How 15 Hundred Is Like 15 Cherries: Effect of Progressive Alignment on Representational Changes in Numerical Cognition


  • The authors would like to thank the administration, teachers, students, and parents from the Worthington School District in Columbus, OH, as well as the Bentworth School District in Bentleyville, PA. Further, the authors would like to thank Julia Kennedy for her help in data collection, Chris Young for his contributions to the “change point” analyses in the General Discussion section, and anonymous referees who provided helpful comments on earlier versions of the manuscript. Portions of these data were presented at the 2007 meeting of the Cognitive Development Society as well as the 30th annual conference of the Cognitive Science Society.

concerning this article should be addressed to Clarissa A. Thompson, Department of Psychology, The University of Oklahoma, 455 W. Lindsey Street, Dale Hall Tower, Room 727, Norman, OK 73019. Electronic mail may be sent to


How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0–1,000, 0–10,000, and 0–100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15:100::1500:10000) might prompt children to generalize their linear representations to ever-larger scales. Experiment 2 assigned second graders (N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations.