I remember to this day the lesson in primary school, when we first started solving word problems. It was sth like 3rd class. Teacher would ask simple question, like "how many apples we had to add to each chest, if there is 4 chests with 7 apples in each, and we need to have total of 32 apples". And kids had to "brainstorm" and translate that into mathemathic process and solve (not algebra, just "first we need to know how many apples we lack, so we substract, then we need to know how many apples per chest we lack, so we divide", we didn't knew algebra yet). If the question wasn't specific, the kid that pointed it out got praise for being observant, and teacher specified what he meant. Most kids liked that lesson, and there was fierce competition to be the first to guess. That was the moment I felt in love with math, before that I thought I'm more of a humanist (which meant it's OK I can't understand decimal fractions ;) ).
I think teaching kids to translate problem into math is very important, not only for math, but also if they want to be economists, computer programmers, etc. I cringe when I read that kids "know math, but don't know which equation to use to solve the problem". My wife taught math in secondary school for a while (in Poland, not USA, but we've recently had reform modeling our schools on those in "the West"). Many kids she taught had no idea how to translate word problem into math problem. They just pattern-matched keywords to equations. It's very sad, and I understand why they hate math - it must be completely frustrating to play this "guess the equation" game.
So - I think there should be more focus on teaching kids to understand the basic word problems, before they even know algebra. To be sure, that they understand when we need to substract x, and when we need to substract from x.
I think teaching kids to translate problem into math is very important, not only for math, but also if they want to be economists, computer programmers, etc. I cringe when I read that kids "know math, but don't know which equation to use to solve the problem". My wife taught math in secondary school for a while (in Poland, not USA, but we've recently had reform modeling our schools on those in "the West"). Many kids she taught had no idea how to translate word problem into math problem. They just pattern-matched keywords to equations. It's very sad, and I understand why they hate math - it must be completely frustrating to play this "guess the equation" game.
So - I think there should be more focus on teaching kids to understand the basic word problems, before they even know algebra. To be sure, that they understand when we need to substract x, and when we need to substract from x.