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Wednesday, June 21, 2017

Quantification and Counting with Freebies

Quantification is the act of counting or measuring; to indicate, determine, or express quantity. This ability follows a developmental sequence.  There are three levels:

1. Global Quantification- This is what I like to call  "eyeballing it."  I do this as a teacher when I don't feel like counting.  For example, grabbing a set that looks like it has 10 in it.  So children in this stage, will judge an amount as less, more or the same based on what it looks like compared with another set.

2. One to One Correspondence- Here children can match object to object pairing them so they are equal amounts. This is a critical step as children are able to attend to each individual unit. 

3. Counting- Children can count to determine an amount and count out an equal amount.  

According to Gelman and Gallistel, there are five principles for counting proficiency:

1. The one to one principle- The child must be able to name one counting word to one item and keep track of those objects that have been assigned a number name and those that have not.

2. The stable-order principle- This requires children to know and repeat the number words in correct order for the duration of items to be counted.

3. The cardinal principle-Here a child needs to understand that the last number named tells you the total amount of objects counted. If a child is asked how many at the conclusion of their count and begins counting again this is a signal they have not mastered this principle.

4. The abstraction principle- children need to understand you can count objects that are not concrete objects such as imaginary objects. 

5.The order irrelevance principle- The order items are counted does not matter as long as each item is counted once.

These understandings do not develop in any particular order and children may be inconsistent in their application of these. 

When teaching young children who are just beginning to acquire counting skills, it is important to use symbolic representations of number. This promotes the progression of counting proficiency.  Most often this takes the form of various dot formations.  These encourage subtizing and addition acquisition.  Numeral dice should be introduced later.  
Using games to teach number sense is an excellent way to keep students engaged.

One game I made for my class was a card game.  I called it "I Win!"  

Download a set of color cards from my Google Drive.

You can get this path game based off the book "Monster's Love Underpants" from my Google Drive.

Initial straight path games simulate a number line. A path game is more difficult because they are abstract. Children do not have a concrete representation of quantities.  With each turn, children move farther along the path and the quantity does not match the amount rolled. Initially, all children should play with their own board.  Questions for path games are, "How many spaces have you moved? How many spaces are left before you get to the end? What will happen if you get a 3 on the next turn?"

Longer more complex path games are great for introducing a second die and promoting addition skills.  If the game ends to quickly with the addition of an additional die, simply add more movers to extend the game. Teacher can model the addition process while playing with the children. Remember to use questioning to promote number sense.

The grid game uses a bingo type board which helps develop one to one correspondence.  With the proper questioning technique you can pose thinking questions involving game play.  For example, "How many more spaces to you need to fill up your row? Do you have more spaces empty or covered? Is the number you rolled too much, too little or just right to finish the row?"

You can download this Pete themed grid game from my Google Drive.

For more games to use in the classroom click on the image below.

One more thing- You can use mini erasers as movers for these path games.

Games based around concepts found in this book.

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