Last week, my daughter Dana took the Algebra Regents Exam,
her first encounter with the Regents system. New York State has had state-set exams for high school academic subjects since my mother was in high school, and they are generally accepted rather matter-of-factly here, with little of the flap that seems to have accompanied the advent of state curricula and state testing elsewhere in the country.
Dana's right of passage got me thinking about my own encounter with the Algebra Regents, in June 1968, at Hamilton High School. Our teacher taught us methodically and conscientiously throughout the school year, and then spent about two weeks reviewing for the Regents. The last day of class, out of the blue, he announced that he was going to teach us one more thing, something that he hadn't taught us during the year.
This was, he explained, a skill that appeared every year on the Regents exam as a one point question. But, in his opinion, it wasn't worth learning. He recommended that we only learn this one last topic if we wanted to try for a perfect 100% score on the Algebra Regents. Otherwise, forget it.
With this introduction, he taught us how to take a square root by hand.
I, aiming for that perfect score, learned and practiced this arcane and painstaking technique. And, as he predicted, I promptly forgot it. He was right, it was a useless skill in the era of slide rules, and became even more useless as the years went by and calculators and computers became my constant companion.
But what did stick with me, and made a huge impression on me, was the notion that some things were more worth learning than others, that in fact some things might not be worth learning at all. This notion struck me as revolutionary, heretical, unpatriotic, insubordinate, an astonishing stance for an authority figure to take.
But now, I am in total agreement: for any given audience and content domain, some things ARE more worth learning than others. Prioritizing what is and is not worth knowing, understanding, and being able to do is the essence of setting learning goals, and setting strong, clear learning goals is the first step in good instructional design. The College Board's redesign of the Advance Placement science courses, and the National Research Council's committee on the framework for new science education standards are investing huge efforts in trying to figure out what to leave out to get away from the 'mile wide and an inch deep' syndrome that plagues so much of U.S. education.
If it's not worth teaching, it's not worth teaching well.
P.S. Just in case you're wondering, here is an explanation of how to calculate a square root by hand and why it works, from the U.S. National Institute of Standards and Technology, no less. It's rather like long division.
P.P.S. The Algebra Regents no longer includes calculating square roots by hand.
This post was editted by Jacob Cohen on Jun, 2017
My high school classmate, Jim Reynolds, reminds me that the name of the insightful algebra teacher was Ron Daniels, now deceased. Jim is a geology professor at Brevard College - www2.brevard.edu/reynoljh/ - additional evidence that upstate New York produces way more than its fair share of geologists per capita.
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