Fran, Henderson & Pingry, and Me: A Tale of Problems vs Exercises

Barry Garelick, via email:

Fran, by Way of Introduction

My high school algebra 2 class which I had in the fall of 1964, was notable for a number of things. One was learning how to solve word problems. Another was a theory that most problems we encountered in algebra class could be solved with arithmetic. Yet another was a girl named Fran who I had a crush on.

Fran professed to not like algebra or the class we were in, and found word problems difficult. On a day I had occasion to talk to her, I tried to explain my theory that algebra was like arithmetic but easier. Admittedly, my theory had a bit more to go. She appeared to show some interest, but she wasn't interested. On another occasion I asked her to a football game, but she said she was washing her hair that day. Although Fran had long and beautiful black hair, and I wanted to believe that she had a careful and unrelenting schedule for washing it, I resigned myself to the fact that she would remain uninterested in me, algebra, and any theories about the subject.

My theory of arithmetic vs. algebra grew from a realization I had during that the problems that were difficult for me years ago when I was in elementary school were now incredibly easy using algebra. For example: $24 is 30% of what amount? In arithmetic this involved setting up a proportion while in algebra, it translated directly to 24 = 0.3x, thus skipping the set up of the ratio 24/30 = x/100. Similarly, it was now much easier to understand that an increase in cost by 25% of some amount could be represented as 1.25x. What had been problems before were now exercises; being able to express quantities algebraically made it obvious what was going on. It seemed I was on to something, but I wasn't quite sure what.

Posted by Jim Zellmer at October 17, 2011 5:10 AM
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