Creating and experiencing Flipped Learning in Multivariable Calculus for Engineering

Hugo Caerols-Palma; Katia Vogt-Geisse

arxiv: 1907.08754 · v1 · pith:F7DVB5ZSnew · submitted 2019-07-20 · 🧮 math.HO

Creating and experiencing Flipped Learning in Multivariable Calculus for Engineering

Hugo Caerols-Palma , Katia Vogt-Geisse This is my paper

Pith reviewed 2026-05-24 18:55 UTC · model grok-4.3

classification 🧮 math.HO

keywords flipped learningmultivariable calculusengineering educationstudent performanceteaching methodologymixed methodsinstructor evaluationstudent perception

0 comments

The pith

Flipped learning sections in multivariable calculus achieve passing rates similar to traditional sections but receive lower instructor evaluations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper describes the creation of short videos and aligned worksheets for pre-class preparation in a multivariable calculus course for engineering students, along with the in-class activities used. It compares student performance and perceptions in a flipped section against a parallel traditional section, finding comparable passing percentages. Perceptions are mixed overall, with repeating students preferring not to choose flipped classes. The course evolved over four years toward a mixed methodology, which raised instructor evaluation scores and increased enrollment compared to fully flipped versions.

Core claim

Flipped learning with pre-class videos and in-class dynamics produces passing percentages similar to those in traditionally taught parallel sections. Student perceptions are mixed, and repeating students tend to avoid flipped classes. Evolving the methodology to a mixed approach over four years increases instructor evaluation scores and student enrollment.

What carries the argument

Parallel section comparison of flipped versus traditional teaching methods, together with longitudinal observation of the shift to a mixed methodology.

If this is right

Similar passing rates indicate that flipped learning can match traditional methods on standard success metrics.
Mixed perceptions and avoidance by repeat students suggest that student choice matters when selecting teaching formats.
Adopting mixed methodologies can improve instructor evaluations and raise course enrollment.
Material creation challenges, such as aligning videos with worksheets, must be addressed for effective implementation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Educators in similar courses may need to survey student preferences before committing to fully flipped formats.
Challenges in creating aligned pre-class materials could apply to other STEM subjects and warrant shared resources.
Blending methods might address acceptance issues without losing potential benefits of active learning.

Load-bearing premise

The flipped and traditional sections had comparable student populations, instructors, and other conditions so that differences in outcomes can be attributed to the teaching method rather than selection bias or other factors.

What would settle it

A randomized assignment of students to flipped or traditional sections followed by direct measurement of passing rates, student perceptions, and instructor evaluations.

Figures

Figures reproduced from arXiv: 1907.08754 by Hugo Caerols-Palma, Katia Vogt-Geisse.

**Figure 2.** Figure 2: The figure shows video number 1 to video number 105 that were posted before each class vs the number of students that watched each of those videos as pre-class preparation. The data corresponds to the implementation of Flipped Learining in Multivariable Calculus during the second semester of 2016 in a section with a total of 54 students enrolled. Initially, while videos 1 to 11 became available, students w… view at source ↗

**Figure 3.** Figure 3: The figure shows the cumulative pre-class preparation represented as the percentage of students that watched an insufficient (less than 40 videos), intermediate (between 40 and 59 videos), and a sufficient (at least 60 videos) number of videos as pre-class preparation throughout the whole semester. The total number of videos that were available throughout the semester is 105. The data corresponds to the im… view at source ↗

**Figure 4.** Figure 4: The figure shows class numbers 1 to 41 vs number of students that attended each class. The data corresponds to the implementation of Flipped Learining in Multivariable Calculus during the second semester of 2016 in a section with a total of 54 students enrolled. i.e. the instructor needs to prepare material for students to work with in class, that is in accordance with what students had prepared, that allo… view at source ↗

**Figure 5.** Figure 5: The figure shows the length of the videos in minutes vs the number of students that watched the video as pre-class preparation, with a correlation coefficient of determination R2 = 0.02018. On the other hand, we did observe a correlation between the total number of videos a student watched during the semester as pre-class preparation (cumulative video views) and that student’s final grade, as can be seen i… view at source ↗

**Figure 6.** Figure 6: The figure shows the correlation between the total number of videos a student watched during the semester as pre-class preparation (cumulative video views) vs the final grade of that student, with a coefficient of determination R2 = 0.31613. course, with respect to how many videos they had watched throughout the semester as pre-class preparation. One can observe that most of the students that watched 41 vi… view at source ↗

**Figure 7.** Figure 7: Each bar represents a range of number of videos out of a total of 105 vs the number of students that watched that amount of videos in each range as pre-class preparation. Each bar shows in dark grey the number of students that failed the course and in light grey the number of students that passed the course, for each video number range setting. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: The figure shows for the three common tests and final exam the average grades for the flipped section (represented with the solid line) and for the traditionally thought section (represented with the dashed line), both lectured in the second semester of 2016. The grade scale is from 1.0 to 7.0, with 4.0 being the minimum grade to pass the course. in average test and exam results between the flipped section… view at source ↗

**Figure 9.** Figure 9: The figure shows the distribution of the average final grades for the flipped section (solid line) and the traditionally thought section (dashed line). Five final grade ranges are considered: 1-2.9, 3-3.9, 4-4.9, 5-5.9 and 6-7.0. 4.3. Student perception Tables 5 and 6 show qualitative results of a free text respond survey that students took at the end of the semester in the flipped section. The tables show… view at source ↗

**Figure 10.** Figure 10: The figure shows for the first semester of each of the years 2015 to 2018, the number of students enrolled (bars with respect to the left vertical axis) and the instructor’s evaluation (solid line with respect to the right vertical axis) in a scale from 1.0 to 7.0, being 1.0 the worst and 7.0 be best. Students that are behind in their academic progress and failed some mathematics course before enrolling i… view at source ↗

**Figure 11.** Figure 11: The figure shows for the second semester of each of the years 2015 to 2018, the number of students enrolled (bars with respect to the left vertical axis) and the instructor’s evaluation (solid line with respect to the right vertical axis) in a scale from 1.0 to 7.0, being 1.0 the worst and 7.0 be best. of 2016 and first semester of 2017), informing students about to enroll that flipped courses require mor… view at source ↗

**Figure 12.** Figure 12: The figure shows the percentage of students that passed the course throughout the years 2015 to 2018. The solid line represents first semesters and the dashed line second semesters results. 5. Discussion and conclusion: Flipped Learning may not be the answer but it helps to move towards a modern way of teaching After our experience of creating and implementing an active methodology, we asked ourselves: Wh… view at source ↗

read the original abstract

This article discusses the process of creating, implementing and experiencing Flipped Learning in a Multivariable Calculus course for second year engineering students. We describe the construction of the teaching material, consisting of short videos for pre-class preparation and aligned worksheets for in-class dynamics, and the activities that were conducted. We discuss difficulties and key aspects to be considered while creating this material and during implementation of Flipped Learning. We present how students reacted to pre-class preparation and how in-class dynamics developed during implementation. We show results on students performance and perception when enrolling in a flipped classroom section. We present comparative results on students performance of a section taught with Flipped Learning vs a parallel section thought in the traditional expository way. We could conclude that flipped courses show similar results in passing percentage than traditionally taught courses, that student's perceptions are generally mixed, and we perceived that students repeating the course preferably do not choose flipped classes. Finally, we discussed the methodological evolution of this course converging to a mixed methodology throughout a four year period, observing that the instructors evaluation decreases in classes that were flipped. Mixed methodologies on the other hand, increased the learning experience of students resulting in an increased instructors evaluation score and higher students enrollment in the course.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A descriptive case study of flipped learning in one multivariable calculus course, with parallel-section comparisons that lack controls for self-selection.

read the letter

The core of this paper is a report on building and running a flipped version of multivariable calculus for engineering students, including video and worksheet materials plus four years of observations on student reactions and outcomes. It tracks how the approach evolved toward a mixed model and notes that repeaters tended to avoid the flipped sections. That is the main substance: a local implementation story rather than new pedagogy or theory. The authors do a reasonable job laying out the practical steps for creating the pre-class videos and in-class worksheets, and they flag real difficulties like student preparation and classroom dynamics. Those details could be useful to someone setting up a similar course. The comparative claims are the soft spot. The abstract states similar passing rates between flipped and traditional parallel sections, yet it also records that repeating students self-selected away from flipped sections. No information appears on how sections were assigned, whether prior performance was balanced, or what the sample sizes were. Without those controls the null result on passing rates cannot be read as evidence that the teaching format made no difference. Perceptions are described as mixed and instructor evaluations are said to drop in fully flipped classes, but again the supporting numbers and methods are not shown. This is the kind of paper that might interest instructors who already teach engineering calculus and want to see one concrete example of materials and timeline. It does not introduce new principles or falsifiable predictions, so it is unlikely to change broader practice. For peer review it is worth sending as a case report, provided the authors add the missing details on sample sizes, assignment, and any statistical checks. The work is coherent on its own terms and shows honest reflection on what worked and what did not.

Referee Report

2 major / 1 minor

Summary. The manuscript describes the development and implementation of flipped learning in a multivariable calculus course for second-year engineering students. It details the construction of pre-class videos and in-class worksheets, implementation challenges, student reactions and performance, a comparison of passing rates with a parallel traditional section, student perceptions, and the four-year evolution toward a mixed methodology, concluding that flipped and traditional sections yield similar passing rates, perceptions are mixed, repeating students avoid flipped sections, flipped classes lower instructor evaluations, and mixed methods raise evaluations and enrollment.

Significance. The detailed account of material creation, implementation difficulties, and methodological evolution provides practical guidance for instructors considering flipped or hybrid formats in STEM courses. The explicit discussion of student self-selection and the shift to mixed methods offers useful observations on real-world adaptation. However, the comparative claims on performance and evaluations rest on unverifiable data, limiting broader significance.

major comments (2)

[Abstract] Abstract: the central claim that flipped and traditional sections produced similar passing percentages supplies no sample sizes, statistical tests, assignment method, or controls for confounders such as prior GPA or student population differences, so the null result cannot be attributed to teaching format.
[Abstract] Abstract: the observation that repeating students preferentially avoid flipped sections is presented as evidence of self-selection, yet the parallel-section comparison offers no information on whether sections were randomly assigned, matched on covariates, or balanced, undermining attribution of outcomes to the intervention.

minor comments (1)

[Abstract] Abstract: 'thought in the traditional expository way' is likely a typographical error for 'taught'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comments below and will revise the abstract to provide necessary context and qualifications for our observational findings.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that flipped and traditional sections produced similar passing percentages supplies no sample sizes, statistical tests, assignment method, or controls for confounders such as prior GPA or student population differences, so the null result cannot be attributed to teaching format.

Authors: We agree that the abstract presents the similarity in passing rates without adequate qualifiers. The data in the manuscript are observational from parallel sections offered in the same term, with no random assignment, statistical testing, or controls for prior performance or demographics. In revision we will update the abstract to report the available sample sizes, state explicitly that sections were not randomly assigned and no covariates were controlled, and rephrase the conclusion as a descriptive observation rather than an implication of equivalence due to teaching format. revision: yes
Referee: [Abstract] Abstract: the observation that repeating students preferentially avoid flipped sections is presented as evidence of self-selection, yet the parallel-section comparison offers no information on whether sections were randomly assigned, matched on covariates, or balanced, undermining attribution of outcomes to the intervention.

Authors: The referee is correct that the abstract does not describe the section assignment mechanism. The note on repeating students reflects observed enrollment patterns across offerings rather than results from a matched or randomized design. We will revise the abstract to characterize this as an instructor observation on student self-selection and to note the absence of information on assignment, matching, or balance, thereby avoiding any suggestion of a controlled comparison. revision: yes

Circularity Check

0 steps flagged

No circularity: descriptive educational report with no derivations or self-referential reductions.

full rationale

The paper is a descriptive account of implementing and evaluating a flipped classroom in multivariable calculus. It reports on material creation, student reactions, performance comparisons between parallel sections, and methodological evolution over four years, drawing conclusions from observed passing rates, perceptions, and enrollment data. No equations, first-principles derivations, fitted parameters presented as predictions, or load-bearing self-citations appear in the text. The central claims rest on direct empirical observations within the study rather than any chain that reduces to its own inputs by construction. This is a standard non-finding for purely descriptive educational reports.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an empirical case study of teaching methods with no mathematical model, free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5746 in / 1073 out tokens · 24729 ms · 2026-05-24T18:55:47.296948+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

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H., & Mazur, E

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Mazur, E. (2014). Peer Instruction: A user manual, Pearson New International Edition

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F., & Schiller, N

Herreid, C. F., & Schiller, N. A. (2013). Case studies and the ﬂipped classroom. Journal of College Science Teaching, 42(5), 62–66. O’Flaherty, J., & Phillips, C. (2015) The use of ﬂipped classrooms in higher education: A scoping review. The internet and higher education , 25, 85–95. Impact Class Project. (2015). Mathematics Department, Purdue University....

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J., Platt, G

Lage, M. J., Platt, G. J., & Treglia, M. (2000). Inverting the classroom: A gateway to creating an inclusive learning environment. The Journal of Economic Education , 31(1), 30–43. De Grazia, J. L., Falconer, J. L., Nicodemus, G., & Medlin, W. (2012, June). Incorporating screencasts into chemical engineering courses. In 2012 ASEE Annual Conference & Expos...

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(2009, October)

Toto, R., & Nguyen, H. (2009, October). Flipping the work design in an industrial engineering course. In 2009 39th IEEE Frontiers in Education Conference , 1–4

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Zappe, S., Leicht, R., Messner, J., Litzinger, T., & Lee, H. W. (2009). ” Flipping” the classroom to explore active learning in a large undergraduate course. In ASEE Annual Conference and

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A., & Foley, J

Day, J. A., & Foley, J. D. (2006). Evaluating a web lecture intervention in a humancomputer interaction course. IEEE Transactions on education, 49(4), 420–431

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H., Quint, C., Norris, S

Wasserman, N. H., Quint, C., Norris, S. A., & Carr, T. (2017). Exploring ﬂipped classroom instruction in Calculus III. International Journal of Science and Mathematics Education , 15(3), 545–568

work page 2017

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Saterbak, A., Volz, T., & Wettergreen, M. (2016). Implementing and Assessing a Flipped Classroom Model for First-Year Engineering Design. Advances in Engineering Education , 5(3), n3

work page 2016

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Sun, Z., Xie, K., & Anderman, L. H. (2018). The role of self-regulated learning in students’ success in ﬂipped undergraduate math courses. The Internet and Higher Education , 36, 41–53

work page 2018

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Hao, Y. (2016). Exploring undergraduates’ perspectives and Flipped Learning readiness in their ﬂipped classrooms. Computers in Human Behavior , 59, 82–92

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Bergmann, J., & Sams, A. (2012). Flip your classroom: Reach every student in every class every day. International society for technology in education

work page 2012

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Moravec, M., Williams, A., Aguilar-Roca, N., & O’Dowd, D. K. (2010). Learn before lecture: a strategy that improves learning outcomes in a large introductory biology class. CBELife Sciences Education, 9(4), 473–481

work page 2010

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Joanne, C. S. M., & Lateef, F. (2014). The ﬂipped classroom: Viewpoints in Asian universities. Education in medicine journal , 6(4). 19 Youtube. Retrieved from http://www.youtube.com Coursera (2018). Understanding Einstein: The Special Theory of Relativity. Retrieved from https://www.coursera.org/lecture/einstein-relativity/course-overview-XoNqA Khan Acad...

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J., & Quintana, M

Galindo, J. J., & Quintana, M. G. B. (2016). Innovacin docente a trav´ es de la metodolog´ ıa ﬂipped classroom: percepci´ on de docentes y estudiantes de educaci´ on secundaria.Didasc@ lia: Did´ actica y Educaci´ on, 7(6), 153-172. learning platform 20

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