I've been focusing on graphs for my classes. All graphs. Euclid and Pythagoras would be proud with the amount of board space I have wasted on triangles, squares, and curves (oh my!). Pythagoras would be even prouder that I neglected to even bring up the irrational numbers in my lectures to my students. Those pesky numbers that cannot quite be written as ratios of two whole numbers. Oh, the humanity! And yet... for some reason... when a particularly frustrated poor girl asked me why these graphs made sense, I assumed that they had the same high school math experience I did. It all went downhill from there...
I filled an entire board with equations. Equations that were simple algebraic expressions. Equations with x's and a's and y's and b's, and slopes. All those frightening letters that any high school graduate would think could never be found in a proper math formula ("doesn't like... math just deal with... like... numbers..?"). I wasted twenty minutes, happily in my math world, showing that indeed taxes put a wedge in market prices, causing a decrease in supply and a decrease in demand. Showing that taxes on consumers would have the same effect as taxes on producers. Showing that consumer and producer surplus were areas of these triangles created in the graph. Showing what was so simple, pure, and beautiful in my mind. And having completed my "Fighting Temeraire" of equations I turned in triumph to my Principles and Micro class and with a flourish said, "THIS is why the graphs make sense!"
You can imagine their looks. I think absolute panic best describes it. "Isn't this a little intense for us?" the girl asked. y=mx+b is too intense for undergrads apparently...
As a great micro professor once said to me: "Never prove theorems to the peasants."
And as Alfred Marshall said: "(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often."
Dad gummit. Alfred Marshall is spinning in his grave.
1 comment:
In all honesty... I sympathize with the undergrads a bit. I may be a genius in the law and history related areas, but if I was in economics, my brain would just... well, leave. I barely understood what you said up there. And I've taken Income Tax law.
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