Comment Tutor's Perspective (Score 1) 1268
If I give a problem like:
f(x) = 2x + 7
g(x) = sqrt( f(x) )*5
Many students can solve this problem; a good portion of them just understand "oh, I do a substitution" - they don't understand fully that the equality of a variable with some expression is WHY their answer is correct. Similarly, something like: 3/15 = x/225 Most students get thsi right; "oh, I just cross-multiply" - but they don't understand WHY cross-multiplication is the correct thing to do. Teachers need to start teaching real math in addition to problem solving methods and heuristics.