Day 16: Axioms > Memorization

This is was the library.  I think the books have escaped.

Six days to my birthday!

Today was a bitter cold morning.  Woke up to a blizzard warning, which turned out to mean a cold day with more wind.  Apparently the RealFeel (I want that to be even more absurd, like ReeeelFeelz or something, because this random misspelling / wordmash game of web 2.0 is pretty silly) was somewhere around -40º or -50º.  Which, I mean, is legitimately cold.

Teaching unit conversion to my test-prep class continues to be a success.  They're so used to things being harder that they seem perpetually surprised when it really is that easy.  It is so nice to be able to fix some of the things I see as horribly broken about the way we teach math to high schoolers.  We wait till college to teach so many smart things (like the simple method of unit conversion, or the matrix solution to a system of equations - which I'm considering throwing at one of my classes) and in retrospect you think "that's no harder than the ugly high school solution, why didn't we just start with the elegant one?".  So I'm teaching the elegant one wherever I can.  Less memorization, more axiomatic math.  If you can learn a rule that answers a question rather than memorizing all the answers to the typical forms that question appears in, that's so much better!

Speaking of, I continue to teach one of my classes how to add and subtract on a number line.  Similarly, many of them have learned addition as an "addition table" in their head rather than an understanding of how addition and subtraction move you around the number line.  I'm really trying to break them of that habit and have them work out the solution based on an understanding of the operation rather than consulting a table in their heads - it's easy to see when an error comes from trying to solve addition problems through memorization because you get wild errors.  If someone writes that 4+3 is 8, then they may have just counted wrong.  If they write that 12 - 3 is -15, they're trying to play the consult-the-table game, where the difference between "12 - 3" and "-12 - 3" is only one negative sign, as opposed to the number-line method where "12" and "-12" are 24 apart, thus an unlikely error.

One more class, today.  This class now has 2-variable equation solutions down.  I think I'm gonna give them a day of catch-up and catch-your-breath, then take them into the world of matrices.  Let's get the elegant multi-function matrix-solution down and then tackle the world with that under our belt!