Deep Learning-Based Project Based Learning on Orthogonal Vector Projection to Enhance Students' Mathematical Problem-Solving Ability and Creativity Assisted by GeoGebra

Abstract

This study investigates the implementation of a Deep Learning-based Project Based Learning (PBL) model integrated with GeoGebra to enhance Grade XI students' mathematical problem-solving ability (PSA) and creativity at MAN 1 Indramayu, West Java, Indonesia. Employing a mixed-method pre-experimental one-group pretest-posttest design (N=26), data were gathered through a Polya-based PSA test (Cronbach's α=0.87), a 24-indicator structured observation sheet across four dimensions, and qualitative analysis of students' GeoGebra project products assessed using Torrance's (1966) four-dimension creativity rubric. Inferential analyses included Shapiro-Wilk normality test, Levene's homogeneity test, Wilcoxon Signed Ranks Test, Hake's (1999) N-Gain analysis, and Spearman's rho correlation. Results show: (1) a statistically significant improvement in PSA (Wilcoxon, Z=−4.46, p<0.001; mean N-Gain=0.691; 88.5% of students in moderate-to-high category); (2) GeoGebra functioned as a cognitive bridge facilitating rich problem representation, with the GeoGebra Exploration dimension recording the highest engagement score (76.1%); (3) mathematical creativity across all four Torrance dimensions developed substantially, with originality most prominent; and (4) a very strong positive correlation between PSA and mathematical creativity (Spearman's rho=0.934, p<0.001). These findings empirically confirm the synergistic effectiveness of integrating PBL, Deep Learning analytics, and GeoGebra in secondary mathematics education and contribute to the empirical literature on creativity-problem-solving reciprocity.