Tag Archives: pythagoras

#modphys 4/180: Geometry Practical

One of the new ideas I encountered through modeling is the practical summative assessment. It seems like a great idea to invigorate the learning process, make testing meaningful, and still maintain high expectations.

My grade 12 math class is doing a bit of review of geometry, and the Pythagorean theorem in particular, so I took them outside for an activity. I marked off a 14 m segment at the edge of a pavement. The students worked in groups to create a straight line that forms an angle of exactly 90 degrees from the edge of the pavement.

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The solution, of course, required the construction of a large right-angled triangle. The students used two 30 m measuring tapes to build the other two sides of the triangle. Activities like this require multiple hands — at least three students per group — which usually leads to one student taking over. Thus, I had the groups do this activity in a couple iterations, requiring rotation of responsibilities.

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I liked that I was able to tie in the etymology of geometry by giving some historical context: we were land surveyors on the Nile floodplains, calculating the Pharaoh’s taxes. I’ll try more assessments like this in the future.

Idea: Pythagoras Cult

As a math teacher, I’m all too familiar with the phenomenon of students learning, and then promptly forgetting, concepts and skills in maths. In fact, our system of teaching maths — revisiting the same concepts year after year after year — seems to be predicated on this very principle. It seems like such a waste of time, of energy, and of instructional headwind.

Thus, I’ve been wondering lately how math teachers can make the key concepts more “sticky”. I’m referring to Malcolm Gladwell’s popular book The Tipping Point, in which he analyses attempts to make key ideas “stick” in the minds of an audience (summary). The memorable example involves Sesame Street and Blue’s Clues, two American television shows that were designed to be “sticky”.

Sesame Street simplified and highlighted key concepts, used colourful muppets, and produced carefully-timed segments. Blue’s Clues, the successor, appears in shorter episodes, with simpler characters and purposefully abrupt dialogue that is designed to draw in the viewer.

Here’s my idea for making Pythagoras’s theorem sticky: Once a class has been introduced to the concept, and learned how to use the basic formula to solve simple problems, the teacher will host an initiation in which students are inducted into a secret society of Pythagoreans.

Pythagoras did, in fact, establish a sort of cult that was part school, part brotherhood (but inclusive of both genders*), and part religion. They were secretive, yet venerated mathematics. A famous tale about a student discovering the irrationality of the square root of 2 may help to illuminate the Pythagoreans, even if the story is invented.

The initiation ceremony should be secretive and it should require that students demonstrate a knowledge of Pythagoras’s theorem. I think it would also be great to make a web site for students to share Pythagorean artwork, proofs, and so forth.

This will be memorable, surely. If we ensure the maths takes center stage, it might also help students to form lastings understandings of this key concept.

* There is very little written record about the activities of Pythagoras and his followers. One clue comes from this description of Plotinus, a sort of academic leader who identified with both the Platonic and Pythagorean traditions, as recorded by Porphyry (source (line 9)):

Several women were greatly attached to him, amongst them Gemina, in whose house he lived, and her daughter, called Gemina, too, after the mother, and Amphiclea, the wife Ariston, son Iamblichus; all three devoted themselves assiduously to philosophy… Not a few men and women of position, on the approach of death, had left their boys and girls, with all their property, in his care, feeling that with Plotinus for guardian the children would be in holy hands. His house therefore was filled with lads [and] lasses…

If this is true, it’s a stunning reminder that the patriarchal inclinations of Western history were not absolute. Here’s some background about our developing understanding of gender role in ancient Greece.