## Assessment… it’s all in the tone of the voice

*February 26, 2008 at 5:01 am* *
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DARIO is one of my outgoing, great-fun students. Fabulous and generous sense of humor, and a little loud and a little mischievous with it. Dario is fun to work with. He also enjoys his math, works hard at it and wants to get it.

Dario was frowning as he tried to follow just why ^{1}/_{x−18} is equivalent to x^{18}.

We reviewed that x^{−18} is the same as ^{1}/_{x18}. So, ^{1}/_{x−18} was the same as 1 being divided by the fraction ^{1}/_{x18}.

As earlier lessons had focused on the laws of exponents, I tried a different tack… thinking about 1 divided by ^{1}/_{4}. We drew a pizza cut into four and talked about the quarters and how four of them made up the whole pizza, and how that was like division, that ^{1}/_{4} divided into a whole pizza four times. We talked about the pattern that seemed to be there, that the denominator of ^{1}/_{4}, became the numerator in the answer 4.

Clearly my flounderings were not helping Dario construct any meaning around all this. Everything screamed that he just couldn’t see it, did not get it. There was no light bulb flashing, or even, about to flicker. But Dario looked at the accumulated doodles and said slowly, “Oh, I get it.” I clapped him on the back and said words to the effect, “I don’t think so Dario, but don’t worry, you will.”

Dario’s friend, Joe pushes across the his work to solve 125^{2x + 4} = 25. Joe is more quiet than Dario.

Dario looks to Joe for help, but also asks probing questions. Dario doesn’t just want the answer, he does want the why behind the answer.

Joe laughs at Dario’s jokes… particularly if they’re good naturedly at the expense of the teacher.

I look at Joe’s work and start to venture that “the exponent…” But before I can get any further the paper has gone and Joe quickly says, “Oh, I get it” and smiles. The work comes straight back, the exponent corrected.

Assessment isn’t right or wrong answers in a test. It’s all in the tone of the voice.

Entry filed under: Assessment + Grading, Thoughts from the classroom, What's on the PiFactory blog.... Tags: Assessment + Grading, formative assessment, grades, grading, math classroom, Pedagogy, summative assessment.

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