RE: Share your classroom ideas here

2017-04-30T22:15:53Z

My name is Natalija Budinski, and I am a math teacher in Primary and secondary school "Petro Kuzmjak" in Ruski Krstur in Serbia. I have become a Scientix ambassador in March 2017. In my opinion STEM is the future of education and I am giving my best to implement it as much as possible to my classes. Also, I am sharing my ideas with colleagues on my blog www.math4all4math.blogspot.com. There is one of the example how could Denis Guedj's book "Parrot Theorem" be applied in math classes in order to teach students the fundaments of mathematics, and open new frontiers to them, as well.
There is no doubt that Pythagoras and Euclid are two important figures of both, ancient and contemporary mathematics. The book describes many interesting facts about their lives, but also reveals that their teaching was approach similar to STEM principles. In the chapter dedicated to the Pythagoras, students can learn about the connection between fractions and music, or area and space object called lunule.
The main topic that I would teach my students following the book chapters would be irrational numbers. This real numbers troubled Pythagoras and during his time it was an unexplored topic. Besides the fact that the hypotenuse of right isosceles triangle is represented with square root of two, not much was known. The book describes the proof of the fact that the square root is an irrational number in the form of dialog, which is easy to follow and useful in the today classroom.
As the story in book develops, Euclid "tamed" irrational numbers. The Euclid's comprehensive work assembled in thirteen books called "Elements" is still relevant. Basics of Euclid's geometry are part of mathematical curriculums worldwide. Among many concepts that Elements elaborate, they provide the explanation how to find the square root of a number. Even though, Elements are rich well of mathematical concepts, they fail in solving problems such as doubling the cube or trisection of an angle.
Mr Ruche noted in the book: "Consider later three major problems of Greek mathematics, squaring the circle, doubling the cube and angle trisection". And later on, at the end of the book, mr Ruche officially announced that those problems are not solvable with compass and straightedge. That can lead lesson to the process of examining Euclidian geometry limitation.
Inspired by the book, I would tackle students with a question if the doubling the cube or trisection of an angle are really unsolvable? Or maybe there are solutions of three famous problems? The story developed in the book would be an excellent introduction to the contemporary mathematical research which provides the solution for mentioned unsolvable problems. What is more the solutions are elegant and can be followed with the high school- mathematical knowledge. They rely on origami techniques and paper folding. At the end of 20th century, origami was axiomatized which made him a mathematical discipline. What is more, origami axioms and theorems provided the solutions for problems of doubling the cube and angle trisection. That means that construction of third root of two became possible with origami.
On the one hand, Euclid's quotation in the book that "There are not royal road to mathematics", reminds us how sometimes mathematics can be hard, but on the other hand, there are interesting ways to explore mathematics. The "Parrot's theorem" led as through history of mathematics, but also opens the door for new enquires which can provide us with interesting lessons based on contemporary mathematical discoveries.

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RE: Share your classroom ideas here