Take this puzzle for example.It's a definite favorite of the kids. If you haven't checked out the Melissa & Doug puzzles, they're awesome. We have 3 of the board puzzles like this one and 3 floor puzzles they make. Seriously, they're great puzzles.
Anyway Jeffrey approaches the puzzle in this manner. He first puts together the flag. Next comes the pirate under the flag and other pirates from there on. He will take pieces that he knows go together, even if they don't 'fit' into the board yet and place them where he thinks they would go. It's a very interesting method of working puzzles but he can prettily easily complete this one and it's 48 pieces.
Erin looks at the puzzle totally differently. She MUST start with the piece in the bottom left-hand corner. She then works across the bottom of the puzzle. When she finishes that row, it's back to the left and she puts in the next row. She will NOT go out of order. She will hold onto pieces, knowing where they go, but won't put them in until the gets to them in line. The biggest issue with this method is that if she can't find one certain piece the whole process comes to a stop. Even if she has other pieces she can easily fit in, she refuses to until she finds the 'missing' piece. Watching her work with the puzzles is really fascinating to me, but she always finishes them.
So two kids, raised by the same parents and their approaches to a simple problem are night and day. How cool it is to watch them learn and grow and turn into their own little thinkers.
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