. How are students supposed to continue to learn, practice, and perform to get to that top level if nobody teaches them how to think and learn on their own?

ICTCM day 2

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[Ed. note: This post was originally written on March 13 while at the ICTCM, but I ran out of time on my $12.95 per day internet access before being able to post it and only now have had the chance to get back online. So it's about 36 hours out of sync.]

Slower day at the ICTCM than yesterday. For one thing, I took some time out in the morning to get the MATLAB course prepped for Monday; and I needed time to finish some grading in the afternoon. But I manage to have a pretty productive day nonetheless.

The main event — one of the primary reasons I came here — was a Geogebra 3.2 minicourse this morning. I’ve been a diehard Geometers Sketchpad user for a long time, but after becoming aware of Geogebra lately, I began to wonder if it might be time for a switch. I have no problem with the usability and features of Sketchpad, but if there’s free software out there that is pretty close to the same quality, the possibility of simply installing it everywhere (like we’ve done on campus with Winplot) is pretty enticing. The question was whether Geogebra’s features and usability matches up well with Sketchpad’s.

After the minicourse, I’d say the answer to that question is definitely “yes”. Particularly impressive is Geogebra’s ability to export entire constructions to HTML as an interactive web page. I have some definitely plans for this kind of thing for the class now. There’s more to learn — unfortunately we didn’t go very deep with the software in the minicourse — but definitely Geogebra will be the software platform for the geometry course this fall. Now I have to decide on a textbook — or to go without. Hope to blog on that later.

Also today I attended a session on using clickers in mathematics courses. I’ve been following Derek Bruff on Twitter for some time (he’s an assistant director at the Vanderbilt Center for Teaching, where I used to be a Master Teaching Fellow) and have gotten interested in using clickers through his work with them. This was a general survey talk, but very well done and it definitely increased my interested in folding clickers into my teaching mix at some point.

Overall the ICTCM is one of the better conferences out there for people who are interested in math, education, technology and the intersections between these. Look for the announcement for ICTCM 2011 coming soon!

What I learned at the ICTCM, day 1

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Busy day here at the ICTCM. I need both an extended time for brain-dumping and a full night’s sleep, and I think the latter is going to win. So here’s a brief listing, in no particular order, of some of the standout items I’ve learned today.

• I learned first thing this morning that rigorous, scientific scholarship of teaching and learning does actually exist, and it’s being done by Dave Pritchard of MIT. Prof. Pritchard was our keynote speaker this morning. In his words, he has basically forsaken a successful career in atomic physics (in which role he mentored or taught three Nobel laureates) to devote his energies to physics education. His keynote this morning gave me enough reading material for a semester and a whole new outlook on what educational research could look like.
• I learned (through Pritchard’s keynote) that there is a school of thought that says partial credit in math and science courses should not be given, because — and I quote — “Partial credit rewards partial understanding”. More to think about here.
• I learned that, thanks to the research of Pritchard and his cohorts, there is a growing field of educational data mining, or one might say educational informatics, out there, designed to take data from online assessment tools and making observations about student learning. There’s even a journal.
• I learned that the difference between novice and expert behaviors in learning pretty much describes all the issues I’ve encountered with the MATLAB course and other courses I’ve taught.
• I learned, through Scott Franklin’s prezi on this subject this morning, that online lectures can be done that aren’t just lectures.
• I learned that Geogebra is pretty cool, and I’ll learn more tomorrow as I take a minicourse on that software.
• I learned there’s a whole website out there — and probably more than this one — for project-based learning ideas.
• I learned that MATLAB has an interactive GUI…. for creating interactive GUI’s. Definitely something to play with later.
• I learned that Gino’s East Pizza is among the best stuff I’ve ever ate, and the copious amounts of it in my stomach right now are a strong argument for sleeping over brain-dumping.

Tomorrow will be a Geogebra minicourse, as I mentioned, and more sessions which I haven’t mapped out yet. We’re getting sporadic wireless access, so I’m able to tweet a lot. More to come!

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.

Working and having a life, redux

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The Chronicle has an article on a Harvard survey of Gen-X professors and their attitudes toward the balance of work and the rest of life. The professors surveyed indicate that they want to be successul in their careers but don’t want to sell out their personal lives in the process. The main survey report is here (PDF, 2.1MB). Here’s a representative quote from one of the interviewees, a business professor, talking about the perils of overwork that Gen-Xers perceive in their older colleagues:

There’s really nothing to be gained by closing your door and working until 11:00 o’clock at night, other than the tenure hurdle that is somewhere out there. If you want to pole vault over it, you go right ahead, but no one here is going to back up the Brinks truck and start dumping all this cash on you, simply because you’ve decided to work like you have three jobs. So that’s the approach I take – sometimes you have to know when there’s this point of diminishing return, where if I keep pounding at this one front, then yes, I may nail it, but at the same time, it will then for a very high cost in other areas.

Although the sample size for this study is painfully small — just 16 professors (the Chronicle article says 12) — the responses are nonetheless fascinating to read and range across a wide variety of work/life balance issues. It’s worth reading the whole thing.

The study is from the same group at Harvard to which I referred in this post from 2006. There, I was responding to comments form some older (or “embedded”) faculty who took the reluctance of Gen-Xers to work until 11:00 PM every night as some form of laziness. Some of the comments at the new Chronicle article tend in that direction also, and conversely there are comments from Gen-Xers that lob equal and opposite stereotypes back at the older faculty.

Unfortunately, until COACHE comes out with a scientific nationwide  study on this issue (with, at the very least, n > 16), all we can do is rely upon anecdotes to understand the issues. But it does seem that most GenX faculty I know share my incredulity at the priorities of some other faculty who place work as the be all-end all of their lives. We also share an extreme irritation toward the inefficient use of time that seems endemic to academia. I shudder to think about how many meetings have I been forced into that have no agenda, spend 45 minutes in chit-chat or irrelevant philosophizing, and accomplish nothing.  And — very especially — we share a kind of hopelessness in considering the rewards structure of academia that gives the loudest applause to those faculty who cut the most out of their lives and say “no” to work the least.

I can only speak for myself (until COACHE gets more data), but I have learned that the best sacrifice to make is not to take time away from your wife and kids so you can get another publication out or hold office hours at 10:00 PM, but rather to lay down hard boundaries around your family and make the crossing of those boundaries by work to be unacceptable. I have learned to say a resounding “no” when work gets to be too much. I have tenure, and surely if I can get tenure then anybody can, but I am coming to understand that I will probably never win one of those prestigious teaching or service awards at my college simply because I maintain those boundaries and protect my family time ruthlessly.

And you know what? So be it. I have three happy and healthy kids who see a great deal of both Mom and Dad every day, who never want for play time or story time, and who know without question that they and their Mom are top priority in Dad’s life. This is more important, more satisfying, and ultimately more crucial to the well-being of the next generation than anything I can possibly crank out in my career. And if it ever gets to the point where my job and my family life cannot coexist, guess which one I’ll jettison without a second thought?

Although hopefully it will never come to that, and I have no reason to think that at my current place of employment it will. And hopefully higher ed as a whole will begin to see that there are a lot of people like me out there and learn to respect our boundaries even as we work to respect the mission of the academy.

Program note: ICTCM coming up

Just a note: I’ll be attending the International Conference on Technology in Collegiate Mathematics (ICTCM) in Chicago next week, March 12–14. I’ll be giving two short talks there:

• “Integrating spreadsheets, visualization tools, and computational knowledge engines in a liberal arts calculus course”, on Friday, March 12 at 11:30 AM. This talk is about how we use these kinds of technologies in our Calculus courses specifically to support the liberal arts mission of the college. I’ll be joined in this talk by my colleague, Justin Gash.
• “Teaching MATLAB to a non-canonical audience”, on Friday, March 12 at 12:30 PM. This is on, you guessed it, the pedagogical and design issues behind the MATLAB course for a general audience which I have blogged about a lot here lately.

I’m also going to be participating in the Geogebra workshop on Saturday in preparation for my junior/senior-level geometry course this fall.

I hope to do a lot of conference-blogging in the meanwhile, and I promise not to use the entire time as a pretext for bashing the TI N-Spire like I did back in 2008. If you’re coming too, let me know.

MATLAB and critical thinking

My apologies for being a little behind the curve on the MATLAB-course-blogging. It’s been a very interesting last couple of weeks in the class, and there’s a lot to catch up on. The issues being brought up in this course that have to do with general thinking and learning are fascinating, deep, and complicated. It’s almost as if the course is becoming only secondarily a course on MATLAB and primarily a course on critical thinking and lifelong learning in a technological context.

This past week’s lab really brought that to the forefront. The lab was all about working with external data sets, and it involved students going to this web site and looking at this data set (XLS, 33 Kb) about electoral vote counts of the various states in the US (and the District of Columbia). One of the tasks asked students to make a scatterplot of the land area of the states versus their electoral vote counts. Once you make that scatterplot, it looks like this:

The reaction of most students to this plot was really surprising. Almost unanimously and without consulting each other, the reaction was: “That can’t be right.” When I’d ask them why not, they would say something like: It looks strange; or, it’s not like scatter plots I’ve done before; or, it just doesn’t look right.

The first instinct of those who felt like they had made a critical error in their plot was to ask me to verify whether or not they had gotten it right. That’s understandable, but it doesn’t go very far because I have a rule that I don’t answer “Is this right?” questions in the lab. (See the instructions in the lab assignment.) Student teams are responsible in the labs for determining by themselves the rightness or wrongness of their work. So it’s time for critical thinking to take center stage — which in this context would refer to using your brain and all available tools and information to self-verify your work. (I wrote about the idea of self-verification here using Wolfram|Alpha.)

Some of the suggestions I gave these teams were:

• Have you checked your plot against the actual data? For example, look at the outliers. Can you find them in the data set itself? And look at the main cluster of data; given a cursory glance through the data set, does it look like most states have a land area less than square miles and an electoral vote count of between 5 and 15?
• Have you tried to create the same scatterplot using different tools? For example, everybody in the class knows Excel (because we teach it in Calculus I); the data are in Excel already, so it would be virtually no work to make a scatterplot in Excel. Have you tried that? If so, does it look like what MATLAB is creating?
• Have you taken a moment just to think about the possible relationship between the variables, and does the shape of the data match your expectations? Probably we don’t really expect much of a relationship at all between the land area of a state and its electoral vote count, even with the outliers trimmed out, so a diffuse cloud of data markers is exactly what we want. If we got some sort of perfectly lined-up string of data points, we should be suspicious this time.

Once you phrase it like this, students pretty quickly gain confidence in their results. But, importantly, most of them have never been put into situations — at least in the classroom — where this sort of thing has been necessary. If critical thinking means anything, it means training yourself to ask questions like this and pursue their answers in an attempt to be your own judge of your work.

I was particularly surprised by the rejection of any scatter plot that doesn’t look like points on the graph of a function. “Authentic instruction” is a term without an operational definition, a lot like the term “critical thinking”, but here I think we may have a clue to what that term means. Students said their scatterplots didn’t “look right”, meaning they didn’t look like what their textbook examples had looked like, i.e. the points didn’t have an overwhelmingly strong correlation despite the existence of a few token outliers. In other words, students are trained by the use of made-up data that “right” means “strong correlation”. So when they encounter data that are very much not correlated, the scatter plot “looks wrong” rather than “looks like there’s not much correlation”. Students are somehow trained to place value judgements on scatter plots, with strong correlation = good and weak correlation = bad. I’m not sure where that perception comes from, but I bet if we gave students real data to work with, it would never take root.

Is Khan Academy the future of education?

Salman Khan is a former financial analyst who quit his day job so that he could form Khan Academy — a venture in which he makes instructional videos on mathematics topics and puts them on YouTube. And he has certainly done a prolific job of it — to the tune of over a thousand short videos on topics ranging from basic addition to differential equations and also physics, biology, and finance.  Amazingly, he does this all on his own time, in a remodeled closet in his house, for free:

I can attest to the quality of his linear algebra videos, some of which I’ve embedded on the Moodle site for my linear algebra course. They are simple without being dumbed down, and what he says about the 10-minute time span in the PBS story is exactly right — it’s just the right length for a single topic.

What do you think about this? What role do well-produced, short, simple, free video lectures like this have in the future of education? Will they eventually replace classrooms as we know them? If not, will they eventually force major changes in the way classroom instruction is done, and if so, what kinds of changes?

Five reasons you should use LaTeX and five tips for teaching it

Over the weekend a minor smack-talk session opened up on Twitter between Maria Andersen and about half a dozen other math people about MathType versus . Maria is on record as being pro-MathType and yesterday she claimed that is “not intuitive to learn”.  I warned her that a pro-  blog post was in the offing with those remarks, and so it comes to this. is accessible enough that every math teacher and every student in a math class at or above Calculus can (and many should) learn and use it for their work. I have been using for 15 years now and have been teaching it to our sophomore math majors for five years. I can tell you that students can learn it, and learn to love it.

Why use when MathType is already out there, bundled with MS Word and other office programs, tempting us with its pretty point-and-click interface? Five reasons.

1. looks better. Seriously. MathType is getting better at visual appeal — it doesn’t look appalling any more — but nothing beats for refinement and polish.
2. is the mathematical typesetting standard in all technical disciplines and in many related fields. Most, if not all, major publications in math, computer science, engineering, and physics use as the preferred typesetting system. arXiv prefers over all other formats.
3. is becoming a standard elsewhere, especially on the web. Last year, Google Documents added an equation editor that is basically a stripped-down editor with a point-and-click interface. The wildly popular online presentation tool Prezi has said that integration is coming. WordPress.com blogs like Casting Out Nines can do , and so can Wikispaces and several other web services. Online typesetters abound, and more are popping up. The web likes open standards, and since MathML is all but impossible to use, fills a gaping need for free, open-source mathematical typesetting. Which brings me to the next point:
4. is free. Free as in beer and free as in freedom. You can download it right now for just about any operating system imaginable, and have the full strength of the system available to you at no cost. And this is a system that has been around for 40 years (if you count TeX) and has millions of users, many of whom actively contribute to the further development of the system by writing specialized packages and macros. This is in stark contrast to MathType, which is proprietary and closed, and although you get the “Lite” version bundled in with office software, the full version will set you back at least $37.
5. is what you make it. You can use with a point-and-click IDE, or you can type everything out by hand with a text editor and compile from the command line, or anything in between. You can tinker with the low-level creation of fonts or just quickly type out a letter. It’s up to the user. Other proprietary programs force a menu-driven point-and-click approach upon you, which you may like but may not like.

Others may add to these in the comments. But if is so great, how come nobody ever seems to learn it until graduate school? I’m not sure, but it’s not because is counterintuitive. It’s not totally obvious, either, but with a little guidance, can make perfect sense even to high school students. If you’re a math or science teacher, make it a project to learn yourself and start using it in your classes, then teach it to your students. Here are five ways to make that a painless process.

1. Use an IDE or a user-friendly text editor rather than a plain, no-frills text editor or EMACS. For Windows machines, use the free TeXNicCenter IDE that gives point-and-click code insertion (or you can just type the code in) with syntax highlighting. On Macs, use TextMate if you have the money and Aquamacs if you don’t; both of these are text editors with tons of great goodies built in. (In TextMate, for instance, typing begin and hitting the Tab key automatically creates an environment with the matching \end{}. ) On Linux, try Kile. These provide user-friendly interfaces and syntax highlighting that take the edge off some of the learning curve.
2. Have someone else do the installation and setup, or provide a total handholding guide for doing it. The only really hard thing about using is simply getting it to work in the first place. This is one of the advantages MathType has over , but the payoff is worth it. New users will need to be walked through the whole process in high-definition detail. But once that’s over, the fun begins.
3. Start small and simple, and build gradually. When first getting students to use , restrict them to just a small, relatively simple document, one that’s mostly text with a little bit of math typsetting required. Small, early successes will convince them that learning is worthwhile. I like to give out my training videos to students and have them learn the system on their own; then have a grace period where students get extra credit for doing their assignments in ; and then start requiring it after the grace period expires.
4. Use it yourself. Students will learn from your example. Try writing your next syllabus in ; and your class handouts; and your tests (perhaps using the excellent exam package). When you use it, and students begin to use it, they see that they are producing math that looks as good as what the pros do, and they get excited.
5. When you give a document made with , also give out the source code that generated it. Students can then look at what you created, ask “How’d s/he do that?”, and get the answer immediately from your code and do it themselves. I myself have learned about half the I know from this method, and adapting/tweaking someone else’s code is a time-honored and very effective means of learning almost anything done on a computer.

Once they are over the initial learning curve and producing beautiful mathematical documents, my students look back on the dark days of MS Equation Editor and wonder, along with me, why anybody would put themselves through something like that. Happy -ing!