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Monthly Archives: March 2014

Dear Friends,

Spring is here in Italy. In my attic room, I can hear the birds singing well-before the dawn. Their songs come through loud and clear, so I’m up with them in the early morning hours. There is still snow on the mountains, although the trees are flowering around these lowers hills. The world seems a beautiful and peaceful place.

This weekend I am finishing Botany Charts. This is the last set of required materials for the course. There are other materials and charts, of course, and these will fill out and complete the basics for an Elementary classroom. In fact, it seems that we could spend a life-time creating materials for the Elementary classroom because any subject area can be presented in a simple and clear way through images. It is left up to the teacher to create the things she will need for her class. We only make the essentials while on the course.

For some fun: the last few days we have begun looking at Montessori materials for the Pythagorean Theorem. Attached are images from the internet (Forgive me: my camera is on the fritz!). These are terribly exciting and wonderful materials and one of the signs, I think, that Montessori done correctly really is an education for life in a deeply intellectual way ~ while integrating the mind and body through sensorial exploration.

The Pythagorean Theorem states that given a right-angled triangle, the sum of the squares formed on the short legs equals the square formed on the hypotenuse. Simple and not too hard at all really! What makes it special, and doubly special for children, are the clear and reasoned steps to arrive at that conclusion.

Pythagoras Material

Montessori devised three materials that help children to explore the proof.  The first is sensorial exploration: the triangles are simply exchanged and viola! it’s obvious that the large square contains the smaller because the triangles fit. The second material is considered and arithmetical proof. The little squares (remember, area is measured by square) fit into the large square. This is also quite easy and rather fun.

Euclid’s proof requires a little more reasoning. We have to know that any triangle is equal to 1/2 the square that has the same base and height. This makes up the ‘middle term’ and hence an essential part of the proof.

EuclidI47a

Next week we will practice with this material a little more and I will show you some more steps. Remember, this work if for children around the age of 9 or 10, or even a little younger!