Changing mental representations using related physical models: the effects of analyzing number lines on learner internal scale of numerical magnitude

Abstract

Understanding the linear relationship of numbers is essential for doing practical and abstract mathematics throughout education and everyday life. There is evidence that number line activities increase learners' number sense, improving the linearity of mental number line representations (Siegler & Ramani, 2009). Mental representations of numbers of children in kindergarten through 2nd grade were examined. Methods of improving mental representation using number line activities were also examined. This experimental study included a pretest, interventions, control, and posttest. Analyses were completed to determine accuracy and linearity of estimation patterns as a reflection of mental representations before and after interventions. Age and achievement test data analyses contributed developmental and mathematics performance information to the study. The findings of this study support existing research indicating children's understanding of number improves with age, with accurate and linear mental representations on a 1 to 100 number line fitting few students in kindergarten, about half in 1st grade and the majority of students in 2nd grade. This study also contributes to our understanding of the educational power of number line activities and interventions. After three short experiences with board games and broken number line puzzles growth is evident, although not significant, for performance on the number line estimation task. Further study must be done to add to our understanding of number line estimation as well as the activities which improve mental representations.