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## Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity (2009) Center for Education (CFE)

### Citation Manager

. "3 Cognitive Foundations for Early Mathematics Learning." Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: The National Academies Press, 2009.

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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
###### Infant Sensitivity to Changes in Set Size

Several studies report that infants track the results of numerically relevant transformations—adding or taking away objects from a set. That is, when an object is added to a set, they expect to see more objects than were previously in the set and when an object is taken away, they expect to see fewer objects than were previously in the set. Wynn (1992a) found that after a set was transformed by the addition or subtraction of an object, 5-month-old infants looked longer at the “impossible” result (e.g., 1 + 1 = 1) than at the “correct” result. However, as for numerical discrimination, subsequent studies suggest that their performance may reflect sensitivity to continuous (cumulative size of objects) amount rather than to numerosity (Feigenson, Carey, and Spelke, 2002). For the problem 1 + 1, infants looked longer at 2, the expected number of objects, when the cumulative size of the two objects was changed than at three, the impossible number of objects, when the cumulative size of the objects was correct—that is, when the cumulative area of the three objects was equivalent to the area that would have resulted from the 1 + 1 addition.

Cohen and Marks (2002) suggested an alternative explanation for Wynn’s results. In particular, they suggest that the findings could be attributable to a familiarity preference rather than to an ability to carry out numerical transformations. For the problem 1 + 1 = 2, they point out that infants more often see one object, as there was a single object in the first display of every trial and thus, based on familiarity, look more at 1 (the incorrect answer). A similar argument was made for looking more at 2 for the problem 2 − 1.

Although their findings support this hypothesis, a more recent study by Kobayashi et al. (2004) provides evidence that infants look longer at 1 + 1 = 3 and 1 + 2 = 3 than at 1 + 1 + 2 and 1 + 2 = 3 when the first addend is a visual object and the second addend consists of a tone(s). This paradigm cannot be explained by the familiarity preference because, for each problem, infants see only one element on the stage.

###### Order Relations

A few studies have examined infants’ sensitivity to numerical order relations (more than, less than). One habituation study showed that 10- and 12-month-olds discriminated equivalent sets (e.g., a set of two followed by another set of two) from nonequivalent sets (e.g., a set of two followed by a set of three) (Cooper, 1984). In another study, Cooper (1984) habituated 10-, 12-, 14-, and 16-month-old infants to sequences that were nonequivalent. In the “less than” condition, the first display in the pair was always less than the second (e.g., infants were shown two objects

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 Front Matter (R1-R12) Summary (1-4) Part I: Introduction and Research on Learning (5-6) 1: Introduction (7-20) 2 Foundational Mathematics Content (21-58) 3 Cognitive Foundations for Early Mathematics Learning (59-94) 4 Developmental Variation, Sociocultural Influences, and Difficulties in Mathematics (95-120) Part II: Teaching-Learning Paths (121-126) 5 The Teaching-Learning Paths for Number, Relations, and Operations (127-174) 6 The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement (175-222) Part III: Contexts for Teaching and Learning (223-224) 7 Standards, Curriculum, Instruction, and Assessment (225-288) 8 The Early Childhood Workforce and Its Professional Development (289-328) Part IV: Future Directions for Policy, Practice, and Research (329-330) 9 Conclusions and Recommendations (331-350) Appendix A: Glossary (351-358) Appendix B: Concepts of Measurement (359-362) Appendix C: Biographical Sketches of Committee Members and Staff (363-370) Index (371-386)