here’s part two:

https://www.artofmathematics.org/blogs/cvonrenesse/steven-strogatz-reflection-part-2 ]]>

that illustrated your “no gradient of confidence” situation perfectly.

it was his first exposure to “two-column proofs”

(presumably of the why-prove-anything-so-obvious

variety, but i don’t remember this much detail

and i promised a true story).

and (i paraphrase wildly) he wanted to know

—in the first line, we copy out the “Given”

part in the first column (as a statement)

and write “given” in the second (as a “reason”).

—so why can’t we just copy the “Prove” part

into the first column and write “prove” as

our “reason”?!

and he wasn’t kidding. he wanted to pass and was willing

to put up with being confused while he found out how.

i worked through quite a bit of the course with him that

semester and he *did* pass. this’ll have been my first

serious bite of the math-teacher bug. i don’t know if

he ever did get the *philosophy*… but he could crank

out some decent two-column proofs if they were

enough like the ones we practiced. thanks, “dave”!

(another great post, ben.)

]]>Here’s another thing.

1. prove, or see a proof of, the irrationality of root(2)

2. What about root(3) ?

3. What about root(2) + root(3) ? This is decidedly not obvious !

It surely does not have to be only geometry.

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