MATHEMATICS COMMUNICATION MISTAKES IN SOLVING HOTS PROBLEMS

Student mistakes in communicating mathematical ideas are still widely practiced. Therefore, it is essential to analyze students' mathematical communication errors in solving mathematical problems so that learning planning can be better. This study aims to describe students' mathematics communication errors in solving higher-order thinking skills in linear algebra and matrix subject. The type of research is a qualitative descriptive study. They were 155 students as subject research. The data analysis started by collecting students' answers and then grouped them according to mathematics communication skills criteria. Later identified and analyzed the errors made by students of each mathematics communication criteria. The results showed that mathematical communication errors on the indicators of writing mathematical situations were concept errors and principle errors. The declaring idea's mathematical communication error is a concept error, a principle error, and an operation error. Furthermore, mathematical communication errors on the indicator state that solving-problem using the language itself is a concept error and operator error.


INTRODUCTION
Learning and communication are integral parts. Kleden (2016) emphasized that in learning activities there was an exchange of information in the form of knowledge and experience between lecturers and students, students and students, also between students and teaching materials, so mathematical communication skills were very much needed. Firdaus and Aini (2019) added that learning activities carried out by students were not limited to memorizing formulas and mastering calculations, but also learning through mathematical communication. Kleden (2016) emphasized that with excellent mathematics communication, students can convey ideas or thoughts appropriately to convince themselves and others. The importance of student mathematical communication is currently a problem that must be considered (Angraini, 2019;Argarini, Yazidah, & Kurniawati, 2020;Astuti &

METHOD
This research is qualitative descriptive research aiming to describe the written mathematics communication errors made by students in completing the HOTS problem on matrix material. The study begins by conducting field observations with the data obtained is that students make some mistakes in conveying the idea of solving a given problem. Based on this problem, instruments were then arranged in the form of HOTS-style test questions to lead to errors and mathematics communication of students. The test questions were validated by two mathematics education lecturers who experts in teaching Linear Algebra and Matrix subjects. The test was given to the students through the lms.umm.ac.id platform. Students collect their answers by uploading handwritten photos or sending typed results to lms.umm.ac.id through their respective accounts. HOTS problems that valid were served in Table 1.
Is it possible that produces a zero matrix?
Provide detailed explanations of the answers! of the matrix 2 and 3 are not zero-matrices, and then test for the student matrix use each idea to find out whether the matrix will produce a zero matrix Create Using their language, students write the possibility of the matrix to produce a zeromatrix Data analysis techniques in this study were carried out through 3 stages: data reduction, data presentation, and concluding. The data reduction stage is carried out by grouping the answers of the two questions based on similar answers into several types of the four classes. This is done to facilitate the analysis based on indicators that have been determined. Then the data obtained are presented in tables and diagrams. And the next step is to conclude the result based on data gathered.

Results
Data obtained from the four classes were 155 student answers. Figure 1 shows that 148 students have less mathematics communication in the Question 1 or first question, and seven students who have excellent mathematics communication. Judging from the number of answers shows that mathematics communication possessed by students is still lacking. Only 4.5% of the total amount has excellent mathematics communication. It shows that students cannot communicate their ideas well so that they have difficulty in problem-solving. Whereas in Figure 2, the number of answers to second question or Question 2 does not differ from Question 1. The number of students with communication is more or less compared to students with excellent communication. But for the second question, there is no difference with the distant numbers, namely 85 students with less mathematics communication and 70 students with excellent communication. It means that students are more able to communicate their ideas in the second question than the first question.  Figure 2 shows that students with good mathematics communication skills are minimal. It can happen because students were making many mistakes when solving problems, such that it did not match the mathematics communication indicator. Table 2 shows that most students made mistakes when stating their problem-solving problems by using their language. These mistakes can be taken because students get used to calculating without looking back on the problem. Another possibility that causes students to have less mathematics communication skills understands the multiple matrices such that students cannot write their ideas clearly. The weakness of understanding the problems is also one of the factors that caused students to make mistakes to determine the solution steps. The percentages of each student's mathematics communication criteria were presented in Table  2.  Table 2 shows that not all students meet the three mathematics communication criteria in solving HOTS problems. The third criterion of mathematics communication, declare the answer to solving HOTS's problem using their language, obtain the most significant percentage of 93.55%. This percentage is the highest compared to the other two indicators. It happens because students are incomplete in writing conclusions of problemsolving. The highest rate in the second question for the category lacking was also found in the indicator, stating the solving results using their language that is 41.94%. Most students did not write the conclusions of the calculation that they obtain. Although students are good at understanding mathematical situations or writing their ideas, it did not mean that students' mathematics communication was excellent.
Each rate of mathematics communication skills showed that not all students fulfilled all criteria of mathematics communication. Students in problem-solving with problems may make mistakes by mathematics communication written owned. The mistakes made by students in completing Problems are presented in Table 3.

Not found
State the results of problem-solving using your language In Question 1, it is wrong to conclude that = .
In Question 2, it is wrong to conclude that will probably produce a zero-matrix

Not found
In Question 1, it was wrong to calculate the 2 2 matrix multiplication.

Mathematical Errors when Understanding Mathematical Situations Clearly
On the indicators of understanding the mathematical situation clearly, students made mistakes, namely misconceptions and principles, but did not make operational errors. In the second question, students did not make misconceptions when understanding mathematical situations. Students created a mistake in the first question. The mistake made by students were wrong in determining the A, B, C matrices. These errors resulted in students not getting AC = BC. The answers of students who make misconceptions when understanding the mathematical situation are clearly shown in Figure 3. Figure 3 shows that students only determine matrix C and then conclude that AC is the same as AB, while matrix A and matrix B are not explained as components. Students make a principles mistake in the form of incorrectly linking the concept of the identity matrix and matrix multiplication. Figure 4 is the answer to students who earned a principles error when they did not understand the mathematical situation correctly. Students make a mistake when multiplying the matrix and stating that the matrix A 2 is the identity matrix.

Mathematical Mistakes when Writing Out Problem-Solving Ideas Clearly
Students make misconceptions, principles, and operations when writing problemsolving ideas on the second problem. But in the first question, no students made mathematical mistakes. In the second problem, students created a misconception, namely not applying the concept of multiplication to matrix A. Students wrote the conclusion that A n produced a null matrix, but did not test the multiplication against A 4 matrix. Figure 5 shows students' mistakes, not doing the calculation concept of matrix A, so that they do not write ideas. Students made a principles mistake in the second problem by not doing the multiplication concept on the matrix A 3 . Students only perform calculations on matrix A 2 so that they do not find the relationship between the A 2 and A 3 matrices in finding the A n matrix. So, it concludes without checking whether A n yields a null matrix ( Figure 6).

Mathematical Errors when Expressing Problem Solving Results in His Language
Students make misconceptions and operational errors when clearly stating the results of solving problems. The mistake made by students when reporting the results of solving the problem was that the multiplication matrix did not recognize ranks so that A n could not be a zero matrix. In Figure 7 showed that students wrote that A n could not be a null matrix because matrix A is not a zero matrix.

Figure 7. Misconceptions when expressing problem solving results in his language
Operation errors made by students when stating the results of solving the problem in the first problem are wrong to conclude that AC = BC. Students get the same results, but the calculations that have been done are not correct. In Figure 8, students state that the results of problem-solving do not match the calculations obtained. It proved that the both multiplication (above), the matrix = have the same result.

Figure 8. Operating errors when stating problem-solving results in his language
Matrix operation does not recognize the power form. The power referred to in matrix operation is the repeated multiplication of a matrix with the matrix itself. The condition of a matrix to be raised is that it must be a square matrix or a square matrix. Thus, the exponent of the square matrix itself is the sum of the powers. if the matrix is nonzero, then is unlikely to produce a null matrix later. For example number 1, if number 1 then whatever n will not change from 1 to 0. Volume 10, No 1, February 2021, pp. 69-80 77

Discussion
The data of Figure 1 and Figure 2 show that the student's mathematics communication ability was needed to be increased. This finding was in line with Firdaus and Aini (2019) research, which found that students' communication is still in the low category. This research also shows that most students did not fulfill the three indicators of mathematics communication, which indicated their mathematics communication skills need to be improved. Firdaus and Aini (2019) also found that students' weakness in mathematics communication can be caused by student mathematics communication indicators that have not been achieved. Moreover, Syafina and Pujiastuti (2020) found that only students with good mathematics ability can fulfill all mathematics communication indicators. This research found that students' ability to state the problem-solving results using their language is the most difficult mathematics communication indicator for students to fulfill. Students' answers do not give reasons with their language style, so it does not state the conclusions of the given problem. This phenomenon is also found in Mirna's (2018) research. Besides, some students still have difficulty writing ideas and knowing the mathematical situation clearly. So that in this study, students made mistakes in concepts, principles, and operations. Students' types of errors are in line with Zulfah's (2017) research that students make mistakes in the form of concept, process, and principles errors.
Student's mistakes influenced the ability of mathematic communication measurement in each indicator. In other words, mathematics communication ability related each other with students' mistakes (Zulfah, 2017). Afifah et al. (2018), in their research, stated that the types of mistakes made by students were concept errors, operation errors, and principles errors. Firdaus (2019) research shows that in solving the Matrix Problem, the type of error made is concept and operation error. Likewise, with this study that students also carried out misconceptions and operations. More specifics, based on Table 3, most students made conceptual mistakes while solving the problems given. This finding can be considered to point out that students may not be able to communicate their idea well because they did not understand the problem. This possibility inline with Abidin et al. (2017) research concluded that a misconception caused another five kinds of students' mistakes. These conceptual mistakes also affect principles mistakes of student's work (Mirna, 2018). For example, in Figure 4, students' misconception about the definition of identity matrix then applied this wrong idea to analyze the situation. Albeit a little, students also make procedural mistakes when they calculate or simplify the algebra form. Students also found this mistake in Parwati and Suharta (2020) research that procedural mistakes are still made frequently by students when solving algebra problems.

CONCLUSION
Students' mathematics communication errors in completing HOTS problem on matrix material are concept errors, principles errors, and operating errors. These errors can occur in every student mathematics communication indicator. In the first mathematics communication indicator that understands the mathematical situation clearly, mistakes made are concept errors and operating errors. The second indicator of mathematics communication is writing ideas clearly; the mistakes made are concept errors and principles mistakes. As for the third mathematics communication indicator that states the problem-solving results using their language, the mistakes made are concept errors and operating errors.