Two teaching paradoxes

Is it possible to explain something too well? That is, something appears very clear to students after it is explained, so they don’t practice (or at least pay attention to their practice because they assume they already understand the topic), and then the lack of practice means they forget what was explained? I’m not meaning “they never learned it in the first place” but rather “they learned it so well that they forgot it because they assumed the memory was permanent”. (This is a slightly different issue than students who assume they learn something but really just keep their misconceptions.)

Are there circumstances where practice can actually lessen understanding; for example, when a student who learns a “trick” that works for an entire worksheet may attempt the same trick in circumstances where it doesn’t work? Thus it may be a bad idea at times to have a student practice a topic without all the special cases? (Specific example: suppose a student practices integer addition using only a positive with a negative number, but doesn’t attempting adding negative numbers with negative numbers until later. Will their earlier practice hinder their learning in the new situation?)

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4 Responses

  1. “s it possible to explain something too well? That is, something appears very clear to students after it is explained, so they don’t practice (or at least pay attention to their practice because they assume they already understand the topic), and then the lack of practice means they forget what was explained?”

    I have been looking at it from a different angle recently. Even though the “concept” might be clear, putting the concept to use is another story. That part can’t be explained, only guided. The student still has to take the steps.

    I think this is more of a question of what is the goal. What do we want the student to take with them. Personally, I wan’t them to have it all.

  2. I find your paradox arises all the time in too-cleverly-written graduate math texts.

    “Ahh yes, this all seems so easy, I can finish this whole chapter in one sitting.. and the next chapter too.. and.. oh wait.. crap, suddenly I’m totally lost and the last place I wasn’t lost was ten pages ago, what the heck?!”

  3. My mother is a huge advocate for gifted education and she said there are studies out there that says gifted students start unlearning when forced to do too much practice. I don’t know what the studies are (sorry!) but my experience as a 7th-12th grade math teacher backs this up I think. My brighter students get really bored when forced to do too much practice and they get sloppy. As they get sloppier, they start to practice bad habits instead of practicing the math. Personally, I like to introduce an idea in a lecture or self discovery format, then have them explore all the different variations on their own or in groups. I like the idea of having them understand what we’re talking about in class, but then having to think about it in a new way and play with it as homework. For some students of course I need to provide more drill and reinforcement but I think letting them explore all the variations immediately is the best way to go. Because your right- if you come back to a variation later, the original logic isn’t fresh anymore and they may misapply the older methods.

  4. Jason,

    When using a traditional lecture format, almost everything looks easy to the students. They passively follow each step we take in solving the problem on the board. They don’t understand there is a big difference between following an explanation of how to solve a problem, and actually taking the steps to solve it themselves, especially when the problem may not look quite the same as the example on the board. The only way I know how to help the students internalize what they have learned is to have them work problems for themselves or in small groups.

    This is especially true for my math anxious students. They have a tougher time with problem solving skills. They require plenty of practice in an environment where they can ask questions without being given the answer directly. Some of my anxious students do better practicing with one or two of their peers. Others want to slog it out alone, and even the slightest noise in the class is distracting. The bottom line is; explanation is not enough. Students have to do it for themselves before they truly learn.

    Thanks for the post – Tim

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