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• #### Index 371-386

is summarized. These cores are quite related, and their relationships are discussed. Box 5-2 summarizes the steps along the teaching-learning paths in the core areas. As children move from age 2 through kindergarten, they learn to work with larger and more complicated numbers, make connections across the mathematical contents of the core areas, learn more complex strategies, and move from working only with objects to using mental representations. This journey is full of interesting discoveries and patterns that can be supported at home and at care and education centers.

#### THE NUMBER CORE

The four mathematical aspects of the number core identified in Chapter 2 involve culturally specific ways that children learn to perceive, say, describe/discuss, and construct numbers. These involve

1. Cardinality: Children’s knowledge of cardinality (how many are in a set) increases as they learn specific number words for sets of objects they see (I want two crackers).

2. Number word list: Children begin to learn the ordered list of number words as a sort of chant separate from any use of that list in counting objects.

3. 1-to-1 counting correspondences: When children do begin counting, they must use one-to-one counting correspondences so that each object is paired with exactly one number word.

4. Written number symbols: Children learn written number symbols through having such symbols around them named by their number word (That is a two).

Initially these four aspects are separate, and then children make vital connections. They first connect saying the number word list with 1-to-1 correspondences to begin counting objects. Initially this counting is just an activity without an understanding of the total amount (cardinality). If asked the question How many are there? after counting, children may count again (repeatedly) or give a number word different from the last counted word. Connecting counting and cardinality is a milestone in children’s numerical learning path that coordinates the first three aspects of the number core. As noted, we divide the teaching-learning path into four broad steps.

In Step 1, for 2- and 3-year-olds, children learn about the separate aspects of number and then begin to coordinate them. In Step 2, for approximately 4-year-olds/prekindergartners, children extend their understanding to larger numbers. In Step 3, for approximately 5-year-olds/kindergartners, children integrate the aspects of number and begin to use a ten and some ones in teen numbers. In Step 4, approximately Grade 1, children see, count, write, and work with tens-units and ones-units from 1 to at least 100.

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