It is with a little bit of unease that I’ve been looking around the Internet at what is available as far as math videos go. I asked my calculus students to consider making a video setting up a related rates problem for extra credit. When I went to look at their videos on YouTube, I was amazed at the number of problems that have been worked out in videos. If you want to see what I mean, look at any of the following sites:

- YouTube (search “Calculus)
- Hippocampus (which even has Calculus in Spanish)
- MathTV (many of these videos are cross-posted on YouTube)
- MIT Open Courseware (some of these have videos)
- Video Calculus (University of Houston)
- Free Video Lectures

I’m guessing that between video solutions and solutions worked out on websites, you could find a worked out solution on the Internet to any related rates problem (or other problem) that could be assigned.

This brings me to a question … if information is becoming so easily available for free (and it is), is there any way that, in good conscience, you could evaluate a student’s mathematical learning without having the student show up to take a proctored exam in person. Students can get the “work” from a variety of websites on the Internet, so even if they don’t have a friend willing to do the work for them, it should be easy enough to do any kind of take-home test by simply searching the net for solutions.

In a writing-intensive class (English or History, perhaps), you would be able to evaluate authenticity of the work of the student by examining a series of drafts that lead to a final paper or because the personality of the student comes out in the work. However, for mathematics, the work for different students looks pretty much the same (assuming it is correct). There would be no way to determine that the student actually learned the material themselves.

Now, you might say … easy enough … just write all new test problems every semester! Have you ever tried to write new related rates problems that are doable at a Calc I level?

(I should mention that what really made me uneasy was the calculus videos involving bikini-clad girls. Some really smart, good-looking guy or gal could make a lot of money online by stripping to almost nothing and producing math lessons to post online. This is probably the only way anyone will ever profit off of making video math content in the future.)

Why the unease? The 2005 CBMS Survey found that “*the predominant instructional modality continued to be the standard lecture method, with this reported as the preferred methodology for all but two courses by percentages that ranged as high as 93%*.”

Well, if all you do in the math classroom is lecture , and lectures are now readily available online for ** free**, then what will

**your**role be in the higher education classroom of the future? I’d be moving towards more active classroom learning if I were a math instructor at the college level. Oh yeah, I am, and I have … phew! Dodged that bullet!

Seriously though, if a student were to learn all their calculus by watching videos, do our colleges have the ability to award these credits towards a degree through some kind of evaluation (like the AP exam)? How about for differential equations? How about Abstract Algebra? As college tuition (and gas) becomes more and more expensive, students (and parents) will be questioning why it is that students need to physically appear in a classroom and pay for tuition to do something that they could do on their home computer (i.e. watch a lecture).

It’s interesting that I’m thinking about such issues this week, as I am going to the Education Summit (and the rest of the conference, with lots of sessions on Learning and Education) at the WorldFuture Conference in Washington DC this weekend. I’m curious whether these other thinkers about education and the future have basically come to the same conclusion as I have:

If all you do in the classroom is lecture, you’re in trouble in the higher education environment of the future. Instructors will continue to work at colleges as facilitators of learning, but the learning will take a variety of forms. There’s more to learning than passively watching a lecture, and it’s about time we figure that out. If you’re within five years of retirement, you’re probably going to be okay. Any more than that and it would be wise to begin to learn alternative pedagogies to math lectures.

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