The profile of mathematical belief of class X students in solving mathematical problems on the material of linear equations and inequalities in one variable with absolute value

Abstract

An effective ability that is very important in supporting students’ learning success in mathematics is mathematical belief. In this study, the profile of students’ mathematical beliefs in solving mathematical problems was investigated, especially in solving mathematical problems on the material of linear equations and inequalities in one variable with absolute value. The research subjects consisted of three students of class X SMKN 8 Malang who respectively were students with low, middle, and high cognitive abilities. Data collection techniques are tests, questionnaires, interviews, and documentation. The data analysis technique uses the steps: data reduction, data presentation, and concluding by checking the validity of the data. Students’ mathematical belief profiles were analyzed based on aspects of mathematical belief by (1): mathematical belief in mathematics education, self, and social context. The results showed as follows: (1) The mathematical beliefs of students with low cognitive abilities were as follows: (a) mathematical beliefs about mathematics education: students who could not understand problems with good, students do not follow the learning in class well and tend to just open the book of learning materials; (b) mathematical confidence in themselves: students can’t plan and make solutions well, students open literature during problem solving; (c) mathematical belief in the social context: students cannot convey the conclusion of the answer, there is a dissonance between students’ beliefs about the solution and the final result; (2) The mathematical beliefs of students with middle cognitive abilities are as follows: (a) mathematical confidence in mathematics education: students can understand problems well, students follow learning in class well, students can solve problems, mathematical confidence in themselves: students can plan completion and realizing it quite well, in working on the problem, students tend to follow the rote pattern of their learning outcomes with the teacher in, (c) students’ mathematical confidence in the social context: there is a synchronization of students’ beliefs about completion with the final result, carried out by means of re-examination; (3) Students’ mathematical beliefs with high cognitive abilities: (a) students’ mathematical beliefs about mathematics education: students can understand problems well, students follow class lessons well and increase their knowledge by learning through other media; (b) mathematical confidence in themselves: students can plan the solution of the problem and realize it well, but have doubts about the correctness of the solution and the final result given; (c) mathematical confidence in the social context: there is a synchronization between students’ beliefs about the problem-solving process and the final results, students can convey conclusions and answers with fairly basic reasons, but do not re-examine so that doubts arise about some of the solutions and final results in their work.