Tuesday, 14 August 2012

About Khan and Bicycle Math

So, tomorrow my "Taylor's Polynomials" web series will be looking at Khan Academy. (No great surprise if you spotted the one particular link, or the hashtag on twitter.) I figure I should get a few things down prior to that video going live, so that:
 - I have a baseline, in case I get feedback from the episode that causes a shift in my opinion.
 - I have a somewhat more in depth explanation I can point at.

For those who have no idea what Khan Academy is, I'll point you at Salman Khan's TED Talk from 2011. You should follow that link and check it out. You may want to do so even if you are aware of what I mean, because one of the things I'm going to pick apart in this posting is Khan's bicycle analogy, occurring at about minute 8. Go ahead, I'll wait. Clicked yet? Come on, interactive videos are all the rage!

Okay then. First, a couple things that trouble me. One aspect Khan mentions regarding his interactive videos is that by watching them, students "don't feel they are wasting the teacher's time" or "don't have to feel embarrassed asking something" again. But isn't it EQUALLY important that students learn how to ask questions? Not just of the teacher, but of each other?

Second, it seems that arming a teacher with all this DATA about where a student is, will ultimately serve to teach the student that, "I'm not sure what I'm having trouble with, but the teacher has all this data, so they'll fix it". It completely shifts the burden of responsibility. It seems like we're headed for "Come on, you have the statistics for my homework, tell me what I'm doing wrong!"

Finally, as I indicated above, I have an issue with Khan's bicycle analogy.  In case you missed it, here's the full text:
"In a traditional classroom, you have a couple of homework-lecture-homework-lecture and then you have a snapshot exam. And that exam, whether you get a 70% an 80% a 90% or a 95%, the class moves on to the next topic. And even that 95% student, what was the 5% they didn't know? Maybe they didn't know what happens when you raise something to the zero power. And then you go build on that in the next concept.

That's analogous to, imagine learning to ride a bicycle. And I give you a bicycle, maybe I give you a lecture ahead of time, and I give you that bicycle for two weeks, and then I come back after two weeks. And I say well, let's see, you've having trouble taking left turns, you can't quite stop. You're an 80% bicyclist. So I put a big C stamp on your forehead. And then I say here's a unicycle.

As ridiculous as that sounds, that's exactly what's happening in our classrooms right now. And the idea is you fast forward and students, good students start failing algebra and calculus all of a sudden, despite being smart, despite having good teachers. And it's usually because they have these swiss cheese gaps that kept building throughout their foundation. So our model is: learn math the way you learn anything, like the way you would learn a bicycle. Stay on that bicycle, fall off that bicycle, do it as long as necessary, until you have mastery."

I have a number of issues with this comparison.

1) Assumes the Motivation

Khan's fix to the problem seems to be that we force the cyclist to graduate to A++ level from a C, before giving them the unicycle. If the student sees the value in this, okay, it can work... in fact, it seems to be the foundation for his whole system. (After all, if a student isn't motivated, they're not going to be inclined to watch math videos.) But what about the following scenario?

"I don't need to learn more about the bicycle," the student says. "Most people drive everywhere, so I'm going to do that." *

"You can't learn the unicycle until you have completely mastered the bicycle."

"Most people drive everywhere, so I'm going to do that," the student repeats slowly, wondering if the instructor has a hearing deficiency.

"But you must learn the unicycle eventually, in order to graduate."

"You're kidding. Fine, fine, give me the unicycle," the student sighs.

"You can't learn the unicycle until you have completely mastered the bicycle."

"Oh, for... do you know how hard it was just to become a 'C' bicyclist?!"

"Mastering bicycling is really important."

The student glares. "Fine, fine, show me more videos, give me more questions..."

"Good work! You're now a 'B' bicyclist. Another three weeks and you might be able to move on."


I don't think offering little prizes for completion are going to change this guy's increasingly negative views about bicycling. For that matter, why are we forcing the unicycle on this guy? He's said he's planning on driving a car. Why don't we put him in a car driving course? (Possible Answer: His parents decided he should be in the unicycle course.)

Thing is, this student has no obvious motivation to learn unicycling (or even bicycling) beyond "you must know this". Whether the format of delivery is an online education system or a physical classroom, I don't see his personal motivations changing. Not without actual interactive feedback.

On the flip side, there is a way to adapt the current education system to Khan's methods, forcing our wayward student to become an 'A++' bicyclist. Fail him.

Don't let the student graduate from Grade 8 (or 7, or 5) until they've achieved whatever level of "mastery" that we require of them, because goodness knows, right now they're passing no matter what. But of course, we can't FAIL someone, because then they would get discouraged, and they'd end up separated from their peer group, and we'd be trampling on their personal interests that may have nothing to do with bicycles, and insert more arguments here.

So don't get me wrong, I'm not necessarily defending the current system either. But it seems like the message society gives these days is: "You can do whatever you want with your life! It's all about success! Oh, but you have to know Math and English." If we're looking for an analogy, perhaps what we're telling students is that they can make whatever cake they like out of life - but they have to incorporate THESE ingredients! (Allez Cuisine!)

So, do students absolutely HAVE to know math, or don't they? If they HAVE to, why can't we do it by sparking that personal motivation, rather than by forcing them to stay in school until they're 18, or forcing them to watch videos until they're blue in the face?

Back to the analogy.

2) Mental isn't Physical

Really clever, picking the bicycle. If we're talking times tables, maybe it works... I suppose you never really forget those. (Do you?) But consider that despite having a Bachelor of Mathematics, I am poor at finance. I've even wondered why I was never really taught much financial math when I was in high school.

Of course, I was. I even have the proof in the form of some of my old high school mathematics notes (complete with Star Trek characters doodled in the margins). But I forgot, because I wasn't really using it from day to day. So why did I forget that, but I still know how to ride my bike?

Scientists say that bicycling connects our brain to certain "motor skills". It's PHYSICAL, not mental. Mathematics isn't the same, at least not as we currently understand it. So just because I've "mastered" the Pythagorean Theorem in Grade 8 doesn't mean I'll realize how it applies when I'm finding the length of a line segment - assuming I haven't forgotten about that theorem completely over the intervening months.

"Mastering" a topic doesn't necessarily fill swiss cheese gaps. Those will develop over time anyway, which I'll remark on during my video. And if I wasn't interested in a zero exponent in the first place, being reminded of it an extra time is unlikely to help. Which brings me to one last thing about the analogy:

3) Assumes the Goal

A unicycle? Really? How many people are there that you know of who ride unicycles? They've learned about the bicycle, which is all that's really needed, right? Why are we forcing unicycles on them?

The answer, of course, is college and university. You don't get into a good university without knowing about the unicycle, never mind that only a select few actually apply that unicycle material after post-secondary. So gosh darn it, we're going to force this knowledge on you, so that you don't end up toiling away in a bicycle repair shop for the rest of your days! (Never mind that maybe you enjoy bicycle repair.)

And while you can tweak Khan's analogy to "tricycle" and "bicycle", the issue is the same... if a guy wants to drive cars*, and moreover he's really GOOD at that, and LOUSY at bicycling, why did he get signed up for the bicycle course?  Simply because if he doesn't know bicycling, he'll never succeed in life?

To sum up, I suppose my issues with the Khan Academy system are as follows. Again, bear in mind that I haven't seen it in action, this is only from what I've read:
 - The "one size fits all lecture" is still there, merely being presented "at the student's own pace", which removes important questioning.
 - The idea of "achieving mastery" can create unnecessary frustration, and ultimately seems to ignore the passage of time.
 - The huge repository of data being generated appears to shift the responsibility of learning from the student to the teacher.

Now, do I think Khan Academy has no use at all? Of course not! It's free content, and a central repository for knowledge - one of the main problems in today's society is that we're faced with too much choice. (Another TED Talk by Barry Schwartz (2005) goes into this quite well.) I've already indicated that strongly motivated students will probably profit. Moreover, as Khan himself said, he is getting feedback from teachers, and the system has been "teacher driven", with refinements being made as necessary.

I simply don't think it's the revolutionary educational model that we should adopt. At least not without a lot more investigation, which the public seems disinclined to do.

*Adapt the student's car analogy to be 'use a calculator' or 'hire an accountant', whatever suits you.


  1. The video approach seems to assume that every student learns the same way. Some students need to ask questions. Others will have questions that the video won't answer - who do they turn to?

    The analogy doesn't work, either. The unasked and unanswered question is "What does bicycle and unicycle riding have to do with what my future is?" There's no connection to other aspects of education or even careers. Needing unicycle to graduate seems silly when the student plans on going into a field that requires, say, snowboarding.

    I have run into this, though not through video education. High school English, for me, was an exercise in boredom. The same thing done every year; sometimes the book didn't change. And, like the student above, I was wondering why I needed English Lit prep when I wasn't planning on going that route in university. (Thanks to high school English, I avoided as many essay-driven courses as possible. From the analogy above, I avoided the bicycle and unicycle courses because I had enough of it in high school, and really needed more snowboarding.)

    You know what happens when a student is bored with a class? The student disengages and stops caring about the marks, even if the class is needed to graduate. This could even mean failing because the repetitive bicycle riding homework is seen as a waste of time. (Then the summer bicycle riding courses come and the homework is done during breaks. Another analogy failure, really.)

    Now, video education isn't necessarily a bad thing, but it should be used along with other means, not as a replacement. Learning styles are far too diverse to use a "one size fits all" approach.

  2. Things also fall apart when you ask whether Khan's videos begin to address what he claims the problem is.
    He says you get the "C" stamp and then get handed a unicycle.
    Isn't that exactly what his videos do?
    If you were having trouble making that left turn, then you should get instruction in left turns (and in looking first without swerving left).
    Khan's videos don't fill in gaps or clear up misconceptions. You're just supposed to practice more.
    That's the exact same spoonful of horrid medicine as "try harder," when what you're trying isn't working. I think of my schoolteacher swim coach's extremely valuable words: "practice makes permanent." All my practice and rewinding with my badly formed model hammer them in... and the videos tend to toss misconception-prone lessons in with the high frequency that procedural experts are prone to, because if you have *already* mastered a procedure, the exceptions are fascinating... but if you haven't, they convince you that really, this math stuff is too complicated and you don't even try to master it).

  3. Thanks for both your remarks... yeah, I haven't seen anything in the aftermath to really change my opinion. Though it seems Khan Academy has recently come out with some good ACTUAL interactive activities for Computer Science (according to others, I haven't had time to check myself).

    Agreed that you don't want to end up with a student who avoids the subject material. Agreed that you need to "try different" not "try harder". And interesting point about the exceptions, I hadn't considered that.