The trouble with what you already know

One of the continual challenges of teaching — and in fact, I’d argue the single most important thing for teachers to master — is the ability to remember what it was like to not yet understand the material you’re presenting.

Believe it or not, there was a time when you yourself did not yet understand feudalism, or Laplace transforms, or the subjunctive mood. And now, there’s a whole group of students in front of who you are in that same boat. To successfully transfer knowledge to them, it is imperative to envision what’s inside their minds, not yours. What preconceptions are they likely to have? Which of the new terms are probably self-explanatory, and which are going to be counterintuitive when first heard? How is the new stuff similar to, but subtly different from, older concepts they’ve already mastered?

Luckily, this is more a matter of remembering than outright imagining, because you were once ignorant about the material yourself. So if you can just reeeeeach back to when you first encountered it, and summon to mind both the blind alleyways you went down and also the things that made it “click,” you have an excellent shot of leading learners through the same process.

Unfortunately this gets harder the longer ago you learned something, and the more deeply embedded it is in your present thinking. I can imagine the thoughts of a student who does not know how Stochastic Gradient Descent works because I only learned that myself a few years ago. It’s harder to imagine what it’s like to not know what variable type to choose, or why creating a subroutine is a good idea.

People have asked me, “what’s the hardest course you teach? Upper-level Machine Learning, Theory of Computation, AI?” My answer is always: “Nope, it’s CPSC 110,” our intro programming course for non-majors. Yes, the material is trivially easy for me. But that’s exactly why it’s the hardest to teach. It’s so hard to remember not already knowing it.

With two notable exceptions (shout-outs to Drs. Lilly Chen and Peter Varman) most of my other professors at Rice — supposedly one of the finest institutions in the world — were surprisingly bad at this. But that mischaracterizes the problem, actually. It wasn’t that they failed in trying to imagine the student’s mindset; it’s they didn’t realize they were supposed to do that. When I recall my undergraduate lectures, one general pattern dominates: professors were teaching material as though their students already knew it. They talked through the essentials of (say) the Rank-Nullity Theorem, saying nothing incorrect and yet not recognizing the great number of things that are bound to occur to new learners. If any of their peers had been sitting in on their lecture, they’d have been thinking, “Yep, yep, that’s the theorem all right, everything Dr. X is saying checks out.” But tragically, although the words were all true, Dr. X had omitted a great deal of what was essential for the learner to hear.

My theory on why this happens is as follows. When you first learn any topic, certain aspects of it are impenetrable because you have misconceptions, faulty assumptions, gaps in your background knowledge, etc. Learning is a matter of fighting through all those errors trying to get your mind to behold only what’s true. Now when you do reach this “truth” stage, it’s an understandable reaction to furiously push away all those mistaken ideas and rabbit-holes that you fell in along the way. After all, they’re what kept getting in the way of you finally reaching the truth. Better kill them dead, you think, so they don’t resurface and drag you back to a wrong way of thinking.

But those misunderstandings and bunny trails are precisely what a future learner is likely to also fall victim to. If you’ve forgotten them, you’ve mislaid your best tool to keep your students’ learning on course. Blazing the trail — calling out, “don’t head down this tempting path…I did that once and I can tell you it’s a dead end” — may be the most important thing a teacher does. We can’t hike for students, but we can help them learn where and where not to hike, speeding up their eventual arrival at the “truth.”

Something I find myself saying in class a lot is: “now when I first learned this, I thought X was true about it. But then I realized: ah, it’s actually not X, but Y that’s true (in some subtle but important way).” Not only do I think such a statement gives students confidence (since the teacher becomes more relatable to them, as a confessed fellow learner rather than a god) but it also helps prevent misunderstandings from sprouting, and it does so close to their root. Just as (or even just before) the student mentally steps down a seductive false path, you’re immediately redirecting them to the true road.

Here’s a technique I recently stumbled upon when prepping for the Bible study that I team-teach for the Chi Alpha student group at UMW. We’re studying 1 Peter this fall, a letter chock full of breathtakingly beautiful ideas…and big words. It occurred to me that before diving into the first chapter, we ought to prepare our minds by refreshing (or learning for the first time) what some of those words mean. My list of twenty key terms included things like apostle, exile, and foreknowledge. We took turns going around the room, each student choosing a term from the list and taking a shot at giving it a definition, which the group tried to improve on. Only after we thought we had nailed down all twenty did we go on to the text.

I have two observations about that experience. One is that I was surprised at which terms students knew down pat and which ones were iffy. I had put a few “gimmes” on the list (e.g., resurrection, trial) that I had included to help build confidence, but which actually revealed some widespread misconceptions. Others that I thought would be challenging (elect, sanctify) were slam dunks. My takeaway here is that the further you are from having learned the material yourself, the more likely you are to be dead wrong about what students will find challenging. And it behooves you to find out.

The other thing I noticed was how smooth the experience of actually reading the text was after this…and how many students came up to me afterwards and specifically cited the “vocab prep” exercise in helping their understanding. Having straightened out some fundamentals in advance helped them not get lost in the sauce as we read. And me knowing beforehand what I needed to emphasize, correct, or just let fly by was invaluable.

A disturbing thought I’ll leave you with is this. My thesis is that the more you know, and know well, the more difficulty you’ll have teaching effectively. If true, this would seem to imply that as an educator acquires more knowledge during her life, she’s inevitably handicapping herself. With each new thing she learns, she makes it more difficult to pass on her learning to others. Do you agree with this conundrum, and if so, what’s an educator to do?

— S


  1. Rae Avatar

    I have yet to teach crochet to someone who has adopted it as a hobby. Guess that makes me an expert, but not at teaching. haha

  2. Lauren Knight Avatar

    I’m curious what your thoughts on the “flipped classroom” approach are – the idea of having students read lecture material or a textbook chapter before coming to class for a lecture in which they are assumed to at least have a basic understanding of the topic of the day. I find that I learn best this way, but I’m sure not everyone does. And I also recognize that for many students, particularly those of college age, finding the motivation to keep on top of readings before each lecture is probably not easy.

    What you talked about with CPSC 110 is exactly where I found myself when I originally tried to learn the fundamentals of programming. I try to constantly tell my peers that I had *very* humble beginnings when I originally started, that I didn’t always have a natural talent for this stuff, and that I had to have an online friend hold my hand the entire time. There were three or more years there where literally every time I wanted to solve a problem using programming, I had to ask my friend for help. I can only imagine how daunting it is to learn how to program in a more academic setting where you are “punished” (via grades) for not understanding the curriculum right away, and where you’re limited to office hours and tutors for guidance. Knowing that newcomers have such a hard time is one of the reasons I’ve wanted to become a tutor for some time now, though actually finding the time in my schedule to make that happen has kept me from doing so.

    1. Lauren Knight Avatar

      And just to clarify, I learned the basics of programming back when I was a teenager.

      I ask about “flipped classroom” because that has been my approach to academia since at least my second or third semester at Germanna. I noticed that I did really well in Computer Science because I had preexisting knowledge on the subject through my hobby, then decided to try to apply the same idea to other subjects. Giving yourself a leg up by familiarizing yourself with the concepts of a class prior to taking them really helps in my experience.

      I didn’t realize this was an actual teaching method until I took my first French class. My professor would have us read our textbook and then come to class to practice what we learned.

    2. stephen Avatar

      I personally have had very little success with the flipped classroom method, especially when it involves reading before class (as opposed to watching videos before class). Part of the problem, I believe, is what you state: “finding the motivation to keep on top of readings.” (That’s a nice way to put it.) But an even bigger problem I’ve noticed over the past decade or so is that students’ reading comprehension has simply diminished. So even if they’re doing the readings, they’re often not getting out of them what they’re supposed to be getting. I’ve tried to carefully trim readings to where I’m assigning the shortest possible section to read, but that hasn’t really been effective either.

      My ancient Luddite self says: “kids these days were raised on multi-media, not text, and they just don’t have enough practice reading text and extracting the ideas from it.” How much that’s actually true, I don’t know for sure, but it does seem like it.

  3. Andrew Davies Avatar

    This sentence should be in bold 100 point font “It wasn’t that they failed in trying to imagine the student’s mindset; it’s they didn’t realize they were supposed to do that.”
    And as a pastor who sometimes teaches people how to preach teach I often say “Imagine that everyone in your congregation is in 6th grade, and none of them have heard one thing about your topic; then you’ll might reach them”.
    It’s also so important for a teacher to be able to think like this so that *they* don’t get stuck thinking they know everything about their subject. This is why it’s hard for paradigm shifts to happen in different fields of study: because no one continues to ask the simple questions (which allow for the shifts).
    Kudos to this article!

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