Poster #36 - Do CP-knowers Know That all Numerically Equal Collections are in One-to-One Correspondence?

• In Event: 1-061 - Poster Session 02
  In Poster Session: PS 02 Section - Cognitive Processes

Integrative Statement

Children’s acquisition of the meaning of number words occurs in two qualitatively distinct steps. First, they learn the meanings of the words for one to three or four one at a time over a long period. Then, they learn the meanings of all of the other number words in their list all at once, suggesting that their understanding of number word meanings changes radically. One change is that they have learned the cardinal principle – i.e., that the last number word of a correct count denotes the cardinality of the counted set. Many have proposed that the change also involves learning how counting encodes a fundamental property of the natural numbers, namely that they form an ordered sequence generated by the successor function. However, previous studies (e.g., Davidson, Eng and Barner, 2012) have found that there are many CP-knowers (children who know the cardinal principle) who do not know this.
The present study investigates whether the acquisition of the cardinal principle involves learning a different fundamental property of the natural numbers, namely that all numerically equal collections are in one-to-one correspondence. For this purpose, we are evaluating Spanish-speaking preschoolers on a correspondence task. On this task, children are presented with dolls and prizes and are told how many of each there are. Sometimes the numbers are equal, and sometimes there are fewer prizes than dolls. On each trial, children are asked to say if there are enough prizes for each doll to get one. The dolls are visible, but prizes are not so that children’s answers have to be based on their understanding of the number words presented by the experimenter, and cannot be based on non-numerical perceptual properties of the collections. We make sure that children understand the task by testing whether they remember the numbers to be compared prior to answering the correspondence question. Also, using a different task, we make sure that children understand the meaning of “each” (“cada” in Spanish). Before the correspondence task, we assess children’s knowledge of the cardinal principle with Give-a-Number, and we ask them to count as high as they can. CP-knowers are tested on 5 and 6 (i.e., 6 vs 6, and 5 vs 6), 8 and 9, and on the highest number in their list and the one immediately preceding it. Non CP-knowers are tested on 1 and 2, and on 5 and 6.
While data collection is ongoing (our final sample will have x Non CP-knowers and x CP-knowers), the results collected thus far (8 Non-CP knowers and 17 CP-knowers; mean age = 4 years 4 months; range 3;1 to 5;7) suggest that there is qualitative difference between non CP-knowers and CP-knowers. Whereas the former cannot solve the correspondence task on any pair of numbers, the latter solve it for all pairs, including the highest numbers in their count list. This suggests that children do learn a fundamental property of the natural numbers when they become CP-knowers (or shortly thereafter), namely that all numerically equal collections are in one-to-one correspondence.

Authors

• Elia E. Soto-Alba, Universidad Nacional Autónoma de México
  Presenting Author

• Mathieu Le Corre, Centro de Investigación en Ciencias Cognitivas, Universidad Autónoma del Estado de Morelos
  Non-Presenting Author