<![CDATA[This study investigated the effectiveness of the Problem-Based Learning with GeoGebra (PBL-GeoGebra) model in teaching systems of linear equations in two variables with respect to students’ mathematical reasoning and self-efficacy. Specifically, this study examines: 1) the simultaneous effectiveness of the PBL-GeoGebra model on students’ mathematical reasoning and self-efficacy, and 2) the difference in effectiveness between the PBL-GeoGebra and expository models. This quasi-experimental study employed a nonequivalent control group design involving Grade 10 students at a public senior high school in Sleman, Indonesia. The test instruments consisted of mathematical reasoning tests, self-efficacy questionnaires, and observation sheets. The data were analyzed using descriptive statistics and Hotelling's Trace MANOVA. The results at a significance level of revealed that: 1) the PBL-GeoGebra model was simultaneously effective in improving students’ mathematical reasoning and self-efficacy ( ; and 2) there was a significant difference in effectiveness between the PBL-GeoGebra and the expository models ( ), with the experimental group demonstrating better mathematical reasoning and self-efficacy than the control group. These findings suggest that the PBL-GeoGebra model is more effective than the expository and support the integration of GeoGebra into PBL to enhance students’ mathematical reasoning and self-efficacy.]]>
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