> ...But you shouldn't be bound by arbitrary rules. Algebra is important, but if you find "x" by doing something other than some arbitrary thing where you subtract both sides, etc., you shouldn't get an F in the class.
In middle school at least this kind of thing was allowed as long as we could show why what we did worked. The idea being that we would have to understand what we did in order to know either when it would work or when it would fail so that we could apply it correctly. If we could do that we weren't given full credit for anything because the homework/tests were meant to check that we understood how to get the correct answer (other than copying from the nerds like me).
In middle school at least this kind of thing was allowed as long as we could show why what we did worked. The idea being that we would have to understand what we did in order to know either when it would work or when it would fail so that we could apply it correctly. If we could do that we weren't given full credit for anything because the homework/tests were meant to check that we understood how to get the correct answer (other than copying from the nerds like me).