Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group


First Advisor

Elizabeth M. Brannon


Symbolic mathematics allows humans to represent and describe the logic of the world around us. Although we typically think about math symbolically, humans across the lifespan and a wide variety of animal species spontaneously exhibit numerical competence without reference to formal mathematics. This intuitive ability to approximately compare, estimate, and manipulate large non-symbolic numerical quantities without language or symbols is called the Approximate Number System. The four chapters of this dissertation explore whether non-symbolic, approximate calculation can function as a bridge between our Approximate Number System and symbolic mathematics for children at the beginning of formal math education and university undergraduates. Chapter 1 explores how non-symbolic and symbolic ratio reasoning relates to general math skill and Approximate Number System acuity in elementary school children. Chapter 2 examines whether children and adults can perform a non-symbolic, approximate division computation, and how this ability relates to non-symbolic and symbolic mathematical skill. Chapter 3 tests the robustness and mechanism of a non-symbolic, approximate addition and subtraction training paradigm designed to improve arithmetic fluency in university undergraduates. Chapter 4 investigates whether the negative relation between math anxiety and symbolic math performance extends to approximate, non-symbolic calculation. Together, Chapters 1 and 2 provide evidence that non-symbolic calculation ability functions as a mechanism of the relation between Approximate Number System acuity and symbolic math. Chapters 3 and 4 identify populations of students for whom practice with non-symbolic calculation may or may not be beneficial. In sum, this dissertation describes how non-symbolic, approximate calculation allows students harness their intuitive sense of number in a mathematical context.

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