Improving university students’ geometrical understanding of derivatives through graphic visualization
DOI:
https://doi.org/10.29408/jel.v12i1.33325Keywords:
calculus, derivative concepts, geometrical thinking, graphic visualization, mathematical representationAbstract
This study addresses university students’ persistent difficulties in developing geometrical thinking, defined as the ability to interpret slopes, understand tangent behavior, and coordinate graphical and symbolic representations, when learning derivative concepts. The study investigates changes in students’ geometrical thinking following instruction supported by graphic visualization. A one-group pretest–posttest quasi-experimental design was conducted with 30 students in mathematics education, limiting causal inference due to the absence of a control group. Data were collected using a six-item open-ended geometrical thinking test and structured classroom observations, which served as triangulation. The results showed significant improvement after the visualization-based instruction. The average pretest score increased from 48.12 to 67.51, with a normalized gain (N-gain) of 0.39, indicating moderate improvement. A paired-sample t-test confirmed a statistically significant difference (p < 0.001). Although the effect size was large (d = 4.17), this finding should be interpreted cautiously given the study design and sample size. Observation data supported these results by revealing improved graphical reasoning, representational coordination, and student engagement. These findings indicate the potential of graphic visualization to support students’ geometrical thinking in derivative learning, rather than to demonstrate definitive instructional effectiveness.
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