From High School to College Calculus: Beliefs about Sense-Making and Mistakes
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From High School to College Calculus: Beliefs about Sense-Making and Mistakes Terrie M. Galanti 1
& Angela
D. Miller 2
# Springer Nature Switzerland AG 2020
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
* Terrie M. Galanti [email protected] Angela D. Miller [email protected] 1
University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, USA
2
George Mason University, 4400 University Drive; MS 1E8, Fairfax, VA 22030, USA
Journal for STEM Education Research
or enacted instructional practices (Clark and Lovric 2008; Gueudet 2008; Selden 2005; Wade et al. 2016). De Guzmán et al. (1998) reported that college instructors deplore weaknesses in their first-year students’ prerequisite knowledge and their overreliance on simplistic procedures; yet there is minimal research on how both student and instructor beliefs about sense-making and mistakes in problem solving might predict college student attitudes toward mathematics. The Committee on STEM Education (2018) recently encouraged K-16 STEM educators to “make mathematics a magnet” (p. 18) with innovative approaches which emphasize deeper learning and real-world problem-solving opportunities in the classroom. While the expansion of “Math Pathways” programs sponsored by the Carneg
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