Infants and Toddlers Learning About Beginning ideas about number and operations develop as infants and toddlers play with objects and interact with the people in their lives. Infants begin to learn about number and quantity as they notice and manipulate objects in their play. For example, older infants delight in putting toys in a container one by one, then dumping them all out and beginning the process all over again. Infants begin to learn such concepts as more, less, and none as they explore quantities in this way. When they add and take away objects, infants can repeatedly observe how quantities are increased or decreased by their actions. Toddlers are increasingly interested in exploring and learning about number and comparing quantities (more, less, same). Adults can see their growing understanding of number and quantity in their actions and their emerging language. For example, a toddler might make equal groups by giving one cup to each friend, or might choose the container with a lot of markers over the one with fewer. Toddlers notice and often comment on who has more or the most. They also learn and use number-words. They begin to learn the counting sequence, and may even try to count groups of objects by touching them and saying number-words. 1
Infants and Toddlers Developing Knowledge About Infants appear to be naturally sensitive to number. Even very young infants can notice numerical differences between very small quantities, such 2 versus 3. The ability to notice when groups differ by one object is limited to very small numbers up to four (e.g., Antell & Keating, 1983; Starkey & Cooper, 1980; Strauss & Curtis, 1981). Infants also notice differences between larger groups of objects as long as the difference is big enough, such as 8 versus 16 (Xu & Spelke, 2000). Concepts about number relations and operations begin to develop very early. Older infants organize objects into groups and change amounts by adding or removing objects. They construct equal groups by putting things together in one-to-one correspondence; for example, one doll in each of Daddy s slippers (e.g., Langer, et al., 2003; Mix, 2002). Toddlers understand in a general way that adding objects to a group increases the number of objects in the group and subtracting objects decreases the number. With very small numbers, their understanding is more exact. When toddlers see one object, such as a ball, hidden in a box and then see one more ball added to the box, they expect to find two balls in the box. When two balls are hidden and a ball is removed, they expect to find one ball (Feigenson & Carey, 2003; Starkey, 1992). Some of children s earliest words refer to quantity. Toddlers begin to understand and use numberwords and other words that refer to quantity, such as more, lots, and all gone. By 2 years of age, many children use the word two accurately to label groups of two objects; for example, two doggies (Mix, 2009; Wagner & Walters, 1982). Most toddlers begin to learn and recite strings of counting numbers, like one-two-three or onetwo-four-six (Fuson, 1988). Toddlers may also begin to try counting objects, by touching or pointing at objects and reciting the strings of number-words they know. For example, a toddler might count the four raisins on her plate by repeatedly pointing and saying two-two-three-five-five (Wagner & Walters, 1982). 2
Materials, Environments, and Experiences that Support Infants and Toddlers Learning about Provide materials for infants and toddlers to manipulate and explore quantity. For very young infants, provide soft animals or other simple toys that a child can hold, mouth, and eventually transfer hand-to-hand. For older infants and toddlers, provide collections of objects such as small blocks, rings, and toy animals. These kinds of objects encourage infants and toddlers to match, group, and sort objects and to manipulate and compare quantities. Provide containers for young children to put objects in and take objects out. Talk about number and quantity when playing with and caring for children. Use language that describes quantity, such as more, less, a lot, and so many. Use number-words (one, two, or three) to label very small groups of objects; for example, "I m giving you more crackers. Now you have three!" Use number-words to compare. For example, compare numbers of body parts: two ears, two eyes, two elbows, two knees; one nose, one mouth; and ten fingers. Count with children. For example, count steps while walking outside or up and down stairs, or count objects pictured in books, touching them one by one. Play games, sing songs, and read books involving number. Play counting games. For example, model one-to-one correspondence by counting as you or the child puts objects into a container one at a time. Play simple board games with older toddlers, such as Snail s Pace Race; or play matching games that create pairs, such as Lotto (with fewer cards, faces up). Sing lively, interactive counting songs, such as One Potato, Two Potato or This Old Man. 3
Share ideas with families about ways to help infants and toddlers learn about number during play and everyday routines. Encourage parents to look for opportunities to count and talk with their children about numbers and quantity during routines, such as mealtime, bathtime, walks, and other shared experiences. For example, on a visit to the park, count the pushes you give on the swing, One, two, three up high you go! or at snack time, Two crackers for you. One for this hand and one for this hand. Point out that playing with everyday materials (collections of lids, pairs of socks and shoes, kitchen containers or safe utensils, cups, or plates that match or form small sets) can help infants and toddlers develop mathematical concepts, including concepts about number and quantity. Ideas for Teachers to Use and to Share with Families: Building Number Concepts with Goodnight Moon Goodnight Moon, by Margaret Wise Brown and illustrated by Clement Hurd Also printed in Spanish (Buenas Noches, Luna) and several other languages The words and the illustrations in the much-loved classic, Goodnight Moon, are rich in opportunities to support number concepts and vocabulary. As the bunny in the book says goodnight to all the things he sees in his room and to the moon outside his window, his words form a simple repeating pattern of goodnights. Infants enjoy hearing the words and looking at the pictures. Toddlers enjoy participating in the story by pointing to items as they are named. Later, as toddlers become more familiar with the story, they can say some of the words. Family members will be pleased to learn that this popular book can help very young children begin to learn math concepts and language. Share some ideas with families about using this book to help their children learn very small number-words (one, two, three), identify how many, count, and compare quantities. As you read the book, point to the objects as you name them. Stress the numbers of things that are named and/or pictured. Look! Three bears sitting on three chairs. I see two kittens and only one mouse. Many things in the great green room come in groups of two (socks, mittens, clocks, slippers). Ask questions that emphasize the number two. Where are the two mittens? Do you see two socks? Can you find two slippers? Ask older toddlers How many? questions. How many clocks are there? How many windows do you see? Let s count them. 4
References Antell, S., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695 701. Feigenson, L., & Carey, S. (2003). Tracking individuals via object files: Evidence from infants manual search. Developmental Science, 6, 568 584. Fuson, K. C. (1988). Children s counting and concepts of number. New York: Springer- Verlag. Langer, J., Rivera, S., Schlesinger, M., & Wakeley, A. (2003). Early cognitive development: Ontogeny and phylogeny. In K. Connolly & J. Valsiner (Eds.), Handbook of developmental psychology (pp. 141 171). London: Sage. Mix, K. S. (2002). The construction of number concepts. Cognitive Development, 17, 1345 1363. Mix, K. S. (2009). How Spencer made number: First uses of the number words. Journal of Experimental Child Psychology, 102, 427 444. Sinclair, H., Stambak, M., Lezine, I., Rayna, S., & Verba, M. (1989). Infants and objects: The creativity of cognitive development. San Diego, CA: Academic Press. Starkey, P. (1992). The early development of numerical reasoning. Cognition, 43, 93 126. Starkey, P., & Cooper, R. G. Jr. (1980). Perception of numbers by human infants. Science, 210, 1033 1035. Strauss, M. S., & Curtis, L. E. (1981). Infant perception of numerosity. Child Development, 52, 1146 1152. Xu, F., & Spelke, E. S. (2000). Large-number discrimination in 6-month-old infants. Cognition, 89, B15 B25. Wagner, S. H., & Walters, J. (1982). A longitudinal analysis of early number concepts: From numbers to number. In G. E. Forman (Ed.), Action and thought: From sensorimotor schemes to symbolic operations (pp. 137 161). New York: Academic Press. 5