Pathways to Calculus in U.S. High Schools

Abstract

In this paper, we present findings from a preliminary analysis of transcript data in the High School Longitudinal Study (HSLS:09), a large-scale longitudinal investigation of academic achievement among U.S. high school students. Using proportional flow diagrams of course-taking patterns, we illustrate differences in calculus completion associated with non-malleable student characteristics such as ethnicity, gender, and socioeconomic status (SES), as well as malleable student characteristics, such as knowledge of mathematics in ninth grade, the level of mathematics course they take in ninth grade, and self-efficacy. Confirming and extending findings from prior literature, we conclude that “tracks” through high school mathematics curriculum, together with students' ethnicity, SES, and self-efficacy, converge as important factors associated with which of the approximately 19% of high school students complete calculus in high school.

Keywords:

• Calculus
• high school mathematics
• post-secondary transitions

ACKNOWLEDGEMENTS

Parts of the work reported here were presented at “The Role of Calculus in the Transition from High School to College Mathematics Workshop” organized by the Mathematical Association of America, Washington, DC, March 17–18, 2016. The authors wish to thank the sponsors and participants in the workshop, and the Teaching Mathematics in Community College Research group, for their feedback on this work.

Notes

1 Schools have varying rules for determining whether a student has earned credit in (passed) a course (e.g., a letter grade of “D” or better). Regardless of the expectations or grading policies, transcript records typically include this designation for all enrolled courses.

2 Full details can be found in Champion and Mesa [4].

3 In this paper, we say that a student has “completed” a high school mathematics course if and only if the student earned credit for the course according to their secondary transcripts. Individual course grades, along with the specific content of the course and/or grading criteria are not available in the public data set.

4 Integrated Mathematics course-taking may be particularly affected by local policies. In addition, HSLS lacks detail about the content or level of rigor in integrated mathematics courses (which can vary greatly).

5 For more on potential gender differences in mathematics course taking at the college level, with particular attention to the role of calculus, see Ellis et al. [12].

6 Twenty-four states (including the District of Columbia) require three Carnegie units of mathematics for graduation (two courses of algebra and one course in geometry); five states require four; two have differential mandates, four units for college-bound students and three units for non-college-bound students; six states have no policies; and 14 require only two units [11]. One Carnegie unit reflects one year of coursework. See: http://ecs.force.com/mbdata/mbprofall?Rep=HS01.

Additional information

Funding

Mathematical Association of America The Role of Calculus in the Transition from High S

Notes on contributors

Joe Champion

Dr. Joe Champion joined the faculty of the Department of Mathematics at Boise State University in 2013. Previously, Dr. Champion taught for three years at Texas A&M University-Corpus Christi. His Ph.D. in educational mathematics is from the University of Northern Colorado, and he also has both B.S. and M.S. degrees in mathematics from the University of North Dakota. His research interests are in academic performance, persistence, and self-efficacy in mathematics, mathematics content knowledge of preservice and in-service teachers, and the design and development of web-based mathematics instruction. In addition to research in mathematics education, Dr. Champion is a frequent collaborator with practicing teachers and professional development providers, serving as a principal or co-principal investigator on more than $2,000,000 of sponsored teacher leadership and professional development projects.

Vilma Mesa

Vilma Mesa is an associate professor of education and mathematics at the University of Michigan, and faculty associate at the Center for the Study of Higher and Postsecondary Education. She investigates the role that resources play in developing teaching expertise in undergraduate mathematics, specifically at community colleges and in inquiry-based learning classrooms. She has conducted several analyses of instruction and of textbooks and collaborated in evaluation projects on the impact of innovative mathematics teaching practices for students in science, technology, engineering, and mathematics. She served as associate editor for the Journal for Research in Mathematics Education from 2000–2004 and is currently serving as associate editor for Educational Studies in Mathematics.