Tuesday, April 27, 2010

to reinforce or not to reinforce

Those who look to defend the practice of assigning homework in school quite often will use the automacity argument. That is, we want children to be able to know their times tables or spelling with a kind of automacity.

I have made the case before that perfection is not a desirable outcome, and now I wish to do the same for automacity. Like the pursuit of perfection, the pursuit of automacity is likely to paralyze rather than energize - and in the end sabatoge learning.

In The Homework Myth, Alfie Kohn explains nicely how sit-and-get-now-spit-and-forget should never be desirable inside or outside of the classroom:

Giving students homework that involves drill and practice is often said to "reinforce" the skills they've been taught in class. This verb is tossed around casually, as if it were sufficient to clinch the case. But what exactly is meant here? Unless it's assumed that practice is reinforcing by definition, one would have to demonstrate that good results are indeed likely to follow from mere repetition. And it's not at all clear that this is true, except under very limited circumstances. For example, it wouldn't make sense to say "Keep practicing until you understand" because practicing doesn't create understanding - just as giving kids a deadline doesn't teach time management skills. What makes sense, at least under certain conditions, is to say "Keep practicing until what you're doing becomes automatic." But what kinds of proficiencies lend themselves to this sort of improvement?
Think about that.

How do you practice an understanding?

It's one thing to say you want a child to practice their times table and be able to bark "36!" in response to the stimulus of "6 x 6", but it is quite another to say that you actually want the child to understand how 6 x 6 can or should equal 36.

Any math teacher who concerns themself with children understanding what is happening when they multiply two numbers will tell you that this process is anything but automatic.

To reinforce the behaviorial response may actually undermine efforts to construct meaning behind mindful learning.


  1. I am going to disagree this time. There is a value in the retention of basic math facts or measurement facts. Understanding is also important but understanding a basic concept does not insure retention. Establishing something like math facts in long term memory is. I use Math Makes Sense with my grade four and fives. It always begins with a conceptual exploration and we use them frequently. Manipulating arrays is one way to arrive at an understanding of 6X6 and its relationship to 2X3 and 1X6. It is worth the time, but two days later this activity may not connect when the simple math fact is presented. Drill and memorization -- simple repetition of experience -- is the answer. I do it in school and when parents ask for homework I mention practicing math facts as a useful activity when needed. Otherwise I encourage them to find a god book to read.

  2. Alan, unless I'm misunderstanding Joe, I don't think he's arguing against the memorization of math facts - just that understanding WHY they're facts is more essential to preparing students for real-life applications of those facts.

    Personally, and I'm thinking Joe probably agrees with me, I'd prefer times tables were learned more naturally. That doesn't mean memorization drills can't be used by students, but it should be the students' choice to memorize at all. I don't teach math, but as an example, students could do a market simulation, being split up into two groups - only a few vendors and the rest of the students would be buyers. Each buyer has a certain amount of each item they need (no more than 12) and each item could cost anywhere from $1 to $12. In this situation, if prices can't be modified by vendors (as they often can't in real life) and demand is much higher than supply is ready for, the students who can process orders most quickly will win the simulation by facilitating the most purchases. The students who can do this will naturally have their multiplication tables memorized. This simulation need only take 2-5 minutes, then other students could take a turn being vendors. As they learn more complex multiplication, the simulation could be made increasingly complex, with more realistic prices, like $14.99. At the end, students could reflect on what happened, and how the vendors can gain a competitive advantage in different situations. The students can learn a lot about economics this kind of simulation too.

    I think this non-forced, more natural kind of learning also helps us educators remember that memorizing information isn't the point - it's what you can do with it that's important. To pretentiously quote myself from a previous post, "it doesn’t make sense to have students memorize information in a textbook. The point isn’t memorization - it’s what you can do with that wealth of knowledge. Students should be allowed to just play the game of chemistry [for example] and use the textbook only when they need more information to solve a problem. If there’s information they keep needing when solving chemistry problems, they’ll be motivated to memorize it for their own benefit."

  3. Joe - what are you saying? Can it be a bit clearer?

    I liken practice with just that: practice. Like playing a piano. Drumming. Art, sketching. I never thought of "practice" being "understanding." I think that's where this conversation is murky.

    Call me old fashioned, but I still like Costa's and Bloom's. When we talk about levels of knowledge in my class, I give the analogy that all levels are important. For example, Level 1, Knowledge. You see a pretty girl in the cafeteria and you want to know her name. You're not going to be able to continue a relationship without it. I can imagine 18 years of marriage and I still don't know my husband's name, but have a deep understanding,evaluative, and creative connection with him.

    So - practice, to me, doesn't equal understanding.

    Practice is practice.

    Did I get it right? :)

  4. I have the same question as Kelly...I'm not sure what your intent is here. The term "homework" can mean many things. The idea of practice, from my perspective, is indisputable. Ask any athlete, musician, actor, painter, writer, etc. how they became proficient and confident at their craft. To be great, things need to become automatic. Great hockey players don't "think" about skating; great dancers don't "count" steps...they just do. Most adults don't "think" about driving...it's automatic...why? Experience (practice, repetition, etc.)

    Gladwell's "Outliers" has a whole chapter dedicated to the "10,000 Hour Rule" of practice. None of that implies "drill-and-kill" or rote memorization. Some things need to be memorized (i.e. what to do at a red light...can't take our time learning this).

    I don't disagree with the notion that we want kids to understand "why" 6x6 is 36, but that doesn't render the whole notion of practice or working at home irrelevant.

    There is a place for everything and the misuse of a strategy is not the strategy's fault. Practice will allow me to move to the deeper level of understanding...doesn't create it, but it opens the door. Again, if a hockey player has to think about skating then he/she will never move to a deeper understanding of the strategy, subtleties, and nuances of the game.

    For me, practice is a means (not an end)that allows the opportunity to go further and/or deeper.


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