MATHEMATICAL COMMUNICATION SKILLS IN SOLVING LIMIT AND CONTINUITY PROBLEMS: REVIEWED FROM INTRA-AND-INTERPERSONAL INTELLIGENCE

The various intelligence of students allows for differences in the mathematical communication skills produced. This study aimed to analyze students’ mathematical communication skills in terms of intrapersonal and interpersonal intelligence. The subjects of this study were students of Mathematics Education Class IV at the University of Mataram. This research method is descriptive with a survey design. This study uses a qualitative approach with stages covering problem formulation, sample selection, research limitations, instrumentation in the form of questionnaires and tests, data collection and analysis, and conclusion. The results of this study indicate that the level of intrapersonal and interpersonal intelligence affects students’ mathematical communication skills. This can provide information to educators to provide appropriate services.

I n d o n e s i a n J o u r n a l o f S c i e n c e a n d M a t h e m a t i c s E d u c a t i o n ( I J S M E ) | 31 and intentions [15]. These two bits of intelligence are interrelated and important for students to have. This intelligence is two of the nine bits of intelligence, the findings of Howard Gardner, which support the implementation of 1 of the 6 pillars of education mandated by UNESCO, namely learning to live together. [16].
Interpersonal intelligence plays an important role in education. Educating students in the 21st century requires a different approach because students learn with the sophistication of technology that is constantly changing and evolving. Students need to be critical, creative, problem solvers, good communicators and can work well with peers. In this case, interpersonal intelligence is needed to achieve all these skills [17]. Some characteristics of students who have interpersonal intelligence, include being able to build and create new social relationships with others effectively, easily empathize with other people's conditions, maintain social relationships with others effectively, can communicate with others both verbally and non-verbally, mastering communication skills such as listening, speaking, and writing effectively, can solve problems or problems that occur in social relationships with other people [18]. While the characteristics of students with intrapersonal intelligence levels recognize their strengths, weaknesses, limitations, emotional intelligence or moods, desires, motivations, intentions, and goals, as well as selfrespect and self-control, are independent, prefer to learn in their way, and tend to be passive in speaking [19].
Based on the results of observations, it was found that mathematics education students have a variety of intrapersonal and interpersonal intelligence. There are 4 categories from the survey results found, namely students with high intrapersonal and interpersonal intelligence, students with high intrapersonal intelligence but low interpersonal intelligence, students with low intrapersonal intelligence but high interpersonal intelligence, and students with low intrapersonal and interpersonal intelligence. Several studies have stated that intrapersonal and interpersonal intelligence affect the way students communicate both verbally and in writing [20]- [21]. Students in class IVA have various communication skills, both verbally and in writing. Therefore, researchers want to analyze more deeply related to students' communication skills in terms of their intrapersonal and interpersonal intelligence.
Several previous studies examined the relationship between intrapersonal and interpersonal intelligence and showed that there was a strong relationship between intrapersonal and interpersonal intelligence on student learning outcomes [22]- [23]. Meanwhile, other research states that there is a significant influence between emotional intelligence on mathematical communication skills. This means that every increase in students' emotional intelligence will improve their mathematical communication skills [24]. Students with higher emotional intelligence have better mathematical communication skills [25]. The differences between this study and previous studies are 1) the selection of the material tested to assess mathematical communication skills about limit and continuity, 2) analyzing mathematical communication skills using written test answer data and oral interview data, 3) applying scaffolding for students who have difficulty through in-depth interviews until the correct answer is obtained. Based on the problems above, the researcher wants to analyze the mathematical communication skills of students in solving mathematical problems about limits and continuity in terms of intrapersonal and interpersonal intelligence.

METHOD
This research method is descriptive with the survey design type. This study uses a qualitative approach with stages including problem formulation, sample selection, research limitations, instrumentation, data collection and analysis, and concluding. [26]. The stages of this research are presented in a diagram as shown in Figure 1 as follows. Quantitative data in this study were obtained from questionnaires and tests needed to measure students' mathematical communication skills and the level of intrapersonal and interpersonal intelligence possessed. Furthermore, the resulting data were analyzed to examine the relationship between students' intrapersonal and interpersonal intelligence on mathematical communication skills in solving mathematical problems. Indicators of students' mathematical communication skills in full are presented in Table 1 as follows.

Fluency
Write or state the formulas needed in solving problems without stuttering and no scribbles or error corrections in the written answers. 3 Construct and communicate explanations and arguments in the context of the problem Accuracy Write down or restate the stages of problemsolving that have been done before correctly.

Fluency
Write or restate the stages of problem-solving that have been done previously without halting.
In this study, the process of delivering material about Limits and Continuity using Google Meet. All student activities in this learning starting from attendance, presentation of teaching materials, discussions/questions and answers via Google Meet video conferences and discussion forums, as well as evaluations/quizzes that can be accessed on the Learning Management System (LMS).
This study aims to analyze students' mathematical communication skills in solving problems in terms of intrapersonal and interpersonal intelligence. The measured mathematical communication skills are divided into two types, namely written and oral. Written communication skills were measured through essay tests, while oral communication skills were measured through observation sheets conducted during interviews [27]. Communication skill levels are classified into three categories, namely high, medium, and low which are presented in Table 2.  [28] The data collected in this study were in the form of intrapersonal and interpersonal intelligence questionnaire data used for the selection of research subjects, data on written test results, and interview tests to measure mathematical communication skills. The results of the intrapersonal and interpersonal intelligence questionnaires resulted in the categories classified in Table 3. The results of this questionnaire indicate that students have different levels of intelligence. With this, lecturers have data about the intelligence possessed by students so that they can be given the right treatment.

RESULTS AND DISCUSSION
The data in this study came from observations, questionnaires, tests, and interviews. Observations were made since the beginning of the study as a background for formulating research problems. Meanwhile, the selection of research subjects came from the results of a questionnaire with certain considerations. Through the intelligence questionnaire data, the researcher selected four respondents as research subjects classified into 4 types, namely one student with high intrapersonal and interpersonal intelligence, one student with high intrapersonal and low interpersonal intelligence, one student with low intrapersonal and high interpersonal intelligence, and one student with both low intrapersonal and interpersonal intelligence as shown in Table 4. Furthermore, for further analysis of mathematical communication skills, it is based on the results of tests and interviews conducted on research subjects from questionnaires. The description of the analysis of students' mathematical communication skills in terms of intrapersonal and interpersonal intelligence with these 4 types of categories in solving mathematical problems, especially in limit and continuous material is presented in detail as follows.

The Results of the Analysis of the Mathematical Communication Skills for AA
AA is a research subject with a high level of intrapersonal and interpersonal intelligence. An overview of the results of the communication skills test for the written test of AA subjects is presented in Figure 2. The results of the answers of AA subjects were analyzed based on indicators of mathematical communication skills in terms of three aspects of the assessment, namely accuracy, completeness, and fluency. The description of the results of the written test and interview test of AA subjects is presented in Table 5 as follows.   AA can show the mathematical terms, notations, and symbols used in the problem. 6 Give a conclusion of the final result of the answer.
AA can write the conclusion of the final answer obtained correctly.
AA can explain the conclusion of the final answer obtained clearly. 7 Review the written answer.
AA did not write down the results of rechecking the answers but in the calculations, there were no errors.
AA is confident in explaining that the answers that have been written are correct and have checked the calculations in the questions. Table 5 shows that AA subjects with both high levels of intrapersonal and interpersonal intelligence have the following characteristics: (1) AA has good written communication skills, including writing answers accurately, procedures and steps are complete, smooth, and there are no calculation errors and (2) AA has excellent oral communication skills, including being able to explain the meaning of questions starting from what is known and asked, explanations of each written completion step, and conveying conclusions from the final results obtained accurately, completely, and fluency. These verbal communication skills are closely related to the interpersonal intelligence possessed by students, namely the ability to interact face-to-face [29]. Therefore, it is easier for AA to provide explanations for the questions asked and there are no obstacles.

The Results of the Analysis of Mathematical Communication Skills for BEA
BEA is a research subject with a high level of intrapersonal and low interpersonal intelligence. Description of the results of the analysis of written and oral communication skills obtained through written tests and interviews as shown in Table 6 as follows. BEA can draw a boundary sketch of the set {( , ): 2 + 2 < 4} However, the graphic components were incomplete, miscalculations were made, and the explanations were short enough that the final answer was wrong.
BEA had a hard time where to start when asked to draw a graph of 2 + 2 < 4 because it was confused by the "less than" sign (<).

5
Write down mathematical BEA made a few mistakes in writing limit notation. BEA only explained the use of limit notation in the question, but there were a │ Ratna Yulis Tyaningsih, et al Review the written answer.
BEA only checks the mathematical calculations in each step of the answers that have been written.
BEA feels doubtful and dissatisfied with the answers that have been written. Table 6 shows that BEA subjects with high levels of intrapersonal and low interpersonal intelligence have the following characteristics: (1) BEA has fairly good written communication skills, including writing complete and fluent answers, but there are some calculation errors and other minor components that cause the answers to be wrong and (2) BEA has poor oral communication skills, including substandard and a little halting in explaining the chosen problem-solving strategy, the settlement steps applied and the conclusions from the final results obtained.
These results indicate that students with high intrapersonal intelligence, but who have interpersonal intelligence tend to do better on the written test than on the oral test. This must be overcome by developing oral communication skills by practicing repeatedly to express what is expected smoothly without text [30]. This is by previous research that in addition to having good knowledge, students must also have the ability to communicate the knowledge or information obtained to be effective [31].

The Results of the Analysis of Mathematical Communication Skills for BA
BA is a research subject with a low level of intrapersonal and high interpersonal intelligence. Description of the results of the analysis of written and oral communication skills obtained through written tests and interviews as shown in Table 7 as follows. . Meanwhile, one of the selected paths is the path along theaxis ( = 0) so that the answer is undefined.
BA can explain the problemsolving strategies used and apply these strategies even though there are errors in path selection.

3
Able to give reasons for written answers. BA can explain the meaning of the sketch that has been described even though there are some errors.

5
Write down mathematical terms, notations, and symbols.
BA made a few mistakes in writing limit notation. It should be written like this: BA can explain the conclusion of the final answer clearly. 7 Review the written answer.
BA does not re-check/recheck answers that have been written correctly.
BA feels less confident in explaining the answers that have been written because they don't check the mathematical calculations Table 7 shows that BA subjects with low levels of intrapersonal and high interpersonal intelligence have the following characteristics: (1) BA has poor written communication skills, including writing complete answers but there is an error in choosing a problem-solving strategy that causes the answer to be wrong. The same thing was found in another study where students with low abilities were able to use concepts/formulas and were aware of the conceptual errors made but did not know how to correct them. Students with this type make more misunderstandings and confusion in choosing a solution strategy and (2) BA has quite good oral communication skills, including being fluent in explaining answers written according to his thoughts, some of which are stated there are still errors so they still need guidance.

The results of the analysis of mathematical communication skills from AH
AH is a research subject with quite low levels of intrapersonal and interpersonal intelligence. Description of the results of the analysis of written and oral communication skills obtained through written tests and interviews as shown in Table 8   AH does not have a proper problemsolving strategy. AH only substituted (0, 0) into the question so that the final answer was wrong.
AH cannot explain what strategy is the most effective for the problem and only explains how to substitute (0,0) into the problem. 3 Able to give reasons for written answers.
AH did not write down the reasons/descriptions and a brief explanation of the written answers.
It is difficult for AH to explain the concepts, formulas, theories that will be used to expedite the procedure for solving the problem. 4 Draw a graph that matches the purpose of the question (for question no. 2) AH sketches the boundaries of the indicated set completely, but there is a slight error. AH draws a closed curve in the form of a circle even though it doesn't use a compass, but says that the set {( , ): 2 + 2 < 4} is open.
AH is difficult to explain the meaning of the sketch that has been drawn but says that the set drawn is open.

5
Write down mathematical terms, notations, and symbols. AH can write limit notation correctly.
AH was able to explain the limit notation used even though an error occurred in the early steps of choosing a problem-solving strategy. 6 Give a conclusion of the final result of the answer.
AH did not write down the conclusion of the final answer completely.
AH could not explain the conclusion of the final answer obtained. 7 Review the written answer.
AH did not re-check/double-check the answers that have been written.
AH is not sure about explaining the answer that has been written. Table 8 shows that AH subjects with both quite low levels of intrapersonal and interpersonal intelligence have the following characteristics: (1) AH has poor written communication skills, including AH does not understand the meaning of the question so that the written answer does not match the purpose of the question and the overall answer written is wrong. There are previous studies show that students with low intrapersonal and interpersonal intelligence have low thinking skills and this has an impact on their written ability to describe information. [32] and (2) AH has poor oral communication skills, including difficulty in explaining written answers because they do not understand the meaning of the question and do not know which formula or strategy is right for the question. Similar to other studies, data shows that students with low intrapersonal and interpersonal skills have difficulty communicating their information to others [33]. Thus it can be concluded that subjects with low intrapersonal and interpersonal intelligence resulted in low written and oral mathematical communication skills as well. Based on previous research, the low level of mathematical communication skills indicates the inability of students to write and convey mathematical ideas systematically [34]. Based on the description of the results of the analysis on four research subjects with different types of cases, it can be concluded that the diversity of levels of intrapersonal and interpersonal intelligence possessed by students produces different mathematical communication skills. The higher the level of intrapersonal and interpersonal intelligence possessed, the better the mathematical communication skills possessed, and vice versa. Even other research mentions that intrapersonal and interpersonal intelligence affect students' mathematics learning achievement [35]. Students will be more successful if they know which intelligence is more dominant in themselves. Meanwhile, less dominant intelligence can be developed with supportive activities [36]. Therefore, the creation of a learning atmosphere and enrichment of activities is needed for the development of intelligence possessed and can improve students' mathematical communication skills.
Based on the analysis that has been carried out in this study, this study has several weaknesses such as the analysis of mathematical communication skills is only limited to research subjects in higher education and certain materials, the level of analysis is less indepth because it only uses tests and interviews, and analysis based on two variables. which are different, namely intrapersonal and interpersonal intelligence. Therefore, for other researchers who conduct similar research, it is recommended that an analysis of mathematical communication skills be carried out for limit and continuity material or other materials that are more in-depth and associated with other more relevant variables. This research can also be used as inspiration and additional information to conduct further assessment and analysis to obtain better similar research by taking into account the existing weaknesses.

CONCLUSION
The results of this study indicate that there are differences in the mathematical communication skills of research subjects in solving math problems in terms of their intrapersonal and interpersonal intelligence levels. These differences include 1) students with both high levels of intrapersonal and interpersonal intelligence have excellent written and verbal communication skills, 2) students with high levels of intrapersonal intelligence but low interpersonal skills tend to be good in written communication but are not fluent in expressing ideas or opinions. verbally, 3) students with low levels of intrapersonal and high interpersonal intelligence tend to be less good in choosing problem-solving strategies and writing answers even though there are some errors but are better in expressing their opinions orally, and 4) students with intrapersonal and interpersonal intelligence levels both of which are quite low tend to be weak in terms of communication both written and verbal.