How many times have I thought that in the last 20 plus years of teaching? OK, not so many times in about the first 5 years because I really had no idea...but especially lately, I find myself thinking it sometimes. How many times do I have to show you how to factor? Why do you absolutely REFUSE to learn it? Maybe I'm just getting cranky : )
I hear it from my department members all the time - the PreCalc teacher says why didn't you guys teach trig well enough last year, the Algebra 2 teachers says why don't these kids know how to factor, the Geometry teacher says why don't these kids know how to simplify a radical, and the Algebra teacher says why didn't those teachers in junior high teach these kids how to work with fractions??
Well, we each know that we could do it better - if WE were only the ones teaching those kids the year before, they'd know all these things! Until you do...until you know you're the one that taught them the year before - you know you taught how to factor a difference of cubes, and then when it comes up in calculus they look at you like you have two heads! You know you had these same kids in geometry, but bring up the relationship between the sides of a 30, 60, 90 degree triangle and blank looks glaze over those otherwise smiling faces.
What to do - how to solve this problem? To be honest, I have had several foreign exchange students over the years, and it seems like they never forget. They never have any computational trouble whatsoever, ask them to factor - no problem, convenient values of trig functions - right there on the tip of their tongue.