## How Adults Understand and Reason about Fractions

We investigated what strategies adults use to compare magnitudes of fractions, and how the strategies vary with overall mathematical knowledge. Because little is known about how people think about fractions, prior research has attempted to assess the extent to which people think of fractions compared to how they think about whole numbers (Bonato, Fabbri, Umilta & Zorzi, 2007; Schneider & Siegler, 2010; Meert, Gregoire, Noel, 2009). In particular, Bonato et al. (2007) has examined the degree to which fractional magnitude comparisons can yield an understanding of the mental representation of fractions. Schneider & Siegler (2010) argue that these assessments cannot be made independently from understanding the strategies for comparison that a particular pair of fractions elicits. The current study extends prior research by comparing fraction magnitude comparison strategies of students at a selective university, with high math proficiency, with those of students at a community college, with lower math proficiency. The goals of this thesis were to identify, explain and define the strategies that are used in fraction magnitude comparisons by adults, investigate how these strategies vary with the math proficiency of the adults, and evaluate whether adults who do not consistently use desirable strategies recognize desirability of good alternative strategies. Our findings indicate that strategy use and consistency of using good and poor strategies vary with overall math knowledge and performance on our magnitude comparison task; that lower performing participants more frequently used strategies that would yield incorrect results and less often recognize when to switch to good alternative strategies compared to the high performing participants.