MPC AIDING STEMMERS 

STEM STUDENTS (THOSE STRIVING FOR degrees in science, technology, engineering, or mathematics) have Calculus 1 as a first hurdle. And for many it’s a formidable one. According to AAAS Science, August 31, 2023: “Of all students who initially pursue STEM degrees, more than half graduate without one, often after struggling through coursework.” However, a new approach to teaching calculus is evolving that makes calculus a “pump and not a filter for the STEM pipeline.” Here are tidbits on MPC, Modeling Practices in Calculus, gleaned from this Science article, together with my usual Internet sleuthing.

Traditional Calc 101. A traditional course in calculus is lecture-driven: The prof presents concepts as theorems and proofs, kinda like classical Euclidian geometry, and then follows up with examples showing applications of the theory. 

Student evaluations, i.e., testing, traditionally follow a similar pattern, regurgitate definitions and theorems, perform calculus operations—and then attempt dreaded “word problems.”

The MPC Approach. In a sense, the Modeling Practices in Calculus turns the process back-to-front. Instructors actively engage students collaboratively with actual problems first. Together, using the math fundamentals already at hand, they model discrete data and rates of change in developing the structure of calculus, its analyses of motion using mathematical functions. Concepts of functions, derivatives, and integrals lead to differential equations, integration, and the grand Fundamental Theorem of Calculus relating the two. 

The idea is expanded in “Principles of Calculus Modeling: An Interactive Approach,” by Donald Kreider, Dwight Lahr, and Susan Diesel, mathematicians at Dartmouth College and Norwich University.

The FIU Study. As described in “Establishing a New Standard of Care for Calculus Using Trials with Randomized Student Allocation,” by Laird Kramer et al, Science, August 32, 2023, “The study was performed at Florida International University (FIU) in Miami, Florida, the fourth-largest public research university in the United States, with 58,787 students, of which 41,795 are undergraduates as of fall 2019. FIU is a Hispanic-serving institution, with 64% of students identifying as Hispanic/Latino/a/. Moreover, 79% of the students identify as members of historically underrepresented racial/ethnic minority groups, and 57% are women.”

“Furthermore,” it’s noted, “institutional conditions created urgency to transform calculus because historic pass rates in introductory calculus averaged 55% (range 13 to 88%) over the six semesters before the project’s pilot.”

Results. As one example, “students in the MPC treatment condition had improved course grades. Average grades were significantly higher by ~0.4 points (4.0 grade point scale) in MPC sections across all semesters of the study (P < 0.001, d = 0.295). This translated to success rates (A, B, or C grades) averaging 11% higher in MPC sections compared with traditional sections.”

Image from AAAS Science, August 31, 2023. 

“Moreover,” the paper notes, “the MPC sections also had lower course late drop rates (departure after the regular drop/add period ends) across all three semesters, suggesting that students more clearly perceived that they were likely to succeed in the course.”

Also, “The likelihood of FTiC [first time in college] students in the treatment [i.e., MPC] group passing the course increased by ~85% compared with FTiC students in the control group [traditional lectures].

Implications. The paper observes, “Applying this study’s 11% average improvement in pass rate to all 2000 first-time calculus students at FIU would translate to 220 additional students succeeding in calculus annually and reducing the instructional load by five sections annually.”

It continues, “Extending this strategy to the ~300,000 students across the nation taking calculus 1 each year, these results translate to the potential for an additional 33,000 students passing calculus each year, saving students an estimated $23.9 million on tuition….  

Plus a whole lot of heartache. ds

© Dennis Simanaitis, SimanaitisSays.com, 2023