Data Compressing the Curriculum

I've written about vodcasting lectures for out-of-class consumption and about the idea of information theory in the past. A recent article in the Chronicle puts these together. The piece highlights a practice of condensing a lecture or topic into a one to three minute video that encapsulates the essence of the material to be taught. This would be followed by an exercise to reinforce the material.

You can see one here:

I can see that this technique would work better with some ideas than others. In particular, this is the kind of delivery that would have the best chance of being successful with low-complexity learning: facts, simple pattern recognition, or simple examples of deductive reasoning. In fact, it occurs to me that one could scientifically study the complexity of a task by reducing the length of the mini-lecture until students don't understand anymore. This would be an upper bound on complexity. So perhaps solving a 2x2 system of linear differential equations has 25-minute complexity, whereas learning the basic facts about the Norman Invasion has 2.4 minute complexity. If this worked, you could actually create a taxonomy of knowledge and skills for a discipline that had some (minimal) scientific grounding.

Alternatives to Lecturing

Earlier this week, I wrote about two physics instructors who use vodcasting as a technique to replace traditional lectures with a more engaged classroom experience. I came across another article today (again on Reddit) from the 1960s, where a Professor Morrison lays out his case for what he calls The Gutenberg Approach. This piece is paired with a letter from 2008 about the discovery and use of this method, where Frank L. Lambert gives the following summary of the problem as he sees it:

The lecture system was crazy for teaching organic chemistry. What are professors doing in a lecture? They’re outlining and explaining the important points (and wasting time mentioning even obvious points) of the text on the blackboard. But why? Gutenberg invented movable type. That made printed textbooks available 500 years ago — even now in chemistry rather than alchemy! Students don’t read them? Of course not, if the whole course is dependent on what the prof puts on a blackboard! Students can’t pick out the most important ideas and facts from a 500-page text (in 1948, or thousand-page now) by themselves. They’re beginners.

This reminded me of something Bertrand Russell said in his biography, which my wife gave me for Christmas a couple of years ago. I can't find the exact quote, but he said that at university he never learned anything from the dons, and resolved that if he became one he would not expect his students to learn anything from him either. I think he was referring more to content than style, but both are clearly important.

The resignation to the students not reading the text is one I've experienced in my own career over the last couple of decades of teaching college math. A textbook literacy project, perhaps run by the school library, might be a way to approach this. Or a general reading campaign (here's an amusing take on that: faceabook).

The solution to the lecture/textbook problem is summarized by Dr. Lambert thus:

[W]hy not give them something a bit better than the [class] notes on the day or the week before the class, not really an outline of the text but more of a guide to what’s important and what’s not in each day’s text assignment. Then the students could read a day’s assignment and know what to look out for as the key points, realizing that the professor is not going to outline it on the board. Instead, she or he will explain in detail a few complex things in the assigned pages, answer any questions about them, and show how to conquer problems like those in the text, always open to questions and for back and forth with students.

This is an argument for a more engaged style like that of the vodcasting approach. The two are quite similar, in fact. The main difference is that a static outline has been replaced by video. The advantages of the second, to me, are that actually hearing words is better than reading them (for evolutionary reasons), and the animation possibilities inherent to the video medium are superior to plain text. Combined, the vodcasting approach has significant advantages for delivering information. For indexing material and outlining the important bits, I can see where a static outline would still be a great thing to have.

How might you try this out? This is a question I'm tossing around. There are the funding and nuts/bolts questions: how to actually record and distribute the material, train the professors, and so forth. Also is the need for a local champion to take on the project. Finally, one would like to assess the results of this, especially given all the time and expense involved. For the last part, Dr. Richard Hake [blog] has long advocated using pre/post tests for the sciences as a way to demonstrate accomplishment, and the research seems to support this position.

I spent some time Googling "alternatives to lecturing" and sifting through the results. Much of it is fairly obvious: use discussion, debate, Q&A, problem-solving, and so forth. More interesting is the idea to use simulations in class. This probably works best for technical fields, but has some advantages. In my experience, simulations can:

• Teach deep connections with directed 'play'.
• Teach software tools used in the profession
• Teach secondary skills like programming
  
• Link to coursework in an obviously applied setting

The first time I taught Computer Organization I wanted to combine an introductory digital logic course with the more advanced topics of designing the CPU, ALU and other bits of a working computer. There were simulators on the market, but they were complicated, expensive, and required high performance workstations. So I built a simplest-possible digital logic simulator in Perl, which I called Zlogic. I've used it over the years to good effect. In class, students learn how digital circuits work and how to write Boolean equations for different kinds of logic. With the simulator, they can enter those same equations and see what happens when they input data and run it. That is, there's a complete trial-and-error loop that can be quickly executed.

Perhaps the real problem with lectures is that they don't engage the learning part of our brain. How do we learn? By trying things and making mistakes until we get it right, I would say. Simulations and similar types of software can provide that.

In an other years-long project, David Kammler at SIU-C and I developed a software package for Fourier Analysis, which can be used to 'play' with the ideas. Here's an example I used in a grant application:

Load a vector, traced from an image. This is a complex list of values (meaning real and imaginary parts) plotted on the complex plane in the usual way.

Next we use a technique that would be learned in the course. We want to compress the information in the vector (the drawing) by looking at its frequency components and removing most of them.

The top part of the graph is the real part, and the bottom is the imaginary. The squiggly lines show the magnitudes of various frequency components. Most of the information is in the low frequencies, so I have zeroed out the higher frequency data to compress it. This is called a low-pass filter in engineering. Now we imagine sending the compressed vector of frequency data to our friend, who isn't fazed by the squiggles. She's had Fourier analysis, and knows that she should unscramble them by using the inverse Fourier Transform. Because we removed some of the information, the reconstruction won't be perfect. Here it is.
This all takes no more than 10 seconds to do, so the try/response cycle is very quick. The effect of the trial is obvious. One can easily go back and try different filter widths to see how much the quality of the final image improves. It's all very fast. In my mind I equate that with the speed of learning; the faster we make mistakes, the better.

An ideal program might be outlined like this:

1. Facilitate the creation and use of vodcasts with a trial group of instructors, providing technology and support, probably through the library in combination with faculty development leadership
2. Help the faculty member develop active classroom strategies to supplement the vodcasts
3. Outline and index vodcasts, and put the technology in place to deliver them over the web
   
4. Provide a textbook literacy program at the library and encourage use by the target group of students
5. Mate the program to a software package that can do simulations quickly and easily
6. Assess with pre/post tests on content

I've probably missed something obvious in this list, but this is a good start for thinking it through. I call this kind of thing making the preliminary mistakes. The quicker you get through those, the better.

Transformational Teaching

The horse and carriage went out kicking and neighing, and left a deep impression in the first automobiles, which were designed to look like a carriage...without the horses. Technology is transforming education before our eyes as well. Two high school science teachers, Jonathan Bergmann & Aaron Sams, claim to have found an optimization that could be revolutionary.

The video I found on reddit is here: Mastery Learning that works!. I have to warn you that it's downright annoying to watch because of the patter and goofy scribbling that takes place over the mostly static images. Fortunately you don't have to watch it; I'll describe it here, and they also have a website you can peruse*.

Vodcasting is what they call their process of prerecording the static part of class presentations for students to review before coming to class. You might compare this to an active reading experience, in a situation where students took reading assignments seriously. An advantage of video is that speech and visuals can overlap--wow, just like on TV! Not only does this appeal to the screen-viewing generations, but also would seem to have some real advantages over reading static text. After all, reading is a relatively new phenomenon in the human experience, but our evolution was undoubtedly driven by speech and visual information. That is, we ought to be hardwired for this sort of thing.

Of course, this is what's been going on in the classroom since the mists of time gathered from the primordial dew. The difference is that with vodcasting, it can be asynchronous. The instructor does one recording, and the students can review individually. Some of the advantages the authors list include:

1. Students who were absent really never missed a class.
2. Less time tutoring students after school
3. An amazing tool when teachers are absent
4. Lessons going out to the world

It's the last one that ought to make the sleeping giant of higher education grimace in his slumbers. Video only has to be done once. This is a waking nightmare for textbook publishers, too.

So what do the teachers do? Because of my training, I think of this technique like data compression. Take all the common parts and lump them together, and then spend time describing the details. For example, look at the string below. How would you describe it to someone over the phone?

123456789123456789123456788

After inspection, you might say "repeat the sequence of digits 1 to 9 three times, except that on the last time, use two 8s instead of 89." The first part takes care of the big pattern, and the customization at the end takes care of the details. With Bergmann and Sams' approach, the teacher spends time on the detail--working through the actual problems students have, solving problems in class in small groups or individually, clearing up questions about the vodcast, and generally dealing with the most important part of learning: getting the details right so that students can demostrate new skills and knowledge.

In school, I always liked the courses best where the instructor took time to have students solve a problem or two in class--the time went faster, and I felt more engaged. I've always tried to emulate that in my own teaching, and encourage students to work together on these occasions too, so they'd develop an active vocabulary in the discipline. But the data compression (as I think of it) that Bergmann and Sams are experimenting with is an order of magnitude improvement on that idea.

I'm curious how well this technique works for other disciplines, such as the humanities. The overall implications for higher education could be profound--the whole curriculum and pedagogy could be turned on its head. High-quality vodcasts generated externally would be potentially used in combination with hands-on class work led by local faculty. Some universities already make available vodcasts (MIT for example). It's hard to say how this and other technological shifts will change the academy, but I think it's fair to say that it will not remain unchanged. The ground is already shifting beneath our feet.

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*My wife tells me that 'peruse' doesn't mean what I think. From Latin, it means to read carefully, she claims. In common usage, it seems to mean 'to skim'. Looking at the Oxford English Dictionary just now, I guess somehow we're both right (emphasis added):

3. trans. To examine in detail; to scrutinize, inspect, survey, oversee; to consider, to take heed of. Now also (influenced by sense 4c): to look over briefly or superficially; to browse.

It appears to be a true oxymoron, like 'pianoforte' that means two opposite things at the same time.