When I was taking my Montessori training, I had the honor of studying under Sister Anthonita Porta. I miss her a lot. All of these years later, I can still see her and hear her voice in my head. One of the lessons I remember most is justification.
When you are presenting a new activity that you have developed, can you justify its benefit? We live in a world where millions of lessons and activities are available at our fingertips on the Internet. That doesn't mean they are always appropriate. Make sure you have a good reason for using something that falls out of the traditional materials in the classroom.
The same is true for children when they are using materials. We teach process, not product. Sometimes, however, a child finds another way to use the material. Does that make it wrong? Not necessarily. This is when those observation skills come in handy. Watch how the child is interacting with the material. Is there some kind of learning going on? It will be obvious if the material is being handled in a destructive fashion. But sometimes, children can discover a new lesson within an older material that we have never thought of before. Perhaps it is being used in a way that makes sense to the child, to help her organize it in her own mind.
I wish I still had the picture of how one of my little girls was doing cards and counters one day. We teach the children to line up the numerals at the top of the rug. Counters are placed in a vertical line under each numeral. This child, though, did her work in a circle, almost as a spiral. She placed the 1 in the center of the rug, with one counter next to it. She placed the 2 on the other side of the counter and added two counters. This continued in a circle around the rug. Your first instinct is to show her how to lay it back out in the more linear style. After all, math is linear. As I thought about it more, though, this method of laying out the counters fit the child's thinking patterns, her personality, and how she operates in her daily life. She was still getting the concept of counting the quantities. She was just exploring a different way to look at them. She has also never repeated that layout again as she has worked with that material.
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