The Difficulty of Students’ Reflective Thinking in Problems Solving o f Linear Program

The identification in this study with the aim is to describe how difficult it is for students to think reflectively when solving math problems, especially in linear programming material. Based on the purpose of this study, the type of research is qualitative with a descriptive exploratory approach. Data collection techniques used are: (1) test instruments; (2) interview instruments, and 3) documentation. Analysis of research data namely: (1) research data reduction, (2) data exposure, (3) data triangulation, and (4) drawing conclusions. The subjects in this study were 24 high school students. Then 2 students were selected as subjects for each category (high, medium, and low). The results of the study show that students with high mathematical abilities have difficulty in reflecting, namely, 1) difficulty connecting new information with previous understanding, so they are not careful when identifying stories in the form of mathematical models, 2) difficulties in aspects of finding relationships and formulating solutions, students mistake the sign of linear inequality two variables, 3) difficulty in evaluating aspects of the completion process, students find it difficult to recall the function graph material to solve problems using the graphical method. Students with moderate mathematical abilities, namely: 1) difficulties in the aspect of connecting new knowledge with previous understanding, students need to be careful in solving contextual problems, 2) difficulties in aspects of finding relationships and formulating solutions, students have difficulty recalling function graph material, difficult to shade the area of settlement, 3) difficulties when students evaluate the completion process. Students find it difficult to prove whether the answer is correct or not by using the graphical method. Students with low mathematical ability, 1) difficulties in the aspect of connecting new knowledge with previous understanding, students find it difficult to translate story problems into mathematical models, it is difficult to recall the material of a two-variable linear inequality system, 2) difficulties in the aspect of finding relationships and formulating solutions, students have difficulty finding coordinates, drawing graphs, finding intersection points, substituting corner points into the objective function. 3) difficulties in evaluating aspects of the completion process, students find it difficult to prove the correctness of the answers obtained by the graphical method. The difficulties experienced by students in reflective thinking were caused by students not remembering previous material related to linear programming, as well as students’ difficulties in the dimensions of fact, concept and procedural knowledge.


Introduction
Education plays an important role in human life, with education and technological advances as well as the current developments; education is needed in all aspects.Along with the advancement of technology and the development of the times, it demands an increase in human resources in order to achieve an advanced and prosperous nation.Tatang (2012, p. 14) Education is an effort that is carried out deliberately and systematically to motivate, foster, assist, and guide a person to develop all potential so that he achieves better quality himself.This is in accordance with the law on the National Education System.

Republic of Indonesia Law Number 20 of 2003 concerning the National Education System Chapter 1 Article 1
Paragraph 1, education is a conscious and planned effort to create an atmosphere of learning and learning so that students actively develop their potential to have religious spiritual strength, self-control, personality, intelligence, noble character, and skills needed by himself, society, nation and state in an effort to develop his academic potential.Learning is one of everyone's activities to get changes in behavior, both in the form of knowledge, skills, attitudes and positive values as an experience from various materials that have been studied.It is often found that students who find it difficult to learn material at school are in mathematics.Mathematics is one of the subjects that play an important role in the world of education.According to Chotimah (2016, pp. 99-100), mathematics is one of the subjects taught at every level of school, both at the elementary, secondary and higher education levels.Hudojo (Ariestyan, 2016, p. 96), the process of learning mathematics occurs as a thinking process, because someone is said to think if they do mental activities.One of the thinking processes that help students to recall previous material in order to solve a given problem is reflective thinking.Sezer (Suharna, 2018, p. 6), states that reflective thinking is awareness to know what information will be used in solving problems.Utami et al. (2020, pp. 36-37), students are said to have high reflective thinking skills if they meet the criteria of reflective thinking indicators including: 1) Being able to link new knowledge with previous understanding.2) Be able to find relationships and formulate solutions.3) Evaluate the completion process.
Based on the results of the interviews that the researchers conducted with the mathematics teacher as well as the homeroom teacher for class XI IPA 1, the results of the interviews obtained that in learning mathematics, especially in linear programming material, students had difficulty translating story problems into mathematical models which caused students to be unable to solve the problems, given on the other hand if the mathematical model is known there are still students who find it difficult to make graphs, determine the area of the set of solutions, and find it difficult to find the optimum value.Widdiharto (Firiani, 2018, pp. 140-141) states that difficulties in mathematics are characterized by not remembering one or more terms of a concept.It is necessary to pay attention to the difficulties experienced by students in solving the given linear programming problems.It is hoped that by knowing the difficulties experienced by students in every aspect, namely the aspect of connecting new knowledge with previous understanding, the aspect of finding relationships and formulating solutions and aspects of evaluating the completion process.Students experience difficulties when solving linear programming questions because there are several difficulties experienced by students namely, in the dimensions of factual knowledge, conceptual and procedural knowledge dimensions

Research Method
This type of research is a qualitative descriptive research.According to Bogdan and Taylor (Prastowo, 2016, p. 23), qualitative methodology is a research procedure that produces qualitative descriptive data in the form of written or spoken words from people and the observed behaviour.Next to determine the level of mathematical ability based on criteria.This grouping of reflective thinking difficulties is based on students' mathematical abilities acquired, so that the grouping is based on the criteria used by Marurotulaily, Horbi, and Suharto (Utami et al., 2020, p. 37), namely three levels.The data collection techniques in this study were test instruments, interviews and documentation, as well as the analytical techniques used, namely data reduction, data exposure, data triangulation, and drawing conclusions.

Results and Discussion
Based on the results of students' mathematical reflective thinking difficulty tests based on the mathematical abilities of 24 students in class XI IPA 1 SMA Negeri 5 Ternate City, it was shown that students who obtained the lowest scores were (7.14) and students who obtained the highest scores were (92,85).This study analyzed the difficulties experienced by students with high, medium and low mathematical abilities according to the indicators of mathematical reflective thinking, namely connecting new knowledge with previous understanding, finding relationships and formulating solutions and evaluating the completion process. Figure