Learning Changes Following a Structured Metacognitive Intervention among Lower-Performing Undergraduate Students in Calculus Limits

Xiaoxia Liu, Sian Hoon Teoh, Geethanjali Narayanan, Walton Wider, Xiaoai Zeng
Pages 2829-2844
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DOI https://doi.org/10.47738/jads.v7i4.1481

Abstract


This study examined within-student learning changes during a six-week structured metacognitive intervention among 46 lower-performing undergraduate students studying calculus limits. Participants were identified using a pragmatic, cohort-relative bottom 30% screening rule and completed content-matched 100-point achievement forms in a one-group pretest-posttest design. Mean achievement increased from 34.70 (SD = 19.56) to 59.54 (SD = 18.12), representing a mean gain of 24.85 points, t(45) = 8.27, p < .001, dz = 1.22. Absolute point gains differed significantly across low-, medium-, and high-difficulty categories, F(2, 90) = 13.87, p < .001, partial η² = .24. Medium-difficulty absolute gains exceeded low- and high-difficulty gains, whereas low- and high-difficulty gains did not differ significantly. Because response-format score maxima differed between forms, scores were normalized to percentages of the available maximum. Percentage-point gains differed significantly across multiple-choice, true-false, and short-answer formats after Greenhouse-Geisser correction, F(1.74, 78.18) = 8.07, p = .001, partial η² = .15. Short-answer gains exceeded those for multiple-choice and true-false formats, whereas the latter two did not differ significantly. Completion time increased significantly by 16.87 minutes, whereas the score-time ratio showed no statistically significant change. These findings characterize within-student performance changes rather than causal treatment effects, as maturation, repeated testing, concurrent instruction, instructor-related influences, and regression to the mean remain plausible alternative explanations. Planning, monitoring, evaluation, cognitive load, and implementation fidelity were not directly measured. Controlled studies incorporating direct process measures, prospective fidelity assessment, and psychometrically calibrated achievement forms are needed to test efficacy and proposed mechanisms.


Keywords


Metacognitive Scaffolding; Calculus Limits; Lower-Performing Students; Self-Regulated Learning; Mathematics Achievement; Time-On-Task; Education Quality

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References


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DOI: https://doi.org/10.47738/jads.v7i4.1481

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