A Comparison of Student’s Mathematical Problem-Solving Ability between Realistic Mathematics Education Assisted by GeoSpace and Direct Instruction

Abstract

This study aims to compare the mathematical problem-solving skills between students who learn using  the Realistic Mathematics Education (RME) model assisted by the GeoSpace application and students who learn through direct learning. This study applies a quantitative method with a quasi-experimental design of the nonequivalent control group design. The research subject consisted of two entire classes at SMP Negeri 1 Jekulo. Class VIII C is designated as the treatment group, while class VIII D acts as a comparison group. The selection of the two classes was carried out through purposive cluster sampling because the researcher did not carry out a randomization process of the groups used. Thus, the generalization of the research results is limited to the context of the school and the class being studied. The research instrument in the form of an essay test was prepared referring to the indicators of mathematical problem-solving ability as formulated by NCTM (2000), which includes the ability to understand problems, plan strategies, implement solutions, and review results. Sample question items require students to model the contextual problem of building flat-sided spaces into mathematical representations. The validity of the content was tested by five experts with the results of Aiken's V = 0.87, internal reliability α = 0.82, and inter-rater reliability r = 0.74. Treatment is provided over six encounters with three main phases of RME learning, namely (1) exploration of realistic contexts, where students solve problems that are close to everyday life; (2) horizontal and vertical mathematicalization using GeoSpace applications to explore three-dimensional models and spatial relationships between building elements; and (3) reflection, when students discuss and review their solutions. GeoSpace itself is an Android-based learning application that facilitates 3D visualization, learning videos, interactive exercises, quizzes, and motivational videos, which help students in representing geometric concepts in a concrete way. Meanwhile, the control group received hands-on learning with teacher explanations and routine exercises without the help of digital media. Data analysis used a t-test of two independent samples to compare the posttest scores of the two groups. The average posttest of the RME + GeoSpace group was 68.30, higher than the control group of 55.45. The results of the t-test showed a significant difference, t(54) = 2.50; p < 0.05, with an effect size d = 0.61 (moderate category, CI 95% [0.14; 1.08]). An analysis of learning enhancement showed that  the N-Gain value of the  experimental group was g = 0.61 (medium category), while the control group g = 0.30 (low category), with significant differences (p = 0.008 < 0.05). These findings confirm that the application of GeoSpace-assisted RME models is more effective in improving mathematical problem-solving skills compared to hands-on learning. The improvement is due to a gradual mathematical process and interactive visual representations that facilitate students' conceptual understanding. However, the results of this study have limitations because they involve only two classes, so it has the potential to cause a clustering effect and a novelty effect. Therefore, further research is recommended to involve more schools or apply Hierarchical Linear Modeling (HLM) analysis to control for variation between classes and test replication of results more broadly.