1. Children’s Number Categories and Their Understanding of Numerical Magnitude Elida V. Laski & Robert S. Siegler Kindergarten Second Grade  Representations of numerical magnitude become more linear with age (Siegler & Booth, 2004; Siegler & Opfer, 2003)  Documented on estimation tasks  Transition from logarithmic to linear  Transition occurs between Kdg. and Second grade for 0 -100 context  Linear representations on smaller numerical contexts prior to larger numerical contexts Method 1. Examine the generality of the logarithmic to linear transition on a categorization task 2. Examine variability of representations across numerical contexts using a categorization task 3. Explore the role of adaptation to numerical context in the transition  Kindergartners, First graders, & Second graders  30 from each grade  middle-to-high income public school  Categorized numbers as low (1), medium (2), or high (3)  In three numerical contexts: 0-20, 0-50, 0-100  Eight numbers presented in all three contexts Results 1. Generality of Transition 2. Variability of Representations KindergartenFirst GradeSecond Grade 0-to-20 0-to-500-to-100 3. Adaptation to Numerical Context Kindergarten Log R 2 =.95 > Lin R 2 =.85 First Grade Log R 2 =.81 < Lin R 2 =.98 Second Grade Log R 2 =.69 < Lin R 2 =.98 Mean Categorizations of Numbers in 0-100 context  Kindergartners’ categorizations were logarithmic, while first and second graders’ were linear  Kindergartners’ number categorizations are more linear on small scales than large scales, while first and second graders’ categorizations were linear in all three contexts Results (cont.) Purpose Background  Children’s numerical categorizations become more flexible with age. First and second graders classify 10-20 as smaller in 0-100 context than in 0-20; kindergartners don’t. Mean Categorizations of Numbers Presented in all Three Contexts Mean Categorization of Number in Different Contexts for Kindergarten & Second Grade 0-to-50 Log R 2 =.90 = Lin R 2 =.89 0-to-20 Log R 2 =.85 = Lin R 2 =.97 0-to-100 Log R 2 =.95 > Lin R 2 =.85 0-to-20 Log R 2 =.67 < Lin R 2 =.95 0-to-50 Log R 2 =.53 < Lin R 2 =.88 0-to-100 Log R 2 =.69 < Lin R 2 =.98 Conclusions  Kindergartners’ to second graders’ subjective number categories showed the same transition from logarithmic to linear representations of numerical magnitude found on estimation tasks  conditions that promote categorization of objects (e.g., comparison) might promote number concept development  Kindergartners’ categorizations were more linear on small scales than large scales  linear representations of number may have less to do with an absolute standard of precision and more with a sense of the relation among numbers within varied numerical contexts  Kindergartners were less likely than first and second graders to adapt to changes of numerical context  likely that the finding reflects an inappropriate emphasis on the magnitude of individual numbers and a disregard for the magnitude of that number in relation to the numerical context  suggests it might be important to provide children with experiences across a range of numerical contexts (e.g., situations in which 18 is NOT a big number) For more information about this project, contact Elida Laski (evl@andrew.cmu.edu) PIER (Program in Interdisciplinary Education Research) Work supported by Carnegie Mellon University’s Program in Interdisciplinary Education Research