# Scott Young on Lectures

I follow a number of education writers and those who write about learning. One of these, Scott Young, is a high achieving recent graduate who seems to be making a living by giving learning advice. His latest claim to fame is his MIT Challenge where he studied a complete 4-year MIT course in one year as a way of learning new skills but also, presumably to prove the effectiveness of his methods.

My opinion is that some of the methods are debatable as they don’t foster really deep understanding of a topic, a number are just ways of quickly mastering the necessary ideas to pass an exam. As an example, in one of the key documents he uses to advertise his Learning on Steroids programme he shows how someone used his methods to learn the mathematical concept of limits. There is a scan on page 7 of the notes. The student writes in a section headed “What is a limit, REALLY?” that “A limit is like a stalker, forever getting close to the target. Forever trying to close the distance between it and the target, but rarely ever succeeds.”

This analogy is deeply flawed. Worse than that, leaving aside the word stalker, it is *precisely* what I have to stop students thinking a limit is. When I set an exam question on the definition of a limit, many students will give rather incoherent answers about “numbers getting close to other numbers but never quite reaching”.

However, what I want students to realize is that the limit of 0,0,0,0,0,0,… is 0, i.e., every element of the sequence is equal to the limit — the sequence doesn’t get closer and closer to the limit. Another good example is interweaving this sequence with 1/n. I.e.,

Can this really be said to be “forever getting close to the target”? Half the time it is equal to the target. A true understanding of the concept of limit

*requires*knowing that the sequence does not have to be getting closer and closer to the target.

Anyhow, having rubbished that bit of work, I don’t think it’s all bad, after all I do receive his newsletter and read his articles. Today’s newsletter has a link to an old post Why the Fuss Over Lectures?

Here I think he is only slightly off, as superficially it looks like he is damning video, rather than lectures in general, but in fact he is stating the important part of education. Videos, lectures and even books are no match for actually *doing* something. As he says:

If you’re serious about learning a subject, by all means watch some videos, but don’t make it your priority. Focus on getting to practice as soon as possible, since that’s where you’ll discover and fill the gaps that create a deep understanding.

Well Kevin,

I would have to say that your interpretation of Young’s methods are as flawed as the other student’s interpretation of limits. Two points here:

1) Young does explicitly say that coming to a rough understanding via analogy is just that rough. The analogies do break down.

2) On the specific analogy, a stalker can get closer and then fall back from the target, as in sequence 0,1/n,0,1/(n+1),0…

Hi!

Thanks for the comments. You are probably right that Young says that analogies break down – if he hadn’t I would have been complaining about that!

Regarding (2), I doubt many students would spontaneously imagine that as stalker behaviour.

My main reason for pointing out Young’s example is that I spend a lot of time encouraging my students away from using analogies when it comes limits because the analogies do break down so quickly and lead to serious misunderstandings. A large number of students use analogy as the means of answering the set exercises and in both the short run and long run it does not help. That raises the question of why do it. There are plenty of cases where reasoning by analogy is useful but I don’t think this is one of them. The subject of analysis grew out of the fact that using analogy and intuition give wrong or contradictory answers. One could argue that that is its reason for being!

Kevin