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Decompressing the Mental Number Line

Young, Christopher John
http://rave.ohiolink.edu/etdc/view?acc_num=osu1250616640

Abstract Details

2009, Master of Arts, Ohio State University, Psychology.
A core finding in the development of numerical estimation has been that performance improves with age. This change has often explained by children switching from inaccurate, logarithmic representations of numeric magnitude to more accurate, linear representations. In this thesis, I propose that developmental changes are more usefully seen as decompression in the magnitudes associated with numbers. To test this decompression hypothesis, I reevaluated the numerical estimates of 728 children with a measure sensitive to slight differences in curvature of response pattern, a power function, and compared it to alternative models of numerical estimation (Study 1a). The power function proved nearly as accurate and unbiased in characterizing “logarithmic” patterns of estimates as the logarithmic function, and it allowed accurate characterization of all children’s estimates (including “linear” patterns, which tended to show some degree of compression). Further, in Study 1b, I found that the compression parameter of the power function (its exponent) proved a better predictor of accuracy than logarithmic/linear status, and it was just as sensitive to differences in age, sex, and experimental conditions as was log/lin status. In Study 2, I then applied the power function to assess the representations used to estimate symbolic and non-symbolic numeric magnitude (Study 2), with the finding that the power function was more sensitive to the similarity of the representations used across the two tasks. Finally, in Study 3, I applied the power function to test the hypothesis that differences between symbolic and non-symbolic numerical estimation are verbally mediated, finding that interference of verbal processes did increase the similarity of estimates across the symbolic and non-symbolic estimation tasks, specifically by making non-symbolic estimation more similar to symbolic.
John Opfer (Advisor)
Jay Myung (Committee Member)
Vladimir Sloutsky (Committee Member)
68 p.
Psychology
Numerical Estimation; Representation; Model Selection; Development

Recommended Citations

Citations

  • Young, C. J. (2009). Decompressing the Mental Number Line [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1250616640

    APA Style (7th edition)

  • Young, Christopher. Decompressing the Mental Number Line. 2009. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1250616640.

    MLA Style (8th edition)

  • Young, Christopher. "Decompressing the Mental Number Line." Master's thesis, Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1250616640

    Chicago Manual of Style (17th edition)

osu1250616640
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© 2009, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.