“I want to make this clear what ever instruction is necessary must be given. We are guided by the children’s development. So when we say ‘follow the child’ I do not suppose the child to be a responsible being able to tell us what they should do, what I mean is; the child possesses characteristics which serve as our guide in giving instruction according to their developmental stage.”
- Maria Montessori, AMS Triangle Magazine 1946/or 1947 (located via internet)
What happened to follow the child in the political correctness of giving the lesson the absolutely right way? What happened to scaffolding and the concept of the zone of proximal development? The idea that there is a place between what you know and what you don't know that is ideal for learning, particularly if it is structured to provide just the ideal amount of support. This makes sense - nothing too easy and nothing so challenging as to be impossible or perpetually frustrating.
These concepts are inherent in Montessori philosophy. The materials are designed to move from one to the next in a progression of concepts, building confidence and support as needed. They aren't perfect though. Sometimes a child just isn't interested in the "right" material, sometimes it needs to be demonstrated in a different way. Sometimes... whatever.
The Hundred Board.
In my training, I learned a presentation method where each group of ten numbers was in it's own box and the child worked with ten numbers at a time. There was no control chart. They learned how to carefully put it away for the next child.
At the next school that I worked with the child had the option of working on a hundred board that was preprinted as a matching or a blank board. They also had the option of completing a paper extension. (In that school it seemed as if the paper extension was the true goal of the children!)
I've heard and seen of schools where the hundred board had all 100 tiles in a box and randomly spread on the rug. I've also seen where the first 40 tiles where in one box and the remaining 60 in a second box. (I don't know the logic of that division...)
Yet children approach the hundred board from all different levels and can learn from it. The other day I watched two girls absolutely euphoric about going to the calendar realizing they needed "a one and a three" and finding "31" for "13" and continuing all through the teens. When they were done, I had them actually write the numbers that they might have seen if they had a control chart and they were still excited. (They were doing this job because they "had a lesson, and were volunteering to clean it up.)
Some children need to match the numbers and can find the hundred board and opportunity for learning numbers and the patterns inherent in building the hundred board. Some children can work independently from a control chart. Many children when they first begin the hundred board will have difficulty with a hundred tiles spread on the rug and will need to find a way to organize their work. "Scaffolding" may include sorting the pieces by the tens, but I've never heard of a formal training presentations that include that. I do, the children need it. It's no different than organizing the pieces of the trinomial cube.
Order is fundamental in many math aspects.
5 comments:
when I present the hundred board, I present it in "levels", and only after the tens board has been mastered:
1-I show them how to separate the tiles into rows of units, teens, twenties, thirties, etc. Then when they build the hundred board they are always working from the top row. I help them set it up because the set-up takes a long time.
2-I show them how to place all the tiles randomly around the board, facing upright (no upside-down numbers). After a few repetitions of this I don't worry about upside down numbers.
3-I have the child take one tile at a time, randomly, and find it's spot on the board.
At any time the child may copy the hundred board onto squared paper. I also have a "first" hundred board paper with the numbers dotted.
For very advanced students I have stories written out, and using the hundred board and a blank paper of 100 squares, the children find the answer to the story on the hundred board (example: Gerry has 10 apples and gives 5 to Sarah. How many are left? or even 85+3+5=) By counting forwards and backwards they can find the answers. They color the correct square on their blank sheet for each answer and when they are done a secret letter will appear!
I love the organized approach of your presentations. You could also add that the separation of boxes into tens would be the first step.
I also love your approach to story problems with the hundred board. I haven't seen that! I may have to make some of those - although the children I'm with at the moment aren't ready for it!
The other material we have that goes with this is a set of cards. On the card is a blank 100 square but with some of the squares highlighted. the first are individual squares, the next are lines, horizontal or vertical and finally clumps of square. The child has to work out by using his knowledge of the tens and units which squares are highlighted.
The other thing we have are envelopes with printed out hundred squares that have been cut into sections, like a puzzle. The child has to put it back together and stick it into their book.
There is so much amazing knowledge in the different ways materials could be presented. I wish there was a way to collect it! Thanks for sharing yours.
I have removed a comment about the hundred board being available on the ipad. The profile was unable to be traced back and I do not support children working the use of young children working on the ipad.
The size alone makes the ipad an ineffective device for this activity.
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