Children begin their understanding of mathematics by at the concept level. They develop an understanding of mathematical language as they explore number patterns under ten in the context of real events and/or concrete materials. Children demonstrate their understanding at this level by building concrete models with a variety of manipulatives and by describing what they have created using mathematical language. The next step is a connecting level between the concept and the symbolic levels. Numerical and mathematical symbols are introduced at the connecting level. Mathematical symbols(+, –, =) are even more abstract than the mathematical language they represent. Both vertical and horizontal equations should be experienced. Children visualize symbols as they solve number problems using manipulatives. They show their understanding at this level by building concrete models with various types of manipulatives to match written equations and by relating equations to manipulatives or to a word problem they have created. The teacher records the mathematical symbols.

Remember when we played the Hand Game? Well, we applied to this game numerical symbols to the groups of objects. Using a print-out of hands and number cards with the numerals and dots to represent the amount. We paired up and one would make up a problem by putting the counters on the hands and the other student would put the numbers the objects represent below the hands, along with the answer to how many all together. Quentin had some trouble with the concept of adding and could not get beyond say there was 6 and 3 there. He could not answer the question, "How many altogether?" until I told him to slide them off the hands and on the table and then he could count them separately, get the answer for the total and then put them back. This is practice in invariance of number for him as well. James and Sam had fun trying to make "hard" problems for each other.

Remember when we played the Hand Game? Well, we applied to this game numerical symbols to the groups of objects. Using a print-out of hands and number cards with the numerals and dots to represent the amount. We paired up and one would make up a problem by putting the counters on the hands and the other student would put the numbers the objects represent below the hands, along with the answer to how many all together. Quentin had some trouble with the concept of adding and could not get beyond say there was 6 and 3 there. He could not answer the question, "How many altogether?" until I told him to slide them off the hands and on the table and then he could count them separately, get the answer for the total and then put them back. This is practice in invariance of number for him as well. James and Sam had fun trying to make "hard" problems for each other.

I love the hand! I would try putting the dots on the fingers and then asking the child to slide all the dots over from left to right so no finger is left out. Numbering the fingers might help at first until it's stored in memory. You come up with the greatest ideas!!!

ReplyDeleteI don't want them to count the fingers. I am sorry I didn't make that clear. The hands are just to represent the two sets of amounts. First the different amounts of items are directly in the hands, and then on the paper hands and then will gradually bridge over to numerals on paper. I am sorry I confused with the hands. I try to discourage finger counting because kids tend to get hooked on it and it takes them longer to learn to live without it as a crutch. I do encourage, however, the ability to look at a number of objects, and know how many it is without counting it out. I wish I had come up with the idea, but I didn't. I am just a collector of good ideas! It is from Math Their Way, a wonderful beginning math program.

ReplyDeleteI love the smile! He looks like he's really enjoying his math :)

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