A Comparison of Methods for Assessing Performance on the Number Line Estimation Task

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.

Keywords

• math cognition
• number line
• behavior genetics
• math achievement