Rules and tools

I was helping an 8 year-old with a math problem the other day.  It looked like this:

She pointed to Luke’s pencil and said “Well, it’s not this one because you aren’t supposed to start in the middle of the ruler.” She then proceeded to try to convince herself in various ways that one of the others (besides Luke’s and Nate’s) was right.

It’s possible that no one actually told her “you aren’t supposed to.”  Someone is more likely to have said “don’t,” by which that person meant “it’s easier math-wise to do it this way.”

But we don’t tend to say things that way.  We tend, in the interest of simplicity, we imagine, to say things like “don’t” and “you should” and so kids get into the habit of turning our words into rules.  Rules that in cases like this make tools (like rulers) more difficult to use.  Every time we tell kids how to do something rather than telling them it’s how we do it, we train them to hear things as rules.  It keeps them from investigating, and then they not only get stuff wrong on tests, they don’t learn how the stuff really works.

In the case of the ruler, if kids have the chance to notice that when you don’t start at zero you have to account for the extra space between zero and the beginning of whatever you’re measuring, they get to realize what the ruler’s actually doing. Rather than feeling, as many of them do, as though the ruler is  just another mystery invented by the adults, and their only chance of survival in the world of adult rules is to do as we say and hope they don’t forget one of the rules.  When they’ve had the chance to explore and really come to understand, they’re less likely to panic if one day a test question comes along, asking them to, like this one did, really notice and account for length. Not to mention that often in the course of real life activity (sewing, building, decorating), it’s actually easier to pinch a measuring tape at, say, two and 14 and hold the resulting 12 inches where you want them than it is to try to anchor the awkward zero end of the tape, and stop at the 12.

One way to help kids find their way to the kind of understanding that will allow them to use tools and knowledge effectively and comfortably is to acknowledge that when we show them how to do things, we’re really just showing them how we do things.


4 Responses

  1. Nicely said, as usual! The first thought I had, however, looking at the pencil, is that a child with a brain like my son’s would be going through a thought process that looks something like this: “Mmm, should i include the eraser or not? ‘Cause a pencil is not an eraser….so maybe they’re really asking about just the pencil, so maybe I’d better subtract the eraser.” So then, 15 minutes later, he’d arrive at the “wrong” answer.

    • Indeed, so many of the great thinkers get hung up in the way you describe. I think it’s a great argument for revealing to kids the mechanism of test creation and how question-makers might be thinking. While much of the test-oriented teaching that goes on in schools now gets in the way of the deeper understanding and powerful learning we’d like kids to have access to, if we’re going to ask kids to take these tests at all, we do them a disservice if we don’t teach them how to, among other things, anticipate the intentions of a question. Such that it’s possible for kids to look at a question like this one and think what your son might but then also something like “This is an achievement test, not a tricky problem-solving test, so whoever wrote this question probably just wants to know if I know how to measure from one end of something to the other; I’ll answer accordingly.”
      This kind of helpful (and potentially quick) test *training* often gets thrown out with the bathwater of *teaching to the test.* We’re a long way, sadly, from valuing and tapping the kind of deep analysis you’re describing in your son. Until we get there, or even closer, we’ll be wise (and kind) to let them in on what’s behind the scenes so they can make educated choices about how they interact with what’s visible.

  2. I know your point wasn’t really about the rulers, but I have a very specific example of how this has affected my students. I teach chemistry at SMCC and in order to properly use a graduated pipet, students need to be able to basically measure in the middle of the ruler as shown above because the tip isn’t a specific quantity – so if you want 5 ml, you have to fill to 6 ml and release to 1 ml (or 7 to 2, etc.). At least once semester, someone is confused and I need to sit down and teach them the concept. It isn’t that they don’t know how to subtract or use a ruler, it’s just that the “rule” is so ingrained that they can’t think (solve problems) beyond it! Anyway, I just thought it was interesting how teaching the “rule”, but not the concept of increments has actually come up with my adult students…

    • Thanks so much for adding that, Jen. It’s been a long time since I spent any time with pipets, or maybe I’d have thought to use them as an example! It’s the perfect illustration, though of course the confusion is unfortunate for your students…

Comments are closed.