Abstract
The debate about how to characterize performance on the number line estimation (NLE) task has yielded a diverse set of accuracy measures. These accuracy measures include characterizing performance by deviation from the correct score with percent absolute error (PAE), modeling the shape of responses via the logarithmic-to-linear shift, and modeling the strategy use via the cyclical power model (one and two cycle). In the present study, accuracy on a symbolic NLE task was examined using phenotypic and quantitative genetic analyses of all four measurements. Data were collected from a same-sex twin sample at ages 12 and 15 (N = 150 pairs) as part of the Western Reserve Reading and Math Project. Linear mixed-effect models were used to compare how well the four NLE accuracy measures predicted math achievement, as measured by the Woodcock Johnson-III Fluency, Calculation, and Applied Problems subtests, after cognitive ability was controlled. NLE accuracy measures were not related to Fluency or Calculation after cognitive ability was controlled, but all NLE accuracy measures were related to Applied Problems at 12 and 15 years old. Although theories about what the NLE task measures have been contested in the literature, the relationship between NLE accuracy and achievement did not differ regardless of the type of accuracy measure used. In addition, the estimates for genetic and environmental influences were proportionately similar across the NLE accuracy measures. Overall, all proposed measures of accuracy in the present sample appear appropriate for prediction of math achievement in adolescents.
Highlights
The debate about how to characterize performance on the number line estimation (NLE) task has yielded a diverse set of accuracy measures
percent absolute error (PAE) and λ were log transformed to correct for skewness [skew before correction (SE): age 12, PAE = 3.4 (.14), λ = 2.1 (.14); age 15, PAE = 1.8 (.14), λ = 3.0 (.14)]
The debate about how to appropriately characterize performance on the NLE task has left an open question about how the theoretical stances reflected in the measurements differentially translate to prediction of math achievement
Summary
The debate about how to characterize performance on the number line estimation (NLE) task has yielded a diverse set of accuracy measures. All proposed measures of accuracy in the present sample appear appropriate for prediction of math achievement in adolescents Fazio, Bailey, Thompson, and Siegler (2014) provide compelling evidence that symbolic and nonsymbolic numerical magnitude estimation independently predict mathematics achievement; though, the relationship between nonsymbolic numerical magnitude estimation and mathematical achievement diminishes after the first grade Both practical and theoretical questions about the nature of numeric magnitude representation remain. The present study and review focus on tasks that use the number to position NLE task with symbolic endpoints (Arabic numbers), there is research that considers effects when the NLE task has non-symbolic endpoints such as dots
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