<![CDATA[This study aims to determine the effectiveness of the Guided Discovery Learning (GDL) model integrated with the Numbered Heads Together (NHT) cooperative approach in improving students’ mathematical problem-solving ability and student engagement. Effectiveness in this research is operationally defined as a statistically and practically significant improvement in students’ scores and engagement compared to conventional learning. This research employed a quasi-experimental design with a nonequivalent control group. The participants were three intact eighth-grade classes at SMPN 1 Jetis Bantul, selected via cluster random sampling. Class VIII A was taught using GDL combined with NHT, class VIII D used GDL without group work, and class VIII B used conventional learning. Data were collected through a mathematical problem-solving test and a student engagement scale, both validated by experts and tested for reliability. Data analysis used One-Way ANOVA followed by a Tukey HSD post hoc test and Kruskal–Wallis to determine significant mean differences among the three groups, complemented by effect size interpretation to assess the magnitude of differences. The results revealed that the GDL with the NHT model was significantly more effective than conventional learning in improving students’ mathematical problem-solving ability (p < 0.05, Cohen’s d = 0.86). However, there was no statistically significant difference between the GDL+NHT and GDL-only groups, indicating that adding NHT did not confer a significant cognitive benefit beyond the GDL model alone. In contrast, the NHT component meaningfully enhanced students’ engagement, particularly in participatory aspects such as oral, visual, and motor engagement, compared to both the GDL-only and conventional groups. The GDL model, either with or without NHT, effectively enhances students’ mathematical problem-solving ability and student engagement compared to conventional instruction. Future studies are recommended to examine this integration in broader contexts and longer durations to explore its potential for sustainable classroom engagement. Keywords: effectiveness, problem-solving ability, student engagement, guided discovery learning model with numbered heads together, quasi-experimental design.]]>
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