No abstract

The purpose of this study is to describe students' mathematical reasoning abilities in solving non-routine problems in terms of learning styles. The type of research used is descriptive with qualitative data. The research subjects were students of class XI IPA. The instruments used are questionnaires, non-routine test questions, and interviews. The data to be taken are data on questionnaires, test questions, and interviews. The data obtained will then be analyzed in a descriptive-qualitative way. The results of this study are that 11th-grade students of MA Muhammadiyah 1 Plus Malang, have several learning styles, namely: visual, kinesthetic, and auditory, respectively: 67%️, 25%️, and 8%. Students with visual learning styles have fairly high reasoning abilities by meeting indicators such as 1) being able to present and make mathematical statements in writing well 2) being able to manipulate y-values, and 3) compiling solutions to existing problems. While students with kinesthetic learning styles, students meet reasoning ability indicators, including 1) writing mathematical statements well, and 2) manipulating target functions, then students with auditory learning styles only have one indicator of reasoning ability, namely: 1) creating and finding solutions to trouble well.

Mathematical representation is an idea interpretation form of solving mathematical problems. The process of mathematical representation is essential to pay attention to, especially in carrying out transformations between forms of representation, because it impacts the final solution obtained. This study describes the flow of students' thinking in carrying out the transformation process from visual to symbolic representation. This descriptive research was carried out with a qualitative approach. This research phase includes preparing representation tests and interview guidelines, giving tests to 48 students, conducting interviews with selected students based on the accuracy of the mathematical representations produced, and evaluation. The evaluation is carried out by reducing the results of the incorrect representation test, presenting visual and symbolic representation data and the transformation process, and concluding the transformation process. The result of the transformation process from visual to symbolic representation in solving the problem of the area under the curve is carried out with a flow of thought, namely translating the shape of the polygon area into a collection of rectangles, determining the width and length of the partition of the polygon area, and determining the area of the polygon area as a collection of rectangles. In determining the area as a collection of rectangles, there are two different processes, making a mathematical model in the form of sigma notation and addition. This study provides insight into the flow of thinking in changing between forms of mathematical representation in the hope that it can anticipate errors in solving the broad problem under the curve.