Exploring High School Students' Mathematical Reasoning in Geometry Using GeoGebra-Assisted Problem-Based Learning

Abstract

The significance of mathematical reasoning in mathematics instruction and the substantial incidence of inadequate mathematical reasoning among high school students prompted this study. This study intends to explore the mathematical reasoning of high school students about three-dimensional geometry using the GeoGebra-assisted Problem-Based Learning (GPBL) model. This research applied a quasi-experimental design including a non-equivalent pretest and posttest control group. The subjects of this research were specifically 12th-grade students from an upper secondary school in Subang. The research contained two classes, with 27 students as the experimental group and 27 as the control group. Interviews were conducted to identify the factors that explain students' difficulties in solving mathematical reasoning problems concerning three-dimensional geometry. The findings indicated that (1) overall, the enhancement of mathematical reasoning among students utilizing the GPBL model was significantly higher than that of students implementing the conventional learning model; (2) referring to students' prior mathematical ability (PMA), the enhancement in mathematical reasoning for students in high, medium, and low PMA groups utilizing the GPBL model was significantly higher than that of students implementing the conventional learning model; (3) the main obstacle discovered by students to solving mathematical reasoning problems involving three-dimensional geometry is their struggle in visualizing problems in a three-dimensional context. GeoGebra assists students in visually constructing three-dimensional geometry problems and evaluating the outcomes of algebraic algorithms with 3D graphical representations.

Keywords

• Mathematical Reasoning
• Geometry
• Problem-Based Learning
• GeoGebra
• Prior Mathematical Ability