REVIEW 2 major objections 5 minor 11 references
Pre/Post-Assessment Cycles in Calculus: Supporting Student Preparation, Reflection, and Learning
T0 review · 2 major / 5 minor · reviewed 2026-07-13 · grok-4.5
Pith's one-line read Semester-long pre/post-assessment cycles give Calculus I students a regular way to preview units, get feedback, and reflect before high-stakes exams.
desk verdict A clear, modest classroom study that documents a usable semester-long pre/post routine in honors Calculus I; the gains and quotes are real, the causal claim is already disclaimed, and the main limits are sample and missing materials. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The pre/post-assessment cycle: a brief online pre-quiz before each major unit (completion credit, solutions returned immediately), paired post-questions on the existing in-person discussion quizzes after the unit, and short reflection prompts on learning, remaining challenges, and change in understanding.
What would settle it
A multi-section comparison or controlled implementation in which matched Calculus I sections that lack the pre/post cycles show the same pre-to-post gains, participation patterns, and student self-monitoring reports as sections that use them.
Extended reading notes
Core claim
Repeated pre/post-assessment cycles, run as low-stakes online previews graded for completion, related post-questions on regular discussion quizzes, and brief reflections, can be integrated into Calculus I so that students preview upcoming ideas, receive feedback, revisit key concepts, and monitor progress, while giving the instructor timely information to adjust instruction; the study reports full participation, significant pre-to-post gains across all six units, and student comments that the cycles supported preparation and self-monitoring.
Load-bearing premise
That the measured gains and student reports can be meaningfully linked to the assessment cycles as a formative structure rather than mainly to ordinary instruction, homework, discussion quizzes, and the selection effects of a single small honors section with no control group.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports a semester-long implementation of pre/post-assessment cycles in one honors Calculus I section (n=43). Six online Canvas pre-assessments (completion credit, 5% of grade) previewed each major unit; related post-assessment items were embedded in the existing weekly discussion quizzes; short reflection prompts asked students what they learned, what remained hard, and how understanding changed. Quantitative results show 100% participation, overall pre mean 69.86% rising to post mean 88.61% (paired t=9.45, p<0.001, Cohen’s d=1.44), significant gains in all six units (largest in Unit 4), and reduced score variance after instruction. Qualitative student comments indicate that previews clarified upcoming material and current knowledge. The author frames the work as a practical formative model rather than a causal claim, notes the absence of a control group, and discusses instructor use of pre-results for real-time instructional adjustment.
Significance. If the descriptive account holds, the paper supplies a concrete, low-overhead template for embedding repeated low-stakes pre/post cycles and reflection into the ordinary rhythm of a multi-section Calculus I course. The design choices—online completion-graded pre-quizzes, reuse of existing discussion quizzes for post-items, and explicit reflection—address practical barriers (instructional time, grading load, student buy-in) that often limit formative assessment in large lower-division mathematics. The unit-by-unit tables and instructor-use examples give other instructors a usable starting point. The contribution is modest and practice-oriented rather than theoretical, but it is well-aligned with the needs of undergraduate mathematics education and builds usefully on the author’s earlier single-unit real-analysis pilot.
major comments (2)
- Conclusion §8 asserts “a positive relationship between post-assessment performance and exam performance,” yet §5.1 only states that correlations with exams were computed; no coefficient, p-value, or table is reported. Either supply the correlation results (or a brief summary) or remove the claim so that the conclusion stays within the data actually presented.
- §5.1.2 and Table 2 report large unit-level gains (especially Unit 4, d=1.55) and interpret them as evidence that the cycles helped identify weaker prior knowledge. Because the post-score for each unit is the average of two ordinary discussion-quiz percentages that already count toward the grade, the design cannot separate the contribution of the pre/post cycle from ordinary instruction and quiz practice. The Discussion already notes that improvement after instruction is expected; the unit-level narrative should be tightened to the same non-causal framing so that readers do not over-read the t-tests.
minor comments (5)
- §5.1: the sentence “The effect size was large…” is missing a space before “The standard deviation…”; a minor copy-edit.
- Table 1 and Table 2: report exact p-values or at least “p < .001” consistently; the current mixed presentation is slightly uneven.
- §4.2 and §5.2: a short example of an actual pre-assessment item (or a brief description of item types) would help readers judge how diagnostic the previews really were.
- References: the 2025 arXiv pilot is cited; once that work is published, update the citation for archival stability.
- §3.2: the distinction from knowledge surveys is clear, but a single sentence noting that students answered mathematical items rather than confidence ratings alone would further clarify the design choice.
Circularity Check
No circularity: descriptive education study with no derivation chain that reduces by construction to its inputs.
full rationale
This is a classroom implementation paper in undergraduate mathematics education (math.HO). It reports participation rates, pre/post percentage scores, paired t-tests, Cohen's d, and student reflection quotes from one honors Calculus I section. There is no mathematical derivation, no fitted parameter renamed as a prediction, no uniqueness theorem, and no ansatz. The self-citation to Gamage (2025) is only background describing a prior single-unit pilot; the Calculus I results (Tables 1–2, 100% completion, unit gains) are independent gradebook data collected in the present course and do not reduce to that citation. Discussion §6 and Limitations §7.1 already state that post-instruction improvement is expected and that causation is not claimed. The paper is self-contained against its own data; score 0 is the correct outcome.
Assumptions & free parameters
assumptions (4)
- domain assumption Formative assessment and feedback can improve teaching and learning when used during instruction (Black & Wiliam 1998; Sadler 1989).
- ad hoc to paper Low-stakes completion-graded pre-assessments still elicit meaningful student engagement, so pre-scores are informative about readiness.
- domain assumption Results from one honors section of 43 students can illustrate a practical model even without a control group.
- ad hoc to paper Averaging two related discussion-quiz percentages yields a valid post-assessment score for each unit.
Cite this review
Pith. "Pith review of Pre/Post-Assessment Cycles in Calculus: Supporting Student Preparation, Reflection, and Learning." pith.science (2026). https://pith.science/paper/EGOGB7FC
@misc{pith2026260709448,
author = {Pith},
title = {Pith review of: Pre/Post-Assessment Cycles in Calculus: Supporting Student Preparation, Reflection, and Learning},
year = {2026},
howpublished = {\url{https://pith.science/paper/EGOGB7FC}},
note = {Machine review of arXiv:2607.09448}
}
read the original abstract
This article describes a semester-long implementation of pre/post-assessment cycles in an undergraduate Calculus I course. The activity was designed to address a common difficulty in lower-division mathematics courses: students often enter a new unit without knowing which prior ideas are relevant, which concepts deserve special attention, or how to judge their own progress before high-stakes exams. Brief pre-assessments were administered before major course units, and related post-assessment questions revisited key ideas after instruction. Students also completed short reflection prompts about what they learned, what remained challenging, and how their understanding changed. The paper analyzes student performance data, participation patterns, and reflective responses to examine how these cycles supported preparation, reflection, and learning. The study contributes a practical model for embedding low-stakes assessment and reflection into the regular structure of an undergraduate mathematics course.
Reference graph
Works this paper leans on
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[1]
A., & Cross, K
Angelo, T. A., & Cross, K. P. (1993). Classroom assessment techniques: A handbook for college teachers (2nd ed.). Jossey-Bass
1993
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[2]
Bermudez, H., & Graysay, D. (2025). Supporting students in exploring, developing, and formalizing mathematical arguments. PRIMUS, 35(1), 102–133. https://doi.org/10.1080/10511970.2024.2445517
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[3]
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education:
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[4]
https://doi.org/10.1080/0969595980050102
Principles, Policy & Practice, 5(1), 7–74. https://doi.org/10.1080/0969595980050102
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[5]
Gamage, C. M. (2025). Impact of Pre-Assessment and Post-Assessment in an Introductory Real Analysis Course. arXiv preprint arXiv:2505.22479
arXiv 2025
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[6]
Jaafar, R., & Lin, Y. (2017). Assessment for learning in the calculus classroom: A proactive approach to engage students in active learning. International Electronic Journal of Mathematics Education, 12(3), 503–520. https://doi.org/10.29333/iejme/628
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[7]
Karaali, G. (2018). On grades and instructor identity: How formative assessment saved me from a midlife crisis. PRIMUS, 28(9), 848–874. https://doi.org/10.1080/10511970.2018.1456495
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[8]
Nicol, D. J., & Macfarlane-Dick, D. (2006). Formative assessment and self-regulated learning: A model and seven principles of good feedback practice. Studies in Higher Education, 31(2), 199–218. https://doi.org/10.1080/03075070600572090
Show all 11 references
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[9]
Nuhfer, E., & Knipp, D. (2003). The knowledge survey: A tool for all reasons. To Improve the Academy, 21(1), 59–78. https://doi.org/10.1002/j.2334-4822.2003.tb00381.x
2003 doi
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[10]
A., & Oehrtman, M
Reed, Z., Tallman, M. A., & Oehrtman, M. (2023). Assessing productive meanings in calculus. PRIMUS, 33(9), 939–964. https://doi.org/10.1080/10511970.2023.2222302 21
2023 doi
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[11]
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional Science, 18(2), 119–144. https://doi.org/10.1007/BF00117714 Declaration Funding: This research received no external funding. Conflicts of Interest: The author declares that there ...
1989 doi
Reviewed July 13, 2026 · model on record in the stance chip above.
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