Understanding rational numbers requires reorganizing our initial understanding of numbers as whole numbers. Coordinating the relationship between the different symbolic formats for expressing rational numbers (i.e., as fractions and as decimals) and their underlying non-symbolic magnitudes is an important component of mathematical development in children (Fazio, Bailey, Thompson, & Siegler, 2014; Siegler & Pyke, 2013; Mazzocco et al., 2013). It is also an important component of decision making in everyday life (Simon, Fagley, & Halleran, 2004; Peters et al., 2006). The goal of the present experiments was to investigate the relationship between rational numbers, expressed in various formats, on one hand and general mathematical achievement and decision-making on the other. Two experiments demonstrated that the format of rational numbers impacts processing: the fraction format hinders magnitude processing compared to the decimal format. Experiment 1 additionally demonstrated that the precision of rational number magnitudes is related to general mathematical achievement. This is evidence that a better understanding of rational numbers is important for more abstract mathematics in adults. Experiment 2 showed that individual differences in rational number ability are also associated with individual differences in bias in decision-making. These findings have practical implications. Educationally, these results suggest that using number lines and intermixing decimal and fraction formats might improve rational number ability and therefore better prepare children for later, more abstract mathematics. Pragmatically, the results of this study suggest numerical ability alone is not a sufficient guard against biased decision making when probabilities are involved. Instead it appears other, non-numerical task features cause bias and need to be identified to make decision making more normative.
University of Minnesota Ph.D. dissertation. December 2016. Major: Educational Psychology. Advisor: Sashank Varma. 1 computer file (PDF); viii, 137 pages.
The Role of Rational Numbers in Mathematical Achievement and Decision Making.
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