Wednesday, November 18, 2009

On the Binomial and Trinomial cubes, or, Finding the Beauty in Math.

To say that I have always had a love/hate relationship with math would be an understatement. As soon as it began to move towards abstraction, I froze. I clammed up. I enjoyed basic algebra, I can admit--but when it came to geometry, or graphing...calculus, trigonometry....I even remember *distinctly* my brother trying to teach me long division, and sitting down again before college to try to memorize my multiplication tables. Sure, I knew how to multiply--but to do it by memory? Fat chance, if the number didn't happen to be 7 or 9.

You see, it wasn't that anyone ever told me that I *couldn't* do math...or at least, I don't remember that. I took remedial classes briefly in reading, and then instantly excelled. "Language Arts" was the highlight of my day in elementary. I fell in love with self-expression and all of the outlets there were for me. That love NEVER developed for math, though. After awhile, it was just so hard that I started telling myself, blankly, that I was stupid and I just couldn't do it. They just jumbled together. The signs didn't make sense. There was one correct answer, but a million ways to do the problem, and everyone I seemed to find was incorrect.


These last two week, my classmates and I have received presentations on the various boxes of constructive triangles, and finally, the binomial and trinomial cube.

I cried.

I *got* it. I saw in the triangles, squares, cubes, the basics of geometry that no AMOUNT of writing formulae had ever given me. I could feel it--the tactile difference, the way the shapes fit together, broke down into other shapes and forms, how they complimented each other. They were beautiful.

...I got it.

This is what I will be offering to children. At 3 years old, when it's all just a puzzle, the absorbent mind takes note of all of the shapes and their relationship to one another. Years later, when looking at a hexagon on the SATs and thinking "How do I figure out the area?", they will have the physical knowledge of having held in their hand the 6 obtuse-angled isosceles triangles that compose it, and they will know what L x H means, because they were taught "Height" of a triangle when they were so young.

Before they ever have to make SENSE of tests, or formulas, they are given an idea to abstract--and the opportunity to fall in love with a concrete representation of a concept they will continue to deal with the rest of their lives. I finally understand why it seemed so natural for so many of the Montessori students I watched joyfully engaged in Math.

They knew it with their hands, and because of that, they knew it in their hearts.