PHD, Kent State University, 2017, College of Education, Health and Human Services / School of Teaching, Learning and Curriculum Studies

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first phase, 72 developmental mathematics students took a written assessment containing disembedding, fraction scheme, and fraction addition/subtraction items. Based upon the results of the assessment, three individuals from the first phase were selected to participate in one-on-one clinical interviews. These interviews were aimed at identifying and describing the cognitive processes underlying the participants' performance on the written assessment items. Results from the quantitative phase indicated statistically significant moderate correlations between disembedding in multiplicative contexts, demonstrated fraction schemes, and fraction addition/subtraction. Moreover, regression analysis revealed that age, fraction schemes score, disembedding score, and number of repeated mathematics courses were all significant predictors of a participant's fraction addition/subtraction score. Analysis of the clinical interviews revealed that norming and the equi-partitioning scheme play an important role in ADM learners' conceptions of fractions. This study quantitatively measured the relationship between disembedding, fraction schemes, and fraction addition/subtraction, which has been hypothesized in prior qualitative research. The results also have important instructional implications. Instructors of ADM courses should use the results of this study as an indication of the importance of determining their students' existing schemes and providing them with opportunities to engage in actions associated with higher-level schemes.

Committee: Karl Kosko (Committee Co-Chair); Joanne Caniglia (Committee Co-Chair); Jay Jahangiri (Committee Member) Subjects: Adult Education; Education; Higher Education; Mathematics; Mathematics Education