Popsicle Pythagoras

Posted by James Rainey - 11 February, 2015

In a recent review of Theodore Sizer and Nancy Faust Sizer's The Students Are Watching, Randolph's own Adam Bernick observes that the authors "highlight the hypocrisy of 'the English teacher who insists that her students read fiction, but who never reads any herself... the social studies teacher who neither knows who the candidates are in a local election nor bothers to vote... the physical education teacher who is, whatever his or her age, grossly out of shape.'"

Well, what about the hypocrisy of a head of school who doesn't teach? I offer the following by way of redress.

Gather up ten popsicle sticks and ten toothpicks...01...and arrange them like so on two sheets of paper.02Let a represent the length of the toothpick and b represent the length of the popsicle stick. Note that the two large squares are equivalently sized with side lengths of a + b.03Now draw diagonal lines as depicted below to create four equally-sized triangles within each square. Let c represent the length of each diagonal line.04Shade the three interior squares.05You have just proved the Pythagorean Theorem. Do you see why?07As Mr. Bernick notes in his review, the Sizers also discuss the concept of "grappling" in their book. "Most teachers are fond of the word 'engagement,' because it means that the students are really taking an interest in the work that the teacher has designed for them. Grappling, however, goes one step further. It presumes that the student has something to add to the story. Either hypothetically or literally, the student is asked to join the struggle, to add his or her input."

grappleThere are many other simple proofs of the Pythagorean Theorem. President Garfield found one. Try to find one of your own. Grapple a little! That tiny and elegant equation is the basis of all trigonometry, which in turn has applications across any number of fields of human endeavor: astronomy, navigation, music theory, optics, pharmacy, chemistry, meteorology, architecture, economics, electrical engineering, probability theory — the list goes on. So many possibilities in a handful of popsicle sticks.

Topics: learning, play, SAIS, Faculty, grappling, Community of Learners, Pythagorean Theorem, "The Students Are Watching", trigonometry


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