Wednesday, October 26, 2011

Number and Math Sense

Children instinctively search for order and sense in their environment. This helps them to see and make connections in the world around them.

In the classroom we have concrete, hands-on materials which represent number ideas.
The math materials can assist the child's need to organize, classify and rank objects.
Kian: Hey it's longest to shortest!

Every hands-on, sensorial impression they experience is filed away in their mind to be recalled later.
Dena knows just how big 10 is because she remembers holding the 10th red/blue rod.
The numerals the children see are the labels for the quantity, the true number group.
Tori is placing the 6th red/blue rod under the numeral that symbolizes that specific quantity.
The numeral card tells the child which rod to bring. Tori has experienced what "6" is, (she had to reach to count from the red end to the blue end) and can now apply that knowledge.

At times disagreements about correct answers may arise.
Rather than simply providing the correct answer, the children involved may hear the question: Can you show me how you got your answer?
The child is then able to demonstrate their thought process, and share their knowledge.
Perhaps a child will hear: I get a different answer, lets each try again and see what we come up with.
Morah Katie: Kian, will you please bring me the 6 red/blue rod?
Kian walks across the classroom and into the "space" room, he has to remember the rod requested, find it and bring it back.
Morah Katie: I get a different answer, let's each count it.
This "double check" allows the child to rethink a strategy, or perhaps simply slow down in the activity. What is important is that the child is provided with an opportunity to repeat the process and/or reexamine their own ideas.
Kian is able to return, self-correct, and bring the correct red/blue rod.

In addition to the manipulative items in the classroom, the classroom is also designed to facilitate the development of mathematical knowledge in indirect ways.

Negotiations and conflict resolution is an indirect way to assist number concepts.
If we have 3 children who want to work at a table with 2 chairs, will there be enough for everyone? What can we do to solve this problem?
Perhaps just bring another chair, or perhaps go to a bigger table.
Guiding the children to find positive solutions help them to see connections and relationships between things.

It is important to have children think about number and quantities of objects which are meaningful to them.
If we sing about 5 green and freckled frogs but have 9 children, how many times will we need to sing the song so everyone gets a turn?
As we sing about 5 stars winking at us, and 1 star shoots away leaving us with 4 (and so on until there are none) we are singing and subtracting!

Each morning the host of the day counts how many friends are at school.
The host and a friend set the snack table for all the children.
What happens if a few children don't have chairs?
The host can recount the chairs at the table, or perhaps count how many children are still standing.
In the end, being sure each child has a chair is an important part of this social experience, as well as building one to one correspondence.

Logical and mathematical thinking is an internal process, in which the child needs to build relationships and connections in their world.
This can only be done and achieved at the child's pace and interest.
The teacher's job is to focus on the process of this construction rather than the results.

There is nothing quite as exciting as watching the face of a child who is in the midst of an "aha!" moment. The fact that the child knows that 8+2=10 is just a bonus.

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