Dot Physics

I am sure I have talked about this stuff before, but it came up recently in a discussion so I figured I should put it here.

Let me draw a picture of learning.


The path of learning goes through the swamp of confusion. Suppose you are in a class and you are confused. This is good. If you are not confused, you are not going through the learning process.

All too often I see a student put their big toe in the swamp. It is icky, so they stop. Their thoughts are:

This can’t be the right way. I am sure I made a wrong turn somewhere. I can’t possibly go through this. If this IS indeed the way to go, I must be dumb or I wouldn’t be confused.

The only way you can get to the mountain peak of understanding without going through the swamp is if you already understood the idea. The real unfortunate thing is that students rarely see the swamp. Too many of their courses have a path that takes through a quick tour of the rose garden. Sure, it smells nice – but did you get anywhere?

I know, my analogy isn’t perfect. A student may say: “well, if the swamp is in the way, why don’t you just take me to the mountain in your helicopter?” In this case, I switch analogies. Can you become a better runner by riding really far in a car? Or do you have to run?


  1. #1 Ben
    February 4, 2010

    I know it is off topic but I was looking through your blogs for articles about roller coasters. A) Should one should wear spectacles (glasses) during a ride? There’s not just the acceleration forces but also the force of the air rushing by. B) Also would the forces be high enough to create medical injury?

  2. #2 Lorenzo
    February 4, 2010

    This really rings true with me. Unfortunately, all too often I find myself finally fully understanding a course or module I did a year or two ago and wishing I had the chance to go back and re-write the assignments. Alas, the swamp is often too big for the time it takes to reach the peak of the mountain of understanding….

  3. #3 Allison
    February 4, 2010

    What I love about your analogy is that I think all too often teachers think of students as either “got it” or “don’t got it” when really, there are true levels of understanding throughout the entire trip. Learning (or having acquired knowledge) is not a binary state as many would love.

  4. #4 Flavin
    February 4, 2010

    If a student asks about your helicopter, instead of switching to the running analogy you could respond, “We’re teaching you to be a mountain climber.”

  5. #5 Rhett Allain
    February 4, 2010


    Yes – that is a better analogy.

  6. #6 Rhett Allain
    February 4, 2010


    Really not sure about roller coasters. My off-the-wall guess would be that they should be safe. However, if you are interested in measuring the acceleration – check this out:

  7. #7 Phil
    February 9, 2010

    IMHO the problem is a bit deeper than you describe.

    The prospective student doesn’t know where your ‘mountain of understanding’ is, or even what it looks like. Their only learning strategy usually amounts to ‘keep struggling through the swamp & you will get there’. Sometimes it works (they get to foothills, and manage a passing grade), and sometimes not (they keep wandering, and fail).

    I’d also point out that if the only advice offered by your so-called guide is ‘if you are not stuck in the swamp, you are not learning’, then the student wouldn’t find the guide particularly useful. They’d just think you’re a bad guide, which isn’t particularly useful if you’re trying to get through to them.

    Given your expressed attitude, I think that it would be beneficial if you attempt to study something completely outside your area of expertise (and that you find boring), just to remind yourself what struggling towards the ‘mountain of understand’ feels like.

  8. #8 Gina
    February 10, 2010

    You’re probably right that it’s more complex. The journey through the Land of Confusion, in the best case, does include a guide person on the mountain. And, a good guide would be suited up, jumping up and down on the top of the mountain, shouting out helpful advice as to the next step (“watch out for that sinkhole to your left”, “there’s a nice foothold at 11 oclock”). But, a person COULD get through the swamp without a guide. Although, a student who has to journey through the swamp and up the mountain on his or her own may be so inefficient at it that by the time they get to top, they are mad and frustrated and may not appreciate the journey (and may not even realize they are in fact at the top).

    But, the most frustrating part for the guide (which I pretend to be in real life) is when the students ask “My shoes are getting dirty. Can you carry me?” There is a widespread misunderstanding that someone else can make the journey for them. Yet that just isn’t possible. The struggle IS the learning journey.

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