I think we really need to start teaching people paying attention to units. Even in math classes.
1/3 + 1/3 is not a correct mathematical description of the problem.
1/3 [students at table A] + 1/3 [students at table B] is.
Let's shorten this to: 1/3 sTA + 1/3 sTB. Then, you factor out the 1/3, to get: 1/3 * (sTA + sTB). And now it's it's impossible to give the wrong answer "2/3".
Or, in other words, it's best to "keep your attention on what the whole is" by keeping it explicitly written out in the equation.
Units is a real eye opener once you do it right. I remember when i studied and could almost verify what I did was correct, I would just check if the resulting unit was what I expected
1/3 + 1/3 is not a correct mathematical description of the problem.
1/3 [students at table A] + 1/3 [students at table B] is.
Let's shorten this to: 1/3 sTA + 1/3 sTB. Then, you factor out the 1/3, to get: 1/3 * (sTA + sTB). And now it's it's impossible to give the wrong answer "2/3".
Or, in other words, it's best to "keep your attention on what the whole is" by keeping it explicitly written out in the equation.