Lately, I've been hearing a lot about kids who "just know" an answer to a problem and don't know how they got it. I must say, at first I felt a bit perplexed. In all my years of teaching and tutoring, I have never come across a single student who "just knew" an answer consistently and couldn't show work. Even if they began by saying that they didn't know how they knew, we could always tease out the line of thinking that led to their answer. What I believe, then, is that it's not okay to become complacent with these very intuitive kids. Showing work for marks is not necessarily a goal for everyone, but being able to communicate thoughts is an important step in learning. Yes, communication is necessary for the sharing of ideas that leads to piggybacking and synergy. More importantly, though, successful communication ensures that a child will understand that their mathematical ideas are valuable, that their logic is valid, that they are capable of "doing math."
Continued...
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