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or pictures (e.g., detailed animals of different sizes rather than circles or squares), lack of symmetry, and irregular arrangements (Clements and Sarama, 2007).

The importance of facilitating subitizing is underscored by a series of studies, which first found that children’s spontaneous tendency to focus on numerosity was related to counting and arithmetic skills, then showed that it is possible to enhance such spontaneous focusing, and then found that doing so led to better competence in cardinality tasks (Hannula, 2005). Increasing spontaneous focusing on numerosity is an example of helping children mathematize their environment (seek out and use the mathematical information in it). Such tendencies can stimulate children’s self-initiated practice in numerical skills because they notice those features and are interested in them.

###### Number Word List

A common activity in many families and early childhood settings is helping a child learn the list of number words. Children initially may say numbers in the number word list in any order, but rapidly the errors take on a typical form. Children typically say the first part of the list correctly, and then may omit some numbers in the next portion of the list, or they say a lot of numbers out of order, often repeating them (e.g., one, two, three, four, five, eight, nine, four, five, two, six) (Fuson, 1988; Fuson, Richards, and Briars, 1982; Miller and Stigler, 1987; Siegler and Robinson, 1982). Children need to continue to hear a correct number list to begin to include the missing numbers and to extend the list.

Children can learn and practice the number word list by hearing and saying it without doing anything else, or it can be heard or said in coordination with another activity. Saying it alone allows the child to concentrate on the words, and later on the patterns in the words. However, it is also helpful to practice in other ways to link the number words to other aspects of the number core. Saying the words with actions (e.g., jumping, pointing, shaking a finger) can add interest and facilitate the 1-to-1 correspondences in counting objects. Raising a finger with each new word can help in learning how many fingers make certain numbers, and flashing ten fingers at each decade word can help to emphasize these words as made from tens.

###### Counting: 1-to-1 Correspondences

In order to count a group of objects the person counting must use some kind of action that matches each word to an object. This often involves moving, touching or pointing to each object as each word is said. This counting action requires two kinds of correct matches (1-to-1 correspondences): (1) the matching in a moment of time when the action occurs and a

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