I am all for finding a way to explain quantitative concepts in a new way. However, it will be extremely difficult to avoid falling into the trap of "reinventing the wheel" if all we're talking about is coming up with a new set of symbols.
A certain recipe serves 3, but the cook is only cooking for 2, so she needs to 2/3 all of the ingredients. The recipe calls for 3/4 cup of flour. The cook measures out 3/4 cup of flour, spreads it into a circle on the counter, takes a 1/3 piece out of the circle and puts it back into the bag. That's 2/3 of 3/4.
Much easier to eyeball 1/3 when it's laid out in a rectangle as opposed to a circle. Author credibility -1
Did you just call the set of symbols evolved by mathematicians for thousands of years mindless? Credibility -2
Finally the two animated examples given are clever but not groundbreakingly clear. -3
It's a neat project but maybe you could think a little harder about defining your problem.
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.
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.
You've given him some arbitrary credibility rating of -3 because his examples weren't exactly how you would have done them, except that you didn't write them, he did. You contribution was to write some bitchy comment about it.
A mere incremental change isn't worth the hardship of giving up the status quo.