Students' Mathematical Communication Skills in Terms of Concrete and Abstract Sequential Thinking Styles

Sequential S7, S8, S9, S10 4 Based on Table 3, the comparison of concrete sequential and abstract sequential was 2: 3. This indicated that the students had more concrete sequential thinking styles than abstract sequential thinking types. A mathematical communication skill test was conducted on four Al-Jabar: Jurnal Pendidikan Matematika Volume 11 Nomor 02 Lintang Fitra Utami, etc 375 research subjects, namely two students with concrete sequential thinking style type and two students with abstract sequential thinking style. 1. The Mathematical Communication Skills of Students' with Concrete Sequential Thinking Styles The following are the subjects S1 and S2's answers on the written text indicator. Figure 2. Subject S1's Answer on the Written Text Indicator Figure 3. Subject S2's Answer on the Written Text Indicator Based on Figure 2, subject S1 did not understand the questions, so that he did not answer the questions according to what was asked. Subject S1 answered the problem by finding the corner points then substituting them with the objective function. Subject S1 did not write down the x and y variables in the objective function. He also incorrectly chose the corner points that must be substituted; thus, the answer was wrong. Figure 3 shows the same thing as subject S1; subject S2 did not answer the problem by describing how to find the minimum cost. He also incorrectly substituted the corner points into the objective function by choosing the smallest cost. From the two answers, it was found that students with concrete sequential thinking style misunderstood the questions and unable to write entirely correct answers using their language. The following are the subjects S1 and S2's answers on the drawing indicator. Figure 4. Subject S1's Answer on the Drawing Indicator Figure 5. Subject S2's Answer on the Drawing Indicator Based on Figure 4, subject S1 could make a graph, although he incorrectly determined the shading area following the predetermined model. Subject S1 did not write down how to find the coordinate points. Figure 5 shows that subject S2 could render graphic images and Al-Jabar: Jurnal Pendidikan Matematika Volume 11 Nomor 02 Lintang Fitra Utami, etc 376 determine the shading area, but only partly correct. Subject S2 was wrong in determining the coordinate points according to the predetermined model and did not write down how to find the coordinate points to make the graph. From the answers obtained, the students could draw a picture, although but partly correct and incomplete. Here are the subjects S1 and S2's answers on mathematical expression indicators. Figure 6. Subject S1's Answer on the Mathematical Expression Indicators Figure 7. Subject S2's Answer on the Mathematical Expression Indicators Figures 6 and 7 show that subjects S1 and S2 could make mathematical models of the problems presented, but there were several errors in determining the sign of inequality. The errors might be because they only understood some of the problem's information, so they could not make mathematical models correctly. 2. The Mathematical Communication Skills of Students with Abstract Sequential Thinking Style The following are the subjects S7 and S8's answers on the written text indicator. Figure 8. Subject S7's Answer on the Written Text Indicator Figure 9. Subject S8's Answer on the Written Text Indicator Al-Jabar: Jurnal Pendidikan Matematika Volume 11 Nomor 02 Lintang Fitra Utami, etc 377 Figures 8 and 9 show that subjects S7 and S8 could write several steps in their language, although incomplete and unclear. It can be seen from the two students' answers where they did not write down the steps to find the intersection point of known inequalities and did not clearly write down what was substituted into the objective function. Here are the subjects S7 and S8's answers on the drawing indicator. Figure 10. Subject S7's Answer on the Drawing Indicator Figure 11. Subject S8's Answer on the Drawing Indicator Figure 10 shows that subject S7 could make graphic images wholly and correctly. It can be seen in the answers where he wrote how to determine the coordinate points of the known inequalities. Then, he entered the coordinate points into the graphic image and determined the shading area correctly. Figure 11 shows that subject S8 could draw a graph and determine the shaded area correctly, although the coordinate points were incomplete. Here are the subjects S7 and S8's answers on mathematical expressions indicators. Figure 12. Subject S7's Answer on the Mathematical Expression Indicators Figure 13. Subject S8's Answer on the Mathematical Expression Indicators Figure 12 shows that subject S7 could make a mathematical model of the problem correctly but incompletely. Subject S7 did not write the conditions for x and y in the mathematical model. Figure 13 shows that subject S8's answer was less careful in writing the inequality sign to the mathematical model.


Introduction
Education plays a vital role in equipping individuals to face global challenges or competition. Education in the 21 st -century requires students to have four competencies called 4C, namely critical thinking, collaboration, creativity, and communication. Fundamentally, learning is a process using communication skills. Communication skills are critical in learning mathematics because it enables the students to express ideas and reflect their mathematics understanding to others (Veva, Usodo, & Pramesti, 2018;Zahri, Budayasa, & Lukito, 2019).
National Council of Teachers of Mathematics (Oktari & Haji, 2018) states that mathematical communication skills are students' skills to use and communicate mathematics (mathematical language). According to Elliott and Kenney (Ratnaningsih, Hermanto, & Kurniati, 2019), mathematical communication skills consist of three aspects: writing, drawing, and mathematical expression. Writing skills are the ability to convey written mathematical ideas using one's language appropriately. The drawing skills are the ability to communicate mathematical ideas in pictures, graphs, tables, and diagrams. Mathematical expression skills can convey mathematical ideas or ideas in real situations into language, symbols, or mathematical models.
Based on the results of observations on July 21, 2020, it was found that many students had difficulty in solving problems. They were asked to come up with ideas on how to make proper plans to solve problems. However, many students made mistakes. The mistakes showed that their communication skills were lacking. Students with good communication skills can express ideas Students' different thinking styles affect their ideas communication method. Therefore, this study described the eleventh-grade science senior high school students based on concrete sequential and abstract sequential thinking styles. The material chosen in this study was the linear program. This study was different from the previous ones because it analyzed and described every aspect of mathematical communication skills from concrete and abstract sequential thinking styles.

The Research Methods
This study employed the qualitative-descriptive approach with a case study research method. Case study research aims to understand one phenomenon by ignoring other phenomena deeply. The phenomenon in this was students' mathematical communication skills. Bogdan and Taylor (Moleong, 2014) define qualitative research as a research procedure that produces descriptive data in the form of written or spoken words from people. It also observed behavior from the emerging phenomena. Research using this method aims to describe the conditions during the research. The sampling technique used was purposive sampling technique to select ten out of thirty-two eleventh-grade science students at a senior high school in Tulang Bawang Barat Regency. The subjects selected in this study were based on several criteria: 1) students who have received Linear Program material, 2) students with concrete sequential and abstract sequential thinking styles, 3) mathematic teachers' recommendations, and 4) students' ability to express written and oral ideas. The instruments used were a test of mathematical communication skills and a questionnaire for students' thinking styles. The flowchart of this study is displayed in Figure 1. The questionnaire for thinking styles was a modification result developed by John Parks Le Tiller. The questionnaire had been validated by three experts in the field of psychology. The indicators of mathematical communication skills can be seen in Table 1 below. Students cannot make mathematical models and solve mathematical language problems (symbols, terms, signs, or formulas).

Moderate
Students write descriptions using their language. However, the explanation is only partially correct, incomplete, and unclear.
Students can draw pictures, diagrams, graphs, or tables, although unclear or without explanation.
Students can make a mathematical model and solve mathematical language ((symbols, terms, signs, or formulas) using an incorrect calculation. 3 High Students write explanations using their language correctly and clearly, but not completely.
Students can draw pictures, diagrams, graphs, or tables clearly, but accompanied by incorrect explanations.
Students can make mathematical models and solve problems using mathematical language (symbols, terms, signs, or formulas) incompletely 4 Excellent Students write explanations using their language correctly, clearly, and completely Students can describe pictures, diagrams, graphs, or tables clearly and correctly Students can make mathematical models and solve problems using mathematical language (symbols, terms, signs, or formulas) correctly and completely

A. Research Results
Based on the research results conducted in class XI IPA 1, which amounted to 10 students, the following data were obtained thinking styles. Based on Table 3, the comparison of concrete sequential and abstract sequential was 2: 3. This indicated that the students had more concrete sequential thinking styles than abstract sequential thinking types. A mathematical communication skill test was conducted on four research subjects, namely two students with concrete sequential thinking style type and two students with abstract sequential thinking style.

The Mathematical Communication Skills of Students' with Concrete Sequential Thinking Styles
The following are the subjects S1 and S2's answers on the written text indicator.  Based on Figure 2, subject S1 did not understand the questions, so that he did not answer the questions according to what was asked. Subject S1 answered the problem by finding the corner points then substituting them with the objective function. Subject S1 did not write down the x and y variables in the objective function. He also incorrectly chose the corner points that must be substituted; thus, the answer was wrong. Figure 3 shows the same thing as subject S1; subject S2 did not answer the problem by describing how to find the minimum cost. He also incorrectly substituted the corner points into the objective function by choosing the smallest cost. From the two answers, it was found that students with concrete sequential thinking style misunderstood the questions and unable to write entirely correct answers using their language.
The following are the subjects S1 and S2's answers on the drawing indicator. Based on Figure 4, subject S1 could make a graph, although he incorrectly determined the shading area following the predetermined model. Subject S1 did not write down how to find the coordinate points. Figure 5 shows that subject S2 could render graphic images and determine the shading area, but only partly correct. Subject S2 was wrong in determining the coordinate points according to the predetermined model and did not write down how to find the coordinate points to make the graph. From the answers obtained, the students could draw a picture, although but partly correct and incomplete.
Here are the subjects S1 and S2's answers on mathematical expression indicators.  7 show that subjects S1 and S2 could make mathematical models of the problems presented, but there were several errors in determining the sign of inequality. The errors might be because they only understood some of the problem's information, so they could not make mathematical models correctly.

The Mathematical Communication Skills of Students with Abstract Sequential Thinking Style
The following are the subjects S7 and S8's answers on the written text indicator.  9 show that subjects S7 and S8 could write several steps in their language, although incomplete and unclear. It can be seen from the two students' answers where they did not write down the steps to find the intersection point of known inequalities and did not clearly write down what was substituted into the objective function.
Here are the subjects S7 and S8's answers on the drawing indicator. Figure 10. Subject S7's Answer on the Drawing Indicator Figure 11. Subject S8's Answer on the Drawing Indicator Figure 10 shows that subject S7 could make graphic images wholly and correctly. It can be seen in the answers where he wrote how to determine the coordinate points of the known inequalities. Then, he entered the coordinate points into the graphic image and determined the shading area correctly. Figure 11 shows that subject S8 could draw a graph and determine the shaded area correctly, although the coordinate points were incomplete.
Here are the subjects S7 and S8's answers on mathematical expressions indicators.  Figure 12 shows that subject S7 could make a mathematical model of the problem correctly but incompletely. Subject S7 did not write the conditions for x and y in the mathematical model. Figure 13 shows that subject S8's answer was less careful in writing the inequality sign to the mathematical model.

B. Discussion
Based on the research results, it was known that there were differences in students' mathematical communication skills in terms of their thinking styles. In the written aspect, students with concrete sequential thinking style cannot understand the problem well but can produce something concrete. Some concept errors made by students with concrete sequential thinking styles resulted in their inability to develop ideas. The students tended only to accept information or material provided by the teacher, and they were uninterested in exploring something abstract. The results were in line with Nurmitasari's research, which states that conceptual errors often obstacles students with concrete sequential thinking styles (Nurmitasari & Astuti, 2019). Meanwhile, students with abstract sequential thinking styles can understand problems appropriately and write down abstract ideas using their language with good reasoning, although unclear. The results were also consistent with research conducted by Rahmy, which states that students with abstract sequential thinking style have difficulty understanding mathematics presentations and making arguments using their language (Rahmy et al., 2019).
Students with a concrete sequential thinking style can make graphs in the drawing aspect, although incomplete and partly correct. They tend to absorb information as it is. Students with abstract sequential thinking styles can draw graphs wholly and correctly because they can absorb lessons and information. Isyrofinnisak states that students with an abstract sequential thinking style understand concepts and analysis in understanding the material. Good mastery of material affects the students' success in determining solutions and transforming problems into images (Isyrofinnisak, 2020).
Students with concrete sequential thinking tend to need direction in absorbing information in the mathematical expression aspect. They tend to be wrong in determining the appropriate symbol to describe a problem. Nurmitasari found that students with a concrete sequential thinking style often make mistakes in symbols mathematical operations. They cannot continue the next operation to completely solve the problem (Nurmitasari & Astuti, 2019). Students with an abstract sequential thinking style can make mathematical models correctly but incompletely because abstract sequential thinking can use and analyze information appropriately. Masruroh's research shows that students with an abstract sequential thinking style have a high academic level because of their logical, mathematical, and rational thought processes to solve mathematical problems (Masruroh, 2018) quickly.
Based on the explanation, it was found that students with a concrete sequential thinking style only fulfilled one indicator of mathematical communication skills, namely, stating a mathematical situation or idea in the form of pictures, graphs, tables, or diagrams. Meanwhile, students with an abstract sequential thinking style could fulfill two indicators of mathematical communication skills, namely expressing a mathematical situation or idea in the form of pictures, graphs, tables, or diagrams and expressing a mathematical situation or idea in the form of a mathematical symbol or model and solving it.
The novelty of this study lies in the measurement of mathematical communication skills. This study found that students' mathematical communication skills with an abstract sequential thinking style tended to be better than students with a concrete sequential thinking style on linear programming material. This result contradicts the results of research by Rahmy where students with a concrete sequential thinking style were better on straight line equation material. Students with a concrete sequential thinking style were better at exploring ideas and formulating generalizations than students with an abstract sequential thinking style (Rahmy et al., 2019). Another study by Depary shows that the physics learning outcomes of students with a concrete sequential thinking style are higher than students with an abstract sequential thinking style (Depary & Mukhtar, 2013).

Conclusion and Suggestion
Based on the research results, students with an abstract sequential thinking style tended to be better than students with a concrete sequential thinking style in terms of mathematical communication skills. Students with an abstract sequential thinking style could make generalizations based on good reasoning in the written text aspect. However, students with a concrete sequential thinking style tended to lack in making abstract guesses. In the drawing aspect, students with an abstract sequential thinking style had a good understanding of theories and concepts to draw graphics well. On the other hand, students with a concrete sequential thinking style could only apply some of the information received to draw graphs. In mathematical expressions, students with an abstract sequential thinking style could process the information implied in the problem to make mathematical models correctly. Meanwhile, students with a concrete sequential thinking style needed some additional information or direction to understand the information to avoid errors in making mathematical models.
Based on the results of the research and several field findings, the researchers suggest further researchers examine in-depth the four Gregorc thinking styles, investigate the factors affecting students' mathematical communication skills, conduct other reviews to determine students' mathematical communication skills, and conduct research on other materials or subjects with a larger population.