Calculus-enhanced energy-first curriculum for introductory physics improves student performance locally and in downstream courses

Abstract

Here we demonstrate the benefits of a new curriculum for introductory calculus-based physics that motivates classical mechanics using a modified version of Hamiltonian mechanics. This curriculum shifts the initial focus of instruction away from forces and the associated vector mathematics, which are known to be problematic for students, to the scalar quantity energy, which is more closely aligned with their previously established intuition, and associated differential and integral calculus. We show that implementation of this calculus-enhanced "energy-first" curriculum resulted in higher normalized gains on the Force Concept Inventory exam for all students and improved performance in downstream engineering courses for students with lower ACT math scores. In other words, the downstream benefits were largest for students with lower math abilities who also pose a larger retention risk. This new curriculum thus has the potential to improve student retention by specifically helping the students who need help the most, including traditionally underserved populations who often have weaker mathematics preparation. We propose future work to investigate whether this new curriculum has lowered the math transference barrier to learning in introductory physics, resulting concomitantly in improvements in student learning of classical mechanics and in student fluency with applied mathematics.

Implementing Competency-Based Grading Improves the Performance of Women and First Generation Students in Introductory Physics

“…Since we implemented a new curriculum for PHSX 211 in the Spring 2015 semester [26], we analyzed the performance of only students completing PHSX 211 between the Spring 2015 semester and the Spring 2019 semester; the total course enrollment for these semesters is 727 students. These data include seven semesters in which ALPaCA grading was not used (635 students between Spring 2015 and Spring 2018) and two semesters in which it was used (182 students in Fall 2018 and Spring 2019).…”

“…Further separate investigation of these data also allowed us to quantify the relative difficulty of each content area in PHSX 211. We found that students struggle with force-based mechanics more than energy-based mechanics [26], and that quantitative problem solving with momentum presents the largest difficulty. Taken together, these results are consistent with previously published studies [25,35,36,37,45] and also suggest how instruction methods and time might be adjusted to better serve the needs of students.…”

“…The data shown in Figure 1 also indicate that the implementation of ALPaCA grading weakened the dependence of course grade on ACT math score. Since ACT math score can serve as a proxy for mathematics ability [26], these data suggest that course grade is less dependent upon prior mathematics ability when ALPaCA grading is used. In addition to implying that ALPaCA grading may allow students to more effectively confront obstacles to learning physics associated with poor mathematics preparation, this observation is 5/15 also consistent with previously published results demonstrating that competency-based grading in algebra-based introductory physics had the largest benefit for students with lowest mathematics ability [40].…”

“…We use broadly defined content areas to limit the number of content areas in the grading system and to more clearly indicate to students the key topics of importance to the course. The numbering of these content areas follows the chronological order of presentation of the associated topic during the semester [26].…”

Committing to instructional improvement in an era of community college reform

“…One example of this type of introductory course redesign was undertaken by physics professors at the University of Kansas. Rather than beginning the course with the topic of forces, faculty developed a “calculus‐enhanced energy‐first” curriculum because the focus on energy aligned better with many students’ intuitive knowledge of physics and allowed students to develop and apply their calculus skills from the start, leading to better subsequent course outcomes (LeGresley et al., 2019). Embedding academic supports can involve collaboration across programs and meta‐majors and with student services staff that brings supports closer to students and the classroom content they are learning.…”