From High School to College Calculus: Beliefs about Sense-Making and Mistakes

Abstract

Despite longstanding efforts in the K-12 STEM education community to create meaningful mathematical experiences across disciplines, mathematics continues to be a siloed subject which is tracked based on ability. With an increasing number of high-achieving students enrolling in Algebra I in Grade 7 or earlier, there is a need for research on the readiness of accelerated STEM-intending students to persist in mathematics at the college level. A mathematical mindset framework was employed to explore the relationships between level of Algebra I acceleration, student (n = 2111) and instructor (n = 141) beliefs about sense-making and mistake-making, and attitudes in first-semester college calculus. Findings from a series of multilevel analyses indicate that interactions between student mathematical mindset and perceived progressive teaching practices influence attitudes toward mathematics. While student-centered instruction had a slightly negative effect on attitude, there was a differential effect in relation to student beliefs about sense-making as a metric of success in mathematics. These findings contribute to empirical understandings of mathematical mindset and the complex transition from high school calculus to college calculus. Implications for interdisciplinary STEM education and persistence in STEM undergraduate study are discussed. Keywords Algebra . Calculus . Mindset . STEM readiness . Multilevel modeling Mathematics continues to be a barrier to STEM degree completion, and the challenges that STEM-intending students face in making the transition from secondary mathematics to college calculus have been broadly acknowledged. Many researchers have explored this transition from secondary to post-secondary mathematics as a "rite of passage" with respect to mathematics understandings, student autonomy, and expected