Literary Math equals Math Literacy
Someone once referred to my list of "literary math books" as "the great list of literacy math books." Their twist on my descriptive term for our homemade approach reminded me of a book called Innumeracy, which is about the mathematical illiteracy of American culture generally -- and they made up their own term (or dug up some obscure term I was not familiar with) of innumeracy for that numerical form of illiteracy.
Looking back on it, I have tried to teach my children numeracy more than math per se. I think that is a very solid approach because, although I took 4 years of advanced math in school, I mostly remember the math concepts that I learned so many years ago, rather than all the formulas. And that has stood me in very good stead: I do extremely well in any class that is math-heavy -- the classes that MOST people tend to struggle with the most.
In the last year (as of April 2003), I have taken two more math-heavy classes (3 if you count my recent Environmental Economics class -- but I don't really count that). I took Intro to Hydrology last Spring Quarter. Hydrology is all mathematical modeling (how else do you 'see' the shape and flow of underground water?). I wound up tutoring many of my classmates through the math portion of it. Explaining so much of it helped me think through the concepts very thoroughly. It was one of the most Fun classes I have ever had and it was nice to finally really get to use all of that 'useless' math I learned in high school.
I also took a class in "GPS Data Sources for GIS". Most of the class was the theory behind how GPS works. The professor was a licensed Surveyor and knew more math than anyone else I have ever met. He could explain ANYTHING. And, since he was a surveyor, he had a View of geometry and Trig that was from the perspective of one of the points in a large Figure from sighting angles with surveying equipment and using geometry on a large scale to correct for places where there is an overhang or other obstacle and you just cannot get clear line of site to the satellites overhead, so you have to take two points nearby and calculate the correct position. This class called on every kind of math I have ever been exposed to -- even from when I used to calculate astrological charts as a hobby, a Zillion years ago (and, shhhh, don't tell anyone I am one of those weirdos that believes in astrology, as it does not jibe with my Respectable Math Geek reputation) because when you calculate a chart, you have to understand latitude, longitude, and the time-value of distance, as well as the Precession of the earth's wobbling axis.
I aced that class -- a class that gave many of my classmates Fits -- and got the extra credit on some test (or two) so my 'average' was 102 at the end of the summer. I also won a bet for 'lunch' with the professor when he made some mistake on the board while trying to explain something. I argued him to a stand-still and, being the most Brilliant and Solid Math Geek I have ever met, naturally, he had as much Confidence that he Was Right as I had. He got tired of arguing with me, he had erased and redrawn the example 2 or 3 times, insisting it had just gotten too complex and I was 'confused', and I kept saying, "I don't care. It is supposed to be a plus sign, not a minus sign. You have made a mistake right here." About 2 minutes after getting disgusted and saying "I will bet you Lunch.." he added said, almost as if to himself, "I feel a Lunch coming on" as it dawned on him that my numbers were the right ones. Afterwards, when he had a minute 'alone' (not in front of the entire class, but after a break when he could speak to me individually), he thanked me for keeping on him and not letting him get the entire class confused. He said "We would have been in a world of hurt, trying to undo the damage, if I got them turned around wrong at this point."
So, as an adult, I have had enormous fun discovering that math actually has real world uses: Surveying, statistics, hydrology, mathematical modeling, GIS, map-making, GPS, architecture (blue prints), calculating how much wallpaper to buy or how much paint, economics and on and on. It has all kinds of fascinating applications -- IF you have a solid enough grounding in it to do the Really Fun Stuff. And Calculus is about the time value of distance as well: it is the math with which you calculate the orbits of planets and other Functions, where you can plot points on an arc or parabola that "X will be here at Y time" and that kind of thing. The higher you go in science, the more math you have to understand. At some point, astronomy and the like involves a great deal of mathematical modeling and it gets blurred where 'science' ends and 'math' begins. They are intricately intertwined for such things.
My experience of real world math as an adult is what shapes my approach to teaching my kids. Memorizing formulas has done very little for me in the real world as an adult but have a strong conceptual foundation has never failed to be a real asset for me. I memorized my way through all kinds of math in high school and I was in my 30's before I discovered that there were actual uses for line-slope formulas and other seemingly Arcane bits of math knowledge that I had never had a use for. This big discovery came when took an introductory statistics class after we began homeschooling. That class was a turning point in my goals for my children: I decided that my oldest son really needed to understand the concepts first and he needed to know what the Point was.
I did two big things: I found a conceptual calculus book to hook him with his interest in Physics and I informed my kids that they had to learn math up through some algebra, but there really was no reason to pursue the usual sequence after that. I offered them statistics as an alternative to geometry and trigonometry that might have more relevance to their daily lives. They jumped at the chance and we have had a lot of fun.
Statistics is a blast to know a bit about, since you hear statistics quoted in the News and so forth so much more than you do, oh, Geometry or Trig. And the book "How to Lie with Statistics" is a great place to start thinking about how people with an agenda can manipulate the Facts and not really Lie but twist things around to say whatever they want you to 'hear'. It is Really eye-opening stuff. Something I think anybody who reads magazines or watches news or argues politics or.... generally Has A Life ought to have some familiarity with. Otherwise you are too vulnerable to being bamboozled by such 'lies'. Since they aren't actually Fallacious, they can be very hard to guard against if you don't understand why they don't hold water.
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