The course I took in math education methods was worse than useless.
Specifically, many education theorists hold that when students discover material for themselves, they learn it more deeply than when it is taught directly. In this vein, the prevailing belief in the education establishment is that although direct instruction is effective in helping students learn and use algorithms and mathematical procedures, it is ineffective in helping students develop mathematical thinking.
According to the establishment, students should be “led” to their discovery of the answers. Providing explicit instruction is considered to be “handing it to the student” and prevents them from “constructing their own knowledge.”