You don't write all the out. I am describing the thought process. It is very quick in real time. And no, children who learn how to subtract by starting in the right hand column, and saying 0 minus 1, you can't do that, so go here, oh it is a 0, go to the 3.... cross out the 3...." do NOT necessarily quickly see the relationship between numbers. Because they don't HAVE to in order to use the algorithm. That's why people teach the algorithms... so kids can get the right answer without necessarily understanding what they are doing. And when they get a completely wrong answer, like off by an order of magnitude, they do not recognize how wrong they are. My favorite example is the 4th grader who couldn't remember the algorithm and added 46 + 27 and got 613. NO CLUE that it didn't make sense as an answer. |