Data-driven instruction has become quite the buzz word in modern education.  In fact, in any of the teacher interviews I’ve sat in on, most prospective teachers mention this.  But when they mention using “data” to inform instruction, most of the time they see this data as quantitative–as numerical in nature–and that these numbers will be the only means through which they’ll develop their instruction.

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Something as simple as a wrong answer can be valuable data.

This, however, is not the case.

In fact, in many cases, this data comes in the form of misconception–misconception we don’t necessarily uncover through a score out of ten, but rather through anticipating the misconceptions and asking the appropriate questions to uncover them.

Recently, my class has been learning about health and wellness: we’ve recorded data from our diets, analyzed the data, and even burned certain foods in order to determine just how much energy is inside the foods we eat.  Naturally, I saw an opportunity for math instruction within this unit, specifically in the form of fractions.  Students have been able to look at portions of their diets in the context of their whole diet, specifically learning about the portions of their diet that should be in each of the four food groups.  In one lesson, in particular, a health and wellness specialist came in, and she taught us how to divide our plates into fractional pieces, showing that one-half of our diet should be green vegetables, while the other remaining fourths could be fruits, grains, and/or protein.  Knowing the average fourth-grade student, I posed the following question:

If I add one half, one fourth, and one fourth, how much do I have?

I was taken aback at how counterintuitive the child’s answer was, even with a visual staring back. But I was simultaneously unsurprised, as the child clearly lacked a conceptual understanding of fractions.  Three-tenths was the answer that I received, as opposed to one whole, and it was with this little misconception–with this invaluable piece of data–that I was able to tailor the lesson on the following Monday to that very misconception.

This visual is incredibly valuable in helping a student see his or her misconception.

Through posing this question, the children were able to identify the student’s method, which was simply adding up the numerators and denominators, respectively, to reach a new numerator and denominator for the sum.  In response, I was able to show them, using the very plates from the preceding Friday, that three-tenths of the plate was actually far less than the three pieces (the two one-fourth pieces and one-half piece) added together.  As a result, I was able to teach about the importance of common denominators when adding fractions.  Suddenly, because I had built on a misconception, the lesson not only had relevance; it had the inertia to carry the lesson through to a meaningful and resilient completion.

Oftentimes, we make the mistake of looking only for correct answers. In reality, though, a classroom full of correct answers is not a classroom at all: it’s a classroom of rote memorization and regurgitation.  Instead, the true power of teaching and the complex nature of synthesis hinges on the teacher’s ability to capitalize on errors.

In essence, a teacher’s artistry relies on misconception and the ability to turn something unknown into something known.

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