Peer Effects on First-Year University Students’ Results: The Role of Classmates’ Academic Performance and Socioeconomic Status

Peer effects in the context of higher education have lately received increased attention. Higher diversity in the composition of new cohorts of students, generated mainly in countries where public and institutional policies have enabled access to students from low socioeconomic conditions and races who unusually attend postsecondary education, make these effects even more relevant. This research estimates and analyzes the effect of peers’ academic performance and course composition by socioeconomic origin on students’ academic achievement at a private Colombian university between 2008 and 2019. The estimates, by Ordinary Least Squares and Multilevel models, support the existence of significant peer effects. There was a positive effect of peers’ performance on Calculus I academic results, principally of medium and high-performance peers, and a null effect of the socioeconomic level in Calculus I, but a significant effect in Communication Skills I, although with a limited impact. By introducing heterogeneities, it is evident that students perceived a greater benefit from performance improvements from peers who are in the same performance category or socioeconomic level. These results provide evidence of the existence, direction, and magnitude of peer effects in Colombian higher education. Additionally, they suggest that the most relevant characteristic of classmates is their academic performance and not their socioeconomic origin.

On Packing Thirteen Points in an Equilateral Triangle

The conversation of how to maximize the minimum distance between points - or, equivalently, pack congruent circles- in an equilateral triangle began by Oler in the 1960s. In a 1993 paper, Melissen proved the optimal placements of 4 through 12 points in an equilateral triangle using only partitions and direct applications of Dirichlet’s pigeon-hole principle. In the same paper, he proposed his conjectured optimal arrangements for 13, 14, 17, and 19 points in an equilateral triangle. In 1997, Payan proved Melissen’s conjecture for the arrangement of fourteen points; and, in September 2020, Joos proved Melissen’s conjecture for the optimal arrangement of thirteen points. These proofs completed the optimal arrangements of up to and including fifteen points in an equilateral triangle. Unlike Melissen’s proofs, however, Joos’s proof for the optimal arrangement of thirteen points in an equilateral triangle requires continuous functions and calculus. I propose that it is possible to continue Melissen’s line of reasoning, and complete an entirely discrete proof of Joos’s Theorem for the optimal arrangement of thirteen points in an equilateral triangle. In this paper, we make progress towards such a proof. We prove discretely that if either of two points is fixed, Joos’s Theorem optimally places the remaining twelve. KEYWORDS: optimization; packing; equilateral triangle; distance; circles; points; thirteen; maximize

Supporting Student Success and Persistence in STEM With Active Learning Approaches in Emerging Scholars Classrooms

Over the last several decades, Emerging Scholars Programs (ESPs) have incorporated active learning strategies and challenging problems into collegiate mathematics, resulting in students, underrepresented minority (URM) students in particular, earning at least half of a letter grade higher than other students in Calculus. In 2009, West Virginia University (WVU) adapted ESP models for use in Calculus I in an effort to support the success and retention of URM STEM students by embedding group and inquiry-based learning into a designated section of Calculus I. Seats in the class were reserved for URM and first-generation students. We anticipated that supporting students in courses in the calculus sequence, including Calculus I, would support URM Calculus I students in building learning communities and serve as a mechanism to provide a strong foundation for long-term retention. In this study we analyze the success of students that have progressed through our ESP Calculus courses and compare them to their non-ESP counterparts. Results show that ESP URM students succeed in the Calculus sequence at substantially higher rates than URM students in non-ESP sections of Calculus courses in the sequence (81% of URM students pass ESP Calculus I while only 50% of URM students pass non-ESP Calculus I). In addition, ESP URM and ESP non-URM (first-generation but not URM) students succeed at similar levels in the ESP Calculus sequence of courses (81% of URM students and 82% of non-URM students pass ESP Calculus I). Finally, ESP URM students’ one-year retention rates are similar to those of ESP non-URM students and significantly higher than those of URM students in non-ESP sections of Calculus (92% of ESP URM Calculus I students were retained after one year, while only 83% of URM non-ESP Calculus I students were retained). These results suggest that ESP is ideally suited for retaining and graduating URM STEM majors, helping them overcome obstacles and barriers in STEM, and increasing diversity, equity, and inclusion in Calculus.

Degree requirements of physiology undergraduate programs in the Physiology Majors Interest Group

Physiology undergraduate degree programs operate in isolation relative to other biological science programs, with little to no understanding of how other institutions structure their course requirements and other degree requirements. The purpose of this report is to preliminarily describe the collective curriculum of physiology programs represented at the Physiology Majors Interest Group (P-MIG) annual meetings from 2018 to 2019. A short preconference survey was sent to attendees that inquired about degree requirements of their respective physiology programs. The requirement for Physiology I (69.2%) with laboratory (66.7%) and Anatomy I (57.1%) with laboratory (42.9%), or combined Anatomy and Physiology I (16.7%) and laboratory (18.2%), were common requirements, but many programs did not require Physiology II (27.3%) or Anatomy II (11.1%). There was nearly consensus on required prerequisites such as Biology (2 semesters with laboratories, 85.7%), Chemistry (2 semesters with laboratory, 88.9%), Physics (2 semesters with laboratory, 75%), Calculus I (61.1%), and Statistics (Biostatistics 42.9%; General Statistics 13.3%). There was less agreement among programs in regards to Calculus II (20.0%), Organic Chemistry (2 semesters, 55.6%), and Biochemistry I (47%), which may be reflective of individual department focus. There was considerable heterogeneity among physiology program course requirements for disciplinary core courses and upper division electives. This report is meant to generate discussion on physiology program curricula in efforts to improve physiology education for majors and assist P-MIG in determining minimal points of consensus as they write the first set of national curricular guidelines for degree programs.

Can I or Can’t I?

Sometimes, we quit things because we really don't want to do them anymore. For instance, I quit piano when I was still in elementary school because I didn't enjoy it. I knew I could keep getting better if I tried, but I felt only joy on the day I knew I would never have to play another note, and I've had no remorse since. But very often, we quit things because we don't think we can do them even if we try. I quit taking math in college, because some part of me doubted my ability to succeed beyond multivariable calculus. I loved derivatives and integrals and everything I was learning at that point—and I especially loved my math professor, Robin Gottlieb. Yet the idea of progressing to upper-level courses was terrifying. Quitting is sometimes the right decision, but in the moment, when we declare, “I'm done! No more for me!” it can be very difficult to know whether we're quitting for the right reasons.