In Praise of Drill and Practice

May 26, 2010 at 10:15 am 15 comments

Last night, Barb and I went out to dinner with our two teens.  (The house interior is getting painted, so it was way easier than trying to eat in our kitchen.)  We got to talking about the last academic year.  Our eldest graduated from high school last week, with only one B in four years, including 7 AP classes.  (While I take pride in our son, I do recognize that kids’ IQ is most highly correlated with mothers’ IQ. I married well.) Our middle child was moping a bit about how hard it was going to be to follow in his footsteps, though she’s doing very well at that so far.

Since our middle child had just finished her freshman year, we asked the two of them which teachers we should steer our youngest toward or away from.  As they compared notes on their experiences, I asked about their biology teacher, Mrs. A.  I couldn’t believe the homework load that Mrs. A. sent home with the kids each night — almost all worksheets, fill-in-the-blank, drill-and-practice.  Sometimes, our middle child would have 300 questions to complete in a night!

Both our kids loved Mrs. A!  No, they didn’t love the worksheets, but they said that they really liked how the worksheets “drilled the material into our heads.”  “She’s such a great teacher!” they both said.  They went on to talk about topics in biology, using terms that I didn’t know.  Our middle child said that she’s looking forward to taking anatomy with Mrs. A, and and our eldest said that many of his friends took anatomy just to have Mrs. A again.

I was surprised.  My kids are pretty high-ability, and this messes with my notions of Aptitude-Treatment Interactions.  High ability kids value worksheets, simple drill-and-practice — what I used to call “drill-and-kill”?

On the other hand, their experience meshes with the “brain as muscle” notions that Carl Wieman talked about at SIGCSE.  They felt that they really learned from all that practice in the fundamentals, in the language and terms of the field.  Cognitive load researchers would point out that worksheets have low cognitive load, and once that material is learned, students can build on it in more sophisticated and interesting ways.  That’s definitely what I heard my kids doing, in some really interesting discussions about the latest biology findings, using language that I didn’t know.

I realized again that we don’t have (or at least, use) the equivalent of worksheets in computer science.  Mathematics have them, but my sense is that mathematics educators are still figuring out how to make them work well, in that worksheets have low cognitive load but it’s still hard getting to what we want students to learn about mathematics.  I suspect that computational worksheets would serve mathematics and computer science better than paper-based ones.  A computational worksheet could allow for dynamics, the “playing-out” of the answer to a fill-in-the-blank question.  Much of what we teach in introductory computer science is about dynamics: about how that loop plays out, about how program state is influenced and manipulated by a given process, about how different objects interact.  That could be taught (partially, the foundational ideas) in a worksheet form, but probably best where the dynamics could be made explicit.

Overall, though, my conversation with my kids about Mrs. A and her worksheets reminded me that we really don’t have much for CS learners before throwing them in front of a speeding interpreter or compiler.  A blank editor window is a mighty big fill-in-the-blank question. We need some low cognitive load starting materials, even for the high ability learners.

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Fear and anxiety over curricular change Teacher’s Materials, Family, and Hawaii

15 Comments Add your own

  • 1. Alan Kay  |  May 26, 2010 at 10:52 am

    Hi Mark,

    Let me put on my molecular biologist hat here for a minute.

    This is a tricky one, and many people have “parts and wholes” confusions regarding this.

    For example, there is a lot of practice required in learning to play music, and a lot of it is technique. But music is not primarily about technique, and getting tons of technique doesn’t guarantee good music. Similarly, there is a lot of problem solving in musical composition, but becoming a good problem solver doesn’t guarantee good compositional results.

    Biology started out as a descriptive field, and retained that character — especially for first courses, even in college — well into the 60s and beyond. (Meanwhile, the biochem of the 20th century and the elucidation of DNA in the 50s were turning the most important parts into something more like a physical science, with great emphasis on structure and dynamics.)

    However, Biology in K-12 continued to be taught as description, with lots of taxonomies and terms. It has been a favorite “first science course” because of this.

    In California, the elementary bio texts have doubled in size (because many of the new terms and descriptions have been added), but of the half dozen or so I sampled a few years ago, none of them actually tackled modern biology for what it is, and these courses are still taught early (they should be the last ones taught).

    Here are two questions to ask grade A bio-students and there teachers.

    1. What is an enzyme and how does it work?

    2. (If they can give a good account of this) How is it possible for an enzyme to “find” the fragments it needs to help put together? (There are 60 billion large molecules in a typical cell and the 3D location *and* orientation of the enzyme and the fragments have to be just right for the process to start — the probability that this can happen seems very low).

    (3. Similarly, the probabilities that evolution could work seem astronomically low. Is there a non-magical way that could allow it to work?)

    I have yet to find a student who has learned this in their biology class, or an 8th or 9th etc. grade teacher who can answer.

    By the way, the A students do know all the terms and some sentences (rather like a Catholic catechism) about the terms, but they clearly have no understanding of modern biology. If you look at the tests, they can answer these, because there are almost no process questions (hard to do with multiple choice).

    It’s not possible to understand modern biology unless you can understand how it works (what things are called is almost irrelevant).

    (Of course, this is too anecdotal to constitute a survey or generalization about your children or students in general.)

    And there’s no question that the real deal in Biology also requires a lot of studying and some serious drill, but the main knowledge and what you “drill on” is rather different than most people think.

    Cheers,

    Alan

    Reply
    • 2. Mark Guzdial  |  May 26, 2010 at 11:34 am

      Hi Alan,

      Why is it important for non-biologists to be able to answer those three questions? My kids and I are able to talk about new findings like Ventner’s new “artificial” cell (and why it’s really not an artificial “cell” though clearly a huge achievement). Maybe we don’t understand it like a biologist, but we have some understanding of what happened and why it’s important. Why isn’t that good enough, as informed citizens? We don’t believe in magic or myth. Recognizing that we don’t understand deeper levels isn’t the same as believing that it’s magic.

      Cheers,
      Mark

      Reply
      • 3. Alan Kay  |  May 26, 2010 at 1:17 pm

        Hi Mark,

        I think this is a very key issue — and things like it are why very little real science is being taught in the schools today.

        Knowing the word “enzyme” without having a sense of what it is and what it does, and how it does it, and why it can work at all is not modern knowledge. It might as well be some statement about any beliefs.

        But a good intuitive understanding iis completely within the range of all high school students (and all JS students). There is nothing tricky about it, except that changes in scale change a lot of gross behavior in our universe.

        And, understanding why evolution might be plausible, even though it seems implausible to commonsense, is much more the scientific route towards understanding anything, rather than the silliness (and the battle) of trying to teach “sentences as facts”.

        The keys here have to do with helping learners gain some sense of the “particle idea of matter”, and of their gross behaviors at the few angstroms level of measurement at room and body temperatures.

        These are part of every 5th or 6th grade science standards but they are not taught as science, don’t wind up understanding, even though it could hardly be simpler.

        A really good one for 10 year olds on up is to try to understand how a vacuum cleaner might work, and “why vacuums don’t suck!”.

        Plausibility experiments about particles and “heat as motion” can be done with a free particle system (such as StarLogo, Etoys Kedama, or NetLogo).

        These are part of the general set of ideas as to why chemistry works at all, etc. Why more heat speeds up chemical reactions, and mixing, etc. Why refrigerators keep food fresh, etc.

        After lots of these, we can talk about some of the actual numbers in Biology.

        For example, a medium sized enzyme (a protein molecule of ~5000 atoms) in an E. coli bacterium in your gut, is spinning at about 1,000,000 revolutions per second! (not minute!). Why? Because it is being bashed by other molecules, especially small water molecules which are traveling very fast.

        This same molecule is also moving its own size about every 2 nanoseconds. (Worth trying to visualize what this might be like if the atoms in the molecule were tennis balls, and the molecule is about the size of a VW).

        The big whammy here is that every large molecule of the 120 million in E. coli has an extremely high chance of touching any other molecule in less than 1/2 second despite that the interior of a cell is completely packed with matter! This plus the incredible rotational speed suddenly makes it very plausible that enzymes could actually work by matching surfaces to ingredients.

        This is not advanced biology, nor is there anything tricky about it. No differential equations. The only math is simple scaling. The experiments can easily be done by students programming a simple particle system. Etc.

        It is absolutely critical above all other things in modern biology to have one’s commonsense reshaped to have in one’s minds eye that everything small is jiggling incredibly!

        For example, why does a bacterium suddenly stop instead of coasting in water when it ceases to wave its flagellae? Because to a bacterium, the viscosity of water is essentially that of asphalt! The actual deceleration of a bacterium in water is about 1 million Gs! They are much stronger than we can imagine!

        Square-cube issues of scale can be approached by e.g. asking students why a grasshopper can jump 100 times its own length. Hint start with why gymnasts tend to be small. Look at how mass and area change with size (the strength of a muscle is proportional to its cross-sectional area, etc. so if you make a being 1/2 size you are reducing its strength by 1/4 but reducing its mass by 1/8, so it is proportionally much stronger, etc.)

        Ivan Sutherland used to ask these questions during PhD orals to see if the candidate could actually think about the world we live in, rather than just remember something they’ve been told.

        A really good one that kids love, is that you can drop a mouse from a plane and it will almost never be hurt when it hits the ground. Humans are almost always hurt, cats are right at the critical point, and often survive huge falls.

        What’s important here is *how* ideas(any ideas) can be thought about outside of commonsense and story like thinking.

        Why evolution could be plausible is really interesting and uses the above ideas plus two more simple ones. (And these can also be beautifully explored with a computer by 5th graders on up (this is what computers are good for)).

        Cheers,

        Alan

        Reply
    • 4. Mark Guzdial  |  May 26, 2010 at 11:44 am

      Hi Alan,

      One other comment: I don’t mean to sell Mrs A short. Worksheets aren’t all that she did. it’s what I saw in the evening, when my kids were working on them. Her classes were more interactive with a variety of activities. It’s that blend of approaches that I think is working there — using the drill-and-practice to learn concepts and language, which are then developed into working models through the classroom activities. That’s what I think we need to develop in computer science.

      I don’t know if my kids can answer those three questions. I’m not sure I can at a level that a biologist would find satisfactory. I’ll ask them, though.

      Cheers,
      Mark

      Reply
    • 5. Matt Glickman  |  May 27, 2010 at 9:52 pm

      Hi, Alan –

      I hesitate to range too far from the topic of the original post (and Mark’s wonderful blog), but I just have to ask: What are your “two more simple” ideas that explain how evolution could be plausible?

      My own take has been that the key is that beneficial mutations must continue to occur with sufficient frequency, which ultimately depends on the mapping from genotypic mutations/variation to phenotypic variation, which itself is subject to evolution (via CS “whammy #3” 🙂 ), which was the subject of my dissertation work.

      But given the other two ideas you’ve pointed to, I imagine your answer is more in the realm of biophysics, which I would really love to hear! (Just a pointer to further discussion elsewhere would be completely sufficient.)

      Tacking back toward the topic of this blog, I have to agree that evolution is exactly the kind of concept computers are ideal for illuminating, which is key because understanding fundamental ideas like evolution is likely critical for citizens to be able to participate in modern democratic society.

      Thanks very much in any case,
      –Matt

      Reply
      • 6. Alan Kay  |  May 28, 2010 at 9:35 am

        Hi Matt,

        One of the things I was trying to emphasize in these posts is that helping people gain a stronger “intuition” than commonsense, really makes a difference (this is the outlook change that science requires).

        So, just a sense of how things change when scale changes can lead to very good visualizations and guesses — for example, on the improbability or probability of chemistry, and especially the structural matchings needed for enzymes to do their thing.

        This is one of the many reasons I like particle systems on computers, because they allow “concrete thinking in the large” for beginners without having to resort to abstractions.

        For example, possible behaviors of gases (or disease vectors in epidemiology, diffusion, etc.) can be explored directly by young learners without having to do statistical reasoning (and this leads to the start of statistical intuition).

        A really fun one — that is extremely difficult for most students to understand in HS and college — is how buoyancy works (not that “things float”, but how and why). This can be gone at directly with just results from the macro world about gravity, collisions, and momentum transfer.

        And, similar to the examples in these comments, much of the case for evolution not being hopelessly improbable, does not require detailed understanding of biochem.

        One of the “powerful principles” is the difference between random, and “random plus a little memory”.

        For example, it is easy to make an Etoy that will “mutate” a random string of 27 letters one to N “mutations” at a time. There are 26 letters in the alphabet plus space, so the probability of making a target sentence is 27 to the 27th power, and even a fast computer doing a billion a second will take a *very* long time (children are amazed just how long … on the order of 10 to the 21st years — much longer than the estimates of the 10 to the 10th or 11th years age of our universe!).

        However, if we have just the tiniest bit of memory for “progress in our target direction”, then the difference is enormous (a simple Etoy to do this will take just a few minutes to “find” the target).

        This nice example is found in Dawkins’ “Blind Watchmaker” book, and Ted Kaehler and I have done quite a few versions of this over the years.

        So the powerful idea here is independent of Biology and works in many areas. For example, much of the simple navigation from bacteria on up consists of just the simplest memory of recent state plus quite random movements, but the result will climb most gradients found in nature.

        This is a kind of a ratchet that is set to go “forward” just a little more than “back”.

        The second idea here is that atoms are both “sticky” and “standoffish” — this provides both integrity of basic ingredients but also enough memory for making ratchets. Add violent heat motion and lots of experiments get done by nature.

        Biologists know that DNA gets quite chewed up just from being bashed by other molecules. There are quite a few of our enzymes whose job it is to make repairs. IIRC, this reduces our damage (mutation) rate by about a factor of 10 and provides much more stability for organisms and species.

        Experiments with an Etoy will show right away that the best mutation rate for “progress” is a low one. And so we should expect (and do find) that there are mechanisms that control this rate in nature.

        Cheers,

        Alan

        Reply
  • 7. Daniel Hickey  |  May 26, 2010 at 11:23 am

    We are struggling mightily in this very issue in my participatory assesment project. We are exploring the potential of open education resources and many of them are drill and practice computer-based tutorials. We abhor the idea of kids struggling in isolation on their own, and many of the embedded assessments are terrible. But from a situative view of leaning, they are an efficient way of helping a group of learners come up to speed the relevant specifics neeeded to naviate the “big ideas” that those specifics need to be grounded with. We are currently working with the Acid Base tutorial from the NSDL and have paired it with a simulation. More later after we pilot test their pairing and our using them in a more socially and conceptually anchored context.

    Reply
  • 8. Alfred Thompson  |  May 26, 2010 at 12:27 pm

    I was talking about something similar with a co-worker just yesterday. We were talking about learning resources for new proucts. All too often we supply a first example that is a small scale enterprise solution. A bit much for all but the most experienced professional to take in. There has to be something *between* learning the alphabit and writing your first novel. I seem to remember that in English there was. But do we have enough and small enough steps in computer science/programming? All too often probably not.

    Reply
  • 9. Hélène Martin  |  May 26, 2010 at 8:01 pm

    I’m going to punt entirely on Alan’s point about shallow knowledge. I think it’s a very interesting related issue but I have no idea how to address it in any meaningful way.

    I’d like to argue that there are folks doing what you describe as the key to Mrs. A’s success in computer science. My interpretation of what she’s doing that works is providing students with support and practice for all levels of knowledge and understanding necessary to succeed in her class (punting on whether that makes students successful biology students and on whether students would like her more or less without the worksheets).

    I think that the same way that Mrs. A ensures students are comfortable with basic vocabulary before asking them to apply biology concepts, we owe it to our students to provide early emphasis on computational building blocks rather than jumping straight to high degrees of abstraction. My favorite example: the general concept of iteration is baffling for lots of students and it’s an important tool for writing any sort of program. Instructors often shortchange students by casually presenting iteration as a syntactic element and then assuming its understanding. There’s too much going on in a simple loop to do that (or recursion or any other way of repeating stuff).

    I think tools like Coding Bat are the equivalent of our worksheets. In fact, I think working through small problems like those on Coding Bat on actual paper rather than with a computer has a lot of value, especially if students are talking to each other and their instructors to discover and address fundamental misconceptions. Also important is that students can’t get away with guessing and checking on paper.

    For some reason, lots of folks who teach CS have decided that students should be able to do something ‘sexy’ on day one. I don’t really understand that expectation, especially when it takes a long time to get to anything particularly compelling in most engineering disciplines, math, medicine, etc. I think it’s much more important to emphasize a solid grounding on valid mental models. What better way to retain and attract students than by making them feel successful and in control of what they are doing?

    Reply
  • 10. And here a miracle happens  |  May 27, 2010 at 7:03 am

    […] was reading a post by Mark Guzdial yesterday (In Praise of Drill and Practice) and was struck by this passage: […] we really don’t have much for CS learners before throwing […]

    Reply
  • 11. Sarita Yardi  |  May 27, 2010 at 9:50 am

    Do you think there’s something about time management and discipline here as well? The kids (and parents) I’m talking to seem to struggle intensely with basic time management and multi-tasking (much of their hw is on the computer and also online). The tasks and expectations are very clear in drill and kill and I wonder how much some kids actually *want* a bit of that when they’re surrounded by everything else.

    Some HS students say they’ll have a friend type random text as a new FB password and not give it to them until after finals to try to stay off. Self-regulation is hard for me let alone K-12. I would be interested what eldest and middle think about this. Especially middle. 😉

    Reply
  • […] was reading a post by Mark Guzdial yesterday (In Praise of Drill and Practice) and was struck by this passage: […] we really don’t have much for CS learners before throwing […]

    Reply
  • 13. Norcross schools  |  May 29, 2010 at 1:12 pm

    Love this discussion. My kids have been most responsive to teachers who had a balance of worksheets and higher cognitive exercises.

    Reply
  • […] was a completely different talk than his SIGCSE talk!  A point that I found interesting related to an earlier blog piece — he said that learning the language of the discipline (the specialized vocabulary) is key […]

    Reply
  • […] a lot of different kinds of learning activities — not just editing and running code (which I’ve been arguing for awhile is really important to support a range of abilities and motivations), but including editing and […]

    Reply

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