I teach high school math and science. Many of my students struggle. Two of them surprised me Friday with their "outside the box" thinking.
I gave the class a chart to complete about powers of ten, from ten-to-the-negative-fifth power to ten-to-the-positive-fifth power. For each power of ten they were to fill in the base, the exponent, how you say it, the fractional equivalent and the decimal equivalent, then look for patterns.
My two surprising students had both flunked algebra last semester, seldom if ever even trying to do the work. Both have behavioral challenges. They were in two different classes, so they definitely did not get their good idea from each other.
Evidently, neither of them listened to the direction where I told the class to stop filling out the "Fractional Representation" column when they got to positive powers of ten. So, each kept on going in the "Fractional Representation" column, but BOTH continued the pattern of putting one over the opposite of the (heretofore) negative power. BOTH looked at the (new) POSITIVE power of ten, realized that the opposite was the negative power, put it in the denominator and wrote a mathematically correct item.
WOW! Not only were they doing the work, they were thinking mathematically rather than guessing, and going beyond what I had explicitly taught. It doesn't get much better than this, folks.
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Of course I had to gush each time this happened, whooping happily and praising them. Each looked puzzled and astounded that a math teacher was gushing happily over their work. I hope it keeps on happening. I hope I didn't frighten them.
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P.S. A good podcast is "Is Algebra Necessary?," the Diane Rehm Show http://thedianerehmshow.org/shows/2012-08-29/algebra-necessary
Image credit: fotodesignjegg / 123RF Stock Photo
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