Pythagorean Relationship and the Romantic Understanding

Imaginative Education

Math is a class that I feel needs a boost of imagination and creativity. As I learn about Imaginative Education, applying the concepts to math is always at the forefront of my mind. My traditional method of “instruction, examples, practice, and correcting” is pretty effective, but except for the two or three kids who get joy out of solving number problems, the students are somewhat unmotivated and disengaged (other than earning a good mark). They don’t look forward to math class, and as a result, I don’t always look forward to teaching it.

When the time came to teach about the Pythagorean Relationship to my Grade 8’s, I decided to give the unit the Heroic Quality of scholarship and reverence. Pythagoras was a Greek scholar, whose teachings were so inspiring that a cult actually arose to apply his concepts to various aspects of life. While I certainly didn’t want to start a cult, I knew that 13 year olds are really into celebrities. If I could create even a fraction (math humour) of the fanaticism that Pythagoras’ ideas generated, it would make this unit about square roots and triangles more exciting.

Going back to the idea that I wanted to make teaching math more interesting for myself, I thought it would be fun to include some drama – I would figure out a costume and enter the classroom pretending to be Pythagoras himself. I would let them know that he was coming, and that they had to know the basics to be worthy of his presence. We would create posters and signs for him like the fans at sporting events and concerts. We would impress him that Canadian kids knew a lot about math, and ask him good questions.

The plan worked well, and they were more motivated during the classes leading up to the visit. I would use phrases like “Pythagoras is going to be pretty impressed that you can calculate squares in your head so quickly!” or “We have to make sure we’re worthy students for a mathematical genius like him to come.” The students were eager for ‘him’ to arrive, and were disappointed when today “was not yet the day” that Pythagoras was coming.

Once they knew the basic concepts of right triangles, hypotenuses, and how to calculate square numbers (2-3 classes), one day during recess I got dressed up in a Santa beard and Jedi robe from a previous Halloween. When Pythagoras entered the room, the kids were definitely the most interested in math class that I’ve ever seen.

We had lots of fun ‘getting to know each other.’ The students constantly tried to get me to break the 4th wall and admit that it was me (“Why are you wearing Mr. Derksen’s glasses?”), and I had just as much fun improvising answers in a horrible Greek accent (“Wonderful things! I ask same question to Mr. Derksen – what is this you wear on face? He say to see better. I say for 35 years I have trouble seeing. Mr. Derksen say I can use for today, since he is away.”) I also asked where the burnt sticks were for me to draw triangles on the floor, and how books worked. Even though it was a math unit, I was able to tie in a lot of Social Studies topics as well. Our Grade 8 Social Studies curriculum focuses on Ancient Times – Greece included. So it was nice to get some cross-curricular lessons in there.

When it was time for the students to hear the lesson, they were avid students, and were eager to learn how a2 + b2 = c2. They also got a kick when Pythagoras told them how dangerous it was to go around spouting this knowledge, for those in power might be upset they were learning about math and put them in prison – or worse. It made them feel a bit rebellious and like they had learned a great secret!

For the next few classes, we did practice questions and word problems. I made sure to humanize the problems – if Billy didn’t build the triangular roof with the right measurements, he would be fired. If James didn’t find the shortest pathway across the lake to be in time for his date with Jenny, she’d probably dump him.

All the while, I let them know that Pythagoras might be convinced to come back and declare them official followers, or Pythagoreans, if they proved themselves worthy. The groups made posters in the shapes of triangles and squares, and were prepared to cheer to make him feel welcome if they saw him again.

And so I donned the costume again, and passed noticeably by the classroom. They shouted for Pythagoras to come in again. He asked them more advanced questions – students worked together in groups to figure them out. If they got it right, he would give them his autograph on their notebooks. He decided that they were worthy to call themselves Pythagoreans, and bade them to spread the knowledge, since Canada was a wonderful place where they were free to do so.

The next time that I do this, I’d like to do a few more things. To bring out the ‘extreme’, it would fun to go into the school yard and measure out the biggest triangle we can fit, and then find the length of the hypotenuse. I’d also like the Grade 8’s to take their posters and go teach a grade 6 or 7 class about the theory, and tell them that someday, they too might meet Pythagoras.

A Summary of Cognitive Tool Use from the Romantic Understanding

Heroic Quality: Reverence & Scholarship

Humanizing of Meaning and Personification

Word Problems involved consequences for the ‘characters’ depending on failure or success.
Getting to know the difference between their modern culture and that of Ancient Greeks.

Change of Context and Role Play

Teacher dresses up as Pythagoras and interacts with students.

Extremes and Limits

Biggest triangle on the schoolyard.

Revolt and Idealism

That it was dangerous to spread ideas like the Pythagorean theorem.

Collections and Sets

Fan Posters for Pythagoras
Autographs