Saturday, November 22, 2014

Pythagorean theorem

The image below shows the use of Freobel's gift number 5 to demonstrate the validity of the Pythagorean Theorem, one of the foundational principles of mathematics. Most students are required to memorize it as
a^2 + b^2 = c^2\!\,  but without being taught its relationship to geometry as shown above. B squared is not just a number multiplied by itself but represents a shape.

In accounting, facility in the addition, subtraction and application of numbers is important. That is one side of math. In engineering, facility with shape is important. That is the side of mathematics that we tend to ignore in school but that can be applied in wood shop.

When I was taught the Pythagorean theorem, it was presented in a purely numeric form, completely divorced from the concept so well illustrated both above and below. Squared and cubed numbers as well as their roots were left dead for me, just as they are too often left for dead in today's math.

Froebel's gift number 5 as used to represent the Pythagorean theorem is shown below.

Make, fix and create...


  1. I don't see how blocks, on their own, provide much in the way of intuition about the Pythagorean theorem.

    Now, using a diagram, such as used by Socrates in "The Meno", to provide a proof of a simple form of the Pythagorean theorem, might provide some useful intuition. But I don't see how the blocks provide additional help.

  2. The blocks would only help if the students were encouraged to compare the numbers of the blocks in the related squares. You can take the squares a and b and reconfigure them in arrangements of equal size to c.