This is a follow up to our no more algebra article, where we criticize the way maths are currently taught. Here, we provide an example of a great math lesson and how it can spark interest in maths in mainstream kids (including girls), not just geeks.
The Pythagoras Theorem Revisited
In traditional US high school teaching, it's presented as a theorem totally out of context, and the focus is on doing repetitive, boring-to-death drill exercises. Here's how I would teach this subject:
*Lets start with the fundamental triangle with sides of length 3, 4 and 5 (whatever the unit is). How many right triangles have integer numbers for their length? Can you identify all of them (is there a finite of infinite numbers of such triangles)? Let's discuss units.
*Now let's focus on the right triangle with sides of length 1, 1 and SQRT(2): is SQRT(2) a rational number? How to disprove this fact? What is a non-constructive proof? How to approximate SQRT(2) by a simple iterative algorithm? How to boost convergence of this iterative algorithm? Obviously, a quantity such SQRT(2) can be represented using a compass and a ruler. But can the number Pi be?
*About 2,000 years ago, a Greek mathematician discovered that SQRT(2) can not be represented as a fraction of two integers. The mathematician in question was eventually murdered for revealing this secret.
Read all story at http://www.analyticbridge.com/profiles/blogs/how-maths-should-be-taught-in-high-school
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