Analysis of students’ understanding of mathematical concepts in the Faraid calculation using modulo arithmetic theory

Abstract

This study aims to determine students' mathematical understanding of the modulo arithmetic concept, the Faraid concept, and the modulo arithmetic application in Faraid calculations. This study employs a combination research method (mixed methods) with Sequential Explanatory Design model in which the quantitative data analysis is supported by qualitative data analysis. Data collection techniques consist of test questions and interviews for sixth semester students of the Mathematics Education Study Program, the Faculty of Tarbiyah, Universitas Ibrahimy, Situbondo, Indonesia. The initial data analysis consists of the Normality Test and the Paired Samples Test. The second data analysis entails research subject selection, data reduction, data presentation, and conclusion. The findings show that: (1) the average value of understanding the modulo arithmetic concept is 84,100, while the average value of understanding Faraid concept is 83,500; (2) the statistical results show the significance of Sig. (2-tailed) is 0.016<0.05 and 0.014<0.05; it can be concluded that there is a significant difference in the results of the mathematical concept understanding test between the concept of modulo arithmetic theory and the application of the modulo arithmetic concept to Faraid calculations, and the Faraid concept with the application of the modulo arithmetic concept to Faraid calculations; (3) the second analysis is the interview, which is divided into three categories: high, medium, and low. The result of the interview is students' understanding of mathematical concepts through the use of modulo arithmetic theory as a new alternative method of solving Faraid calculations.