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Children's Number-line Estimation Deconstructed Open Access


Other title
mathematical thinking
cognitive development
number-line estimation
Type of item
Degree grantor
University of Alberta
Author or creator
Piatt, Carley G
Supervisor and department
Bisanz, Jeffrey (Psychology)
Volden, Joanne (Communication Sciences and Disorders)
Examining committee member and department
Zwaigenbaum, Lonnie (Pediatrics)
Nicoladis, Elena (Psychology)
Lemaire, Patrick (Psychology)
Wiebe, Sandra (Psychology)
Department of Psychology

Date accepted
Graduation date
Doctor of Philosophy
Degree level
Number-line estimation is an important, useful, everyday skill that has been linked to numerical cognition and mathematical achievement more generally. Despite numerous investigations in the last decade and the importance of number-line estimation as a mathematical concept, gaps remain in our knowledge of how number-line estimation develops. Averaging across individuals and ignoring trial-by-trial variability on the number-line estimation task may result in overlooking important information. I reviewed the number-line literature, identified several shortcomings in current knowledge, and developed and applied an alternative approach to study how 24 students in each of Grades 2, 4, and 6 make number-line estimates on 0-100 and 0-1000 lines. As in previous research, measures of accuracy and linearity on number-line estimation were taken as measures of implicit conceptual number-line knowledge. Explicit conceptual number-line knowledge was measured by assessing students’ explicit understanding of, for example, proportions and scale on the 0-100 number line. To measure procedural knowledge self-reports were collected from students as they estimated targets on number lines on a tablet, and a task analysis of number-line estimation was used to guide the classification of number-line processes into solution procedures. Several key findings emerged. First, children’s explicit knowledge about the number line, such as their understanding of equal intervals and proportions, increased with age and was positively correlated with a linear pattern of number-line estimates. This result is important because it is the first time a measure of explicit conceptual number-line knowledge has been linked to performance on the number-line task with children in Grades 2, 4, and 6. Second, a task analysis of the processes used in number-line estimation guided the identification of how processes were combined into solution procedures. The task analysis allowed for the coding of observations and students’ self-reports, which revealed immense variability in the solution procedures students used. Further, identifying students’ solution procedures paved the way for successfully identifying tactics, the profile of solution procedures students selected as a function of target. As expected, older students used more conceptually advanced tactics compared with younger students. Even when controlling for grade, the use of advanced tactics was generally related to having more explicit number-line knowledge. Moreover, distinct patterns of discrepancy in estimation emerged as a function of tactics, giving rise to the conclusion that number-line estimation is a product of not only implicit conceptual number-line knowledge but also what children explicitly know about the number line and the procedures they used to estimate. Finally, having mapped the ways in which students estimated, I investigated the ways in which students adjusted their number-line estimation tactics across two ranges and found that successful adjustment from the 0-100 to the 0-1000 line was often associated with more explicit conceptual number-line knowledge. Moreover, I found that several kinds of shifts in tactic led to adaptive performance on the number-line task. Overall, these results shed new light on what develops in children’s number-line estimation by creating a window into children’s explicit conceptual and procedural number-line knowledge.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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