"Much easier to eyeball 1/3 when it's laid out in a rectangle as opposed to a circle."
Maybe for you, but certainly not for me, and I'm guessing most bakers would agree with me. Bakers are used to circles because of pies. I can eyeball a third of a circle, but I'd have trouble eyeballing a third of a rectangle that I couldn't fold.
Further, the baker often works by feel, so an exact is not needed in these circumstances.
"Did you just call the set of symbols evolved by mathematicians for thousands of years mindless?"
Perhaps a better word would have been arbitrary, but there's no fundamental reason we pick y=mx+b. Y, M, X, and B are picked arbitrarily, and we do pick them without questioning whether these are optimal for initial learning.
I grokked math as a kid, but it was precisely because I was able to make the leap that the language of math was arbitrary and substitutable while other kids were stuck not understanding the meaning.
I grokked math as a kid, but it was precisely because I was able to make the leap that the language of math was arbitrary and substitutable while other kids were stuck not understanding the meaning.
Then we need to teach them that, not a new set of symbols. Again, I think the crucial insight here which you uncovered is that people are distracted/confused by the symbology, perhaps trying to take everything too literally.
By the way, the way to "eyeball" a third is to use your two hands (rotate them so palms facing each other) to divide into sections A B and C; since we can very accurately eyeball a 50/50 split, you simply compare A to B and B to C, then adjust your hands until A=B and B=C. Bam, you have thirds. Once you get good at this you just mentally visualize invisible dividers instead of actually using your hands.
When it comes to a circle, if you are staring at pies all day then maybe you are better than average, but many studies have shown that humans are horrible at discerning angles other than 180 and 90 degrees.
Maybe for you, but certainly not for me, and I'm guessing most bakers would agree with me. Bakers are used to circles because of pies. I can eyeball a third of a circle, but I'd have trouble eyeballing a third of a rectangle that I couldn't fold.
Further, the baker often works by feel, so an exact is not needed in these circumstances.
"Did you just call the set of symbols evolved by mathematicians for thousands of years mindless?"
Perhaps a better word would have been arbitrary, but there's no fundamental reason we pick y=mx+b. Y, M, X, and B are picked arbitrarily, and we do pick them without questioning whether these are optimal for initial learning.
I grokked math as a kid, but it was precisely because I was able to make the leap that the language of math was arbitrary and substitutable while other kids were stuck not understanding the meaning.