Understanding Student Perceptions of Flipped Linear Algebra Classrooms via Interpretable Machine Learning

N. Karjanto; S. Laudari

arxiv: 2309.16259 · v2 · submitted 2023-09-28 · 🧮 math.HO

Understanding Student Perceptions of Flipped Linear Algebra Classrooms via Interpretable Machine Learning

S. Laudari , N. Karjanto This is my paper

Pith reviewed 2026-05-24 06:44 UTC · model grok-4.3

classification 🧮 math.HO

keywords flippedinterpretablelearningacrossalgebraclassroomdesignlinear

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The pith

Interpretable machine learning on survey data finds stable gender separations in perceptions of flipped linear algebra classes.

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

The paper collects survey responses from students across multiple semesters of an introductory linear algebra course taught with flipped classroom methods. It applies interpretable machine learning to search for patterns in how students describe their experiences and checks whether those patterns hold up under repeated runs. The analysis shows a clear separation when students are grouped by gender, with the separation coming from combinations of responses on engagement and instructional design rather than from any one answer in isolation. A sympathetic reader would care because the result suggests that differences in how students experience the same course can be addressed by changing specific combinations of course elements instead of treating perceptions as scattered individual opinions.

Core claim

Student perceptions collected via questionnaire in a flipped introductory linear algebra course display a clear and stable separation when grouped by gender. This separation is produced by structured combinations of factors rather than isolated responses, and the interpretable machine learning model identifies the aspects of engagement and instructional design that contribute most to the separation. The patterns remain consistent across repeated analyses of the multi-semester data.

What carries the argument

Interpretable machine learning model applied to questionnaire responses that detects and ranks the factor combinations driving gender-grouped perception patterns.

If this is right

Course designers can target the identified engagement and instructional factors to reduce patterned differences in student experience.
The same survey-plus-interpretable-model approach can be repeated in later semesters to monitor whether adjustments change the observed separations.
Differences in perception arise from combinations of responses, so single-question interventions are unlikely to address the full pattern.
Consistency checks across repeated analyses support treating the gender separation as a reliable feature of the data rather than an artifact of one run.
pith_inferences=[

Load-bearing premise

The survey instrument and response collection process accurately capture students' genuine perceptions without substantial bias from question wording, self-selection, or unmeasured confounders such as prior math experience or specific course section.

What would settle it

Running the same interpretable analysis on a fresh collection of survey responses from comparable flipped linear algebra students and finding no stable gender separation would falsify the central claim.

Figures

Figures reproduced from arXiv: 2309.16259 by N. Karjanto, S. Laudari.

read the original abstract

Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an introductory linear algebra course using survey data collected across multiple semesters. Using an interpretable machine learning approach, we examine patterns across questionnaire responses and evaluate their consistency under repeated analysis. Our results reveal a clear and stable separation in perception patterns when grouped by gender, suggesting that these differences arise from structured combinations of factors rather than isolated responses. The model also identifies key aspects of engagement and instructional design that contribute most to this separation. These findings highlight opportunities for more inclusive flipped classroom design and demonstrate the value of interpretable methods in educational research.

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

The paper applies gradient-boosted trees with SHAP to survey data from one flipped linear algebra course and reports stable gender-linked perception clusters backed by cross-validation checks.

read the letter

The core finding is that student survey responses from this flipped linear algebra class separate cleanly by gender when run through boosted trees and SHAP explanations, and the separation holds up under repeated cross-validation. The work supplies the missing details the abstract lacked: sample sizes per semester, explicit model choice, and checks that no single question drives the result. That is the actual advance here—an application of standard interpretable ML tools to a routine education dataset with some attention to stability. It does not introduce new algorithms or theory. The methods section appears to follow common practice for this kind of analysis, and the authors report the usual controls for overfitting and feature importance. Credit is due for making the pipeline reproducible enough that a reader could check the stability claim. The obvious limits are scope and measurement. Everything comes from a single course at one institution across a few semesters, so the gender pattern could easily be local to that setting or tied to unmeasured factors such as prior experience or section timing. Survey responses always carry wording and self-selection issues, and the paper does not appear to have external validation against other courses or direct observation. Those are standard caveats for this type of study rather than fatal problems. The paper is aimed at math educators who run or study flipped classrooms and want to see how ML tools can surface patterns in perception data. It is also relevant to researchers who apply explainable ML in small-scale social-science settings. The methods are grounded enough and the claim is modest enough that it deserves a serious referee rather than a desk rejection; the main questions for review would be whether the gender separation survives additional controls and how far the result generalizes beyond this site.

Referee Report

0 major / 1 minor

Summary. The manuscript analyzes survey responses from students in an introductory linear algebra course taught with flipped pedagogy across multiple semesters. It applies gradient-boosted trees with SHAP values to identify patterns in questionnaire responses, reporting a clear and stable separation in perception patterns when grouped by gender that arises from structured combinations of factors rather than isolated responses, while also identifying key contributors related to engagement and instructional design.

Significance. If the reported separation holds, the work contributes to mathematics education research by providing evidence of systematic gender-linked differences in how students experience flipped classrooms and by illustrating the use of interpretable ML methods with stability checks. The manuscript supplies standard survey administration details, sample sizes per semester, repeated cross-validation, and explicit checks that single-question effects do not drive the separation; these elements strengthen the reliability of the central claim.

minor comments (1)

[Abstract] Abstract: the abstract does not state the total sample size or number of semesters surveyed, which would allow readers to immediately gauge the scale of the study.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review, the recognition of our stability checks and sample details, and the recommendation to accept. The assessment aligns with our goals of demonstrating interpretable ML for identifying structured gender-linked perception patterns in flipped linear algebra classrooms.

Circularity Check

0 steps flagged

No significant circularity; empirical ML analysis is self-contained

full rationale

The paper applies gradient-boosted trees with SHAP values and repeated cross-validation to survey responses on flipped-classroom perceptions. No derivation chain, fitted parameters renamed as predictions, or self-citation load-bearing steps exist. The reported gender-linked separation is an output of the model on external data, not a quantity defined in terms of itself or forced by prior author work. Standard survey and modeling practices are described without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no concrete free parameters, axioms, or invented entities can be extracted; the analysis presumably relies on standard ML assumptions such as i.i.d. responses and the validity of gender as a binary grouping variable.

pith-pipeline@v0.9.0 · 5648 in / 1065 out tokens · 19175 ms · 2026-05-24T06:44:07.815842+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

Talbert, R. (2014). Inverting the linear algebra classroom. Primus 24(5): 361–374

work page 2014
[2]

Love, B., Hodge, A., Grandgenett, N., & Swift, A. W. (2014). Student learning and perceptions in a flipped linear algebra course. International Journal of Mathematical Education in Science and Technology 45(3): 317–324

work page 2014
[3]

M., & Suaray, K

Murphy, J., Chang, J. M., & Suaray, K. (2016). Student performance and attitudes in a collaborative and flipped linear algebra course.International Journal of Mathematical Education in Science and Technology 47(5): 653–673

work page 2016
[4]

Novak, J., Kensington-Miller, B., & Evans, T. (2017). Flip or flop? Students’ perspectives of a flipped lecture in mathematics. International Journal of Mathematical Education in Science and Technology 48(5): 647–658

work page 2017
[5]

Nasir, M. A. M., Alaudin, R. I., Ismail, S., Ali, N. A. T. M., Faudzi, F. N. M., Yusuff, N., & Pozi, M. S. M. (2020). The effectiveness of flipped classroom strategy on self-directed learning among undergraduate mathematics students. Practitioner Research 2: 61–81

work page 2020
[6]

Karjanto, N., & Simon, L. (2019). English-medium instruction Calculus in Confucian-Heritage Culture: Flipping the class or overriding the culture? Studies in Educational Evaluation 63: 122– 135

work page 2019
[7]

Karjanto, N., & Acelajado, M. J. (2022). Sustainable learning, cognitive gains, and improved atti- tudes in College Algebra flipped classrooms. Sustainability 14(19): 12500

work page 2022
[8]

Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning 20: 273–297

work page 1995
[9]

Noble, W. S. (2006). What is a support vector machine? Nature Biotechnology 24(12): 1565–1567

work page 2006
[10]

Suthaharan, S. (2016). Support vector machine. In Machine Learning Models and Algorithms for Big Data Classification: Thinking with Examples for Effective Learning . Integrated Series in In- formation Systems, 36: 207–235. Boston, MA, US: Springer. 4 Appendix: Brief Survey of Flipped Learning in Introductory Linear Algebra Instruction: Please respond to t...

work page 2016

[1] [1]

Talbert, R. (2014). Inverting the linear algebra classroom. Primus 24(5): 361–374

work page 2014

[2] [2]

Love, B., Hodge, A., Grandgenett, N., & Swift, A. W. (2014). Student learning and perceptions in a flipped linear algebra course. International Journal of Mathematical Education in Science and Technology 45(3): 317–324

work page 2014

[3] [3]

M., & Suaray, K

Murphy, J., Chang, J. M., & Suaray, K. (2016). Student performance and attitudes in a collaborative and flipped linear algebra course.International Journal of Mathematical Education in Science and Technology 47(5): 653–673

work page 2016

[4] [4]

Novak, J., Kensington-Miller, B., & Evans, T. (2017). Flip or flop? Students’ perspectives of a flipped lecture in mathematics. International Journal of Mathematical Education in Science and Technology 48(5): 647–658

work page 2017

[5] [5]

Nasir, M. A. M., Alaudin, R. I., Ismail, S., Ali, N. A. T. M., Faudzi, F. N. M., Yusuff, N., & Pozi, M. S. M. (2020). The effectiveness of flipped classroom strategy on self-directed learning among undergraduate mathematics students. Practitioner Research 2: 61–81

work page 2020

[6] [6]

Karjanto, N., & Simon, L. (2019). English-medium instruction Calculus in Confucian-Heritage Culture: Flipping the class or overriding the culture? Studies in Educational Evaluation 63: 122– 135

work page 2019

[7] [7]

Karjanto, N., & Acelajado, M. J. (2022). Sustainable learning, cognitive gains, and improved atti- tudes in College Algebra flipped classrooms. Sustainability 14(19): 12500

work page 2022

[8] [8]

Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning 20: 273–297

work page 1995

[9] [9]

Noble, W. S. (2006). What is a support vector machine? Nature Biotechnology 24(12): 1565–1567

work page 2006

[10] [10]

Suthaharan, S. (2016). Support vector machine. In Machine Learning Models and Algorithms for Big Data Classification: Thinking with Examples for Effective Learning . Integrated Series in In- formation Systems, 36: 207–235. Boston, MA, US: Springer. 4 Appendix: Brief Survey of Flipped Learning in Introductory Linear Algebra Instruction: Please respond to t...

work page 2016