For years I have wanted to write a Mathematics curriculum for thinkers like me -- I love what is usually called the "Discovery Method" -- where the student discovers the entirety of the problem/solution their own selves.
So today, I made a 3 page handout of "everything you need to know in Algebra" because, yes, you can indeed put it on 2 to 3 pages. These things are just tools so that you can "do" math. I have another 3 page handout in the works for Geometry and another for Trig. Then I am going to depart from the beaten path -- I am going to ask the girls to discover mathematics.
Chaos and I got into a big discussion about the Greeks and how they "did" math without Arabic Numerals -- it's mind blowing how the Greeks did it. Math is so much more difficult when you can't use the numeral 6, but have to write out "six" every single time. How the heck did the ancients build what they built without the "tool" of Arabic numbers? We are going to use the traditional Euclidean tools of straight edge and compass and I am going to pull out my big box of Polydrons for them to use and explore.
I believe what is most lost in today's mathematics education is this sense of wonder -- and the fact that most ancient mathematicians looked to math as a way to explore God and Creation. Pythagoras once said something like this: "Mathematics is the ruler of form and idea and the cause of God and demons." He believed that to explore Mathematics is to explore the very nature of the Deity. He discovered the first tenets of today's theory of music as well -- he is the one who first discovered the relationships of ratio to pitch. He believed that all of creation is rational and was so despondent that the square root of 2 is indeed irrational that he committed suicide.
To quote Wikipedia:
One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an unseen characteristic that can be encountered by the study of mathematics.The pursuit of Math and Science initially is a pursuit to understand creation -- and thus to understand the mind of God. I want my kids to understand where math begins -- and wonder about how this universe works. So today we start -- who knows where it will lead?
Edited: Oooo.... I have to find "Donald Duck in Mathmagic Land" today!! Yeah! I think it's upstairs somewhere....
Edit number 2: This is so cool! What a wonderful website for this!