Having been disappointed with the lax curriculum of the American public school systems, I have begun to subject my kids to some extra math work at home. Nothing too grueling, but just enough to give them an edge, and perhaps spark some interest in that subject.
The other day, I had my third-grader fill in an entire multiplication table. Multiplication tables might seem draconian in today's computer driven age, but I think any person should at least know the basic one-digit multiplications by heart.
So as I sat her down to fill in the empty boxes of the table, I expected her to do a few and get frustrated fast. Instead, to my surprise, she breezed through the table in a few minutes and proudly called me to make an inspection.
I had no idea that she already knew her multiplications so well, but just before giving her my congratulatory kiss, she confessed the truth. In running the numbers, she had noticed a pattern of sequential number values and kept repeating it without paying attention to the actual digits being multiplied. For example for the "2" row, she would just write in the numbers, adding 2 sequentially, like 2, 4, 6, 8, 10, and so on.
This certainly wasn't the intended lesson, and she had seemingly cheated the system. But through it, I learned a lesson myself and that is, even for children there are a number of ways of solving a problem. Some solutions are easy, and some are hard. But as long as they are ethical, who am I to label the easy solutions cheating?