5 ms·

Immediately means "without executing an entire algorithm".

• thaumasiotes 12y ago
  Perhaps, if the student had done some rote learning of algorithms, they wouldn't have come up with 1.5 at all.
  • nmrm 12y ago
    > if the student had done some rote learning of algorithms, they wouldn't have come up with 1.5 at all. When you see "7/12 is 1.5", is your first thought "one sec, let me calculate that and see if the answer is correct"? Or do you just know, without any computation, that the statement must be false? If you understand division, it's far easier to explain why this answer is wrong without appealing to an algorithm than by appealing to an algorithm. And besides, the very example we're discussing proves this isn't the case! The student was able to use the algorithm correctly; his error was at the boundaries of the standard algorithm -- correct input and interpreting output properly. Simply practicing arithmetic will not prevent you from ever making a silly (or not-so-silly) mistake. Rote practice of the algorithm without also acquiring an intuition for the meaning of division won't help. With correct guidance, practicing the algorithm can help students form this intuition, but that requires an a priori realization that we need to teach something other than just the rote algorithm, even if we teach it by discussing executions of the algorithm on specific inputs and outputs.