Electronic Thesis and Dissertation Repository


Doctor of Philosophy




Dr. Daniel Ansari


Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in school-relevant math achievement. Children’s ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children’s performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues a quick (two-minute) paper-and-pencil tool was designed to measure children’s ability to compare symbolic and nonsymbolic numerical magnitudes. Individual differences in children’s performance on this test were then correlated with individual differences in arithmetic achievement.

Chapter 2 demonstrated that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. Results also revealed that symbolic scores accounted for unique variance in children’s arithmetic scores when controlling for age, IQ, reading skills and working memory.

Chapter 3 assessed the soundness of the paper-and-pencil test. Results indicated that the paper-and-pencil test demonstrated criterion-related validity, levels of convergent validity and test-retest reliability. Findings again revealed that only children’s performances on symbolic items accounted for unique variance in arithmetic scores.

In Chapter 4, further evidence of the convergent validity of the paper-and-pencil test was demonstrated and again, symbolic processing accounted for unique variance in children’s arithmetic achievement. Results also demonstrated that participants’ performance on the paper-and-pencil test in kindergarten was a significant predictor of their math grade in Grade 1.

Together these three studies give evidence to suggest that a simple two-minute paper-and-pencil test is a valuable and reliable tool for assessing basic magnitude processing in children from kindergarten to the third grade.