life. faithful.

 It was Galileo who wrote something along the lines of, "Mathematics is the language God used to create the universe." Learning math, then, is a whole lot like learning the alphabet and basic grammar rules of a new language--you learn the symbols and how to combine them, what can go together and what can't, what interesting new sounds come from those combinations...all the basic mechanics that lie behind how the language functions. If that's where you leave it, the language  exists  for you, but it hasn't really come to life. The next step, to continue the story of mathematics as a language, is to take the alphabet and start to form words. This is the world of mathematic expressions. It's where we realize that if 3(2) means we have 3 groups of 2, we can extend that to say 3x means we have 3 groups of some unknown number, x. From there, it doesn't take much to move to 3t + 4.9t^2 telling us that we multiply some number by 3, then that same number is multipl...

  I had all my kids home this past weekend, which doesn't happen very often any more since two of them are in college. We got to have an easy day at home, which also doesn't happen very often. There was nothing planned, nothing any of us had to do. Nobody had basketball or homework or any of the typical things that take up our time in this season. Nathan got up early to go sit in the woods for a couple hours...he calls it hunting, but I think the main draw may be time in the quiet, away from a house full of teenagers! Those teenagers got to sleep in and get caught up on some much needed rest. When everyone was up, a couple of my kids started looking for something to eat. I told them to wait a few minutes and I would make breakfast. That's a pretty common occurrence when all of us are home, so they know that when I say I'm making breakfast it is usually going to be a "stick to your ribs" kind of meal. I didn't tell them what I had in mind, though--they just...