## Comment Tutor's Perspective (Score 1) 1268

As a high school math tutor for one of the large national test prep companies, I can say with complete certainty that even when the "box" is replaced with a variable name, students still do this. I find that it's not so much that they don't grasp that the = symbol means equality as much as that they don't realize what equality means.

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.

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.