Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability

Abstract

Non-Euclidean geometry is an abstract subject and difficult to learn, but mandatory for students. The ethnomathematics approach as a learning approach to improve students’ spatial abilities. The aim of this research is to discover new elements of the spatial abilities of non-Euclidean geometry; determine the relationship between spatial abilities for Euclid, Lobachevsky, and Riemann geometry. This study used the micro genetic method with a 2×2 factorial experimental research design. The sample of this research is 100 students of mathematics education. There are three valid and reliable research instruments through expert trials and field trials. Data collection was carried out in two ways, namely tests and observations. Quantitative data were analyzed through ANCOVA, and observational data were analyzed through the percentage of implementation of the learning trajectory stages. The result is that the spatial ability of students who are given the ethnomathematics learning approach is higher than students who are given the conventional learning approach for Lobachevsky geometry material after controlling for the effect of Euclidean geometry spatial ability. Also, the same thing happened for the spatial abilities of Riemann geometry students. The learning trajectory is conveying learning objectives (learning objective); providing ethnomathematics-based visual problems; students do exploration; students make conclusions and summaries of exploration results; and ends with students sharing conclusions/summaries about concepts and principles in geometric systems. It was concluded that learning non-Euclid geometry through learning paths with an ethnomathematics approach had a positive impact on increasing students’ spatial abilities.