Multiplication Facts and the Intermediate Algebra Student

Abstract

The present dissertation was written in journal-ready format to understand multiplication fact automaticity (MFA) within the domain of Intermediate Algebra and the extent to which MFA is related to student completion and/or success. The studies were conducted at a small, public university in the southwestern United States. Implications included the consideration of MFA (at or above the sample median of 94%) in placement, instructional, and curricular practices to better equip developmental mathematics students for success in Intermediate Algebra. In the first study, the author examined whether students with high MFA were more successful in Intermediate Algebra than those with low MFA. Even though scientific calculators were permitted throughout the course and on all tests, the average unit test scores and end-of-course grades were statistically significantly higher for students who scored at or above the sample’s median score (high) on an MFA test than students below the median (low). The sample consisted of 448 students enrolled in Intermediate Algebra. Placement scores, attendance, time-lapse between institutional enrollment and first mathematics course, and withdrawal decisions were not statistically significantly correlated with MFA status. The purpose of the second study was to determine whether differences occurred between medians of MFA scores and student competencies on five specific types of problems from Intermediate Algebra assessments: (1) linear equation with fractions, (2) system of linear equations, (3) factor by grouping, (4) simplify a rational expression, and (5) simplify a radical expression. Purposive sampling was used and resulted in the participation of 365 Intermediate Algebra students. Statistically significant differences existed on MFA median scores between groups for problems 3, 4, and 5. In contrast, no statistically significant differences existed on MFA scores for problems 1 and 2. The purpose of the third study was to explore, through personal interviews, the lived experiences of students who withdrew from Intermediate Algebra. Purposive sampling techniques were used to invite eight students to participate in this phenomenological study. Interviews were transcribed verbatim resulting in 123 significant statements. Findings revealed six emerging themes: student goals, false course-expectations, the decision to withdraw, mathematics experiences, strategies for success, and mathematics self-efficacy.