Mathematical Critical Thinking in Trigonometry Under E-Module-Supported Project-Based Learning: An Explanatory Sequential Study Across Self-Reported Modality Preferences
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Mathematical critical thinking (MCT) involves interpreting information, analyzing relationships, evaluating procedures, inferring conclusions, explaining reasoning, and regulating problem solving. This study examined pretest-posttest changes in MCT during e-module-supported Project-Based Learning (PjBL) in trigonometry and explored variation across self-reported Visual, Auditory, and Kinaesthetic (VAK) preferences. A quantitatively driven explanatory sequential mixed-methods design was used with Grade XI students at a public senior high school in Cirebon Regency, West Java, Indonesia. From 180 students screened, 72 were included in the quantitative sample (n = 24 per VAK group). Students completed an MCT pretest and posttest around six 90-minute PjBL sessions. Qualitative follow-up used interviews with 12 purposively selected students, classroom observations, and student artifacts. Mean MCT scores increased from 43.95 (SD = 6.26) to 78.18 (SD = 5.77); the mean within-student change was 34.23 points, 95% CI [32.26, 36.20], t(71) = 34.66, p < 0.001, Cohen's dz = 4.08. All six MCT dimension indicators showed statistically significant pretest-posttest changes after false-discovery-rate adjustment. No statistically significant differences were detected among VAK groups for posttest MCT or normalized gain, and ANCOVA controlling for pretest performance yielded the same inferential conclusion. Qualitative analysis identified overlapping patterns of visualization, verbalization, digital manipulation, trial-and-check reasoning, peer discussion, and reflection. The integrated findings document marked within-student change alongside heterogeneous reasoning processes, but the single-group design precludes causal attribution of the observed changes to PjBL or the e-module.
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