STUDENTS’ MATHEMATICS EDUCATIONAL VALUES IN PROBLEM- SOLVING AT SENIOR HIGH SCHOOL

In mathematics, the ability to understand, reason, and connect mathematics is included in the value of mathematics education. The fact shows that the values of mathematics education have not been fully integrated in mathematics learning, as a result, it affects the quality of the learning process. This study aimed to describe senior high school students’ mathematical educational values on problem-solving tasks. It was a qualitative-descriptive study. The subjects were six students of Grade X of SMAN 1 Indralaya. The data were collected through observation, test and interview to perceive the students’ activity while working on the mathematical problem, to determine the mathematic educational values, and to confirm the students’ solutions toward the problem. The results of the study showed that the relational understanding and theoretical knowledge were the indicators that occurred in all subjects, whereas the reasoning indicator was less dominant. For further research, it is suggested to discover the correlation among all mathematical educational values.


INTRODUCTION
The Indonesian national education purpose, as mentioned in the 2013 curriculum, is to prepare Indonesians to possess life skills in order to be a faithful, productive, creative, innovative 2094| and affective citizen, and also to enhance their capability to contribute towards the society, nation, state, and human civilization (Permendikbud, 2016).
During mathematics instruction, students are expected to not only obtain knowledge through learning materials, but also to understand the values contained (Clarkson, Seah, & Pang, 2019). The values described in mathematics classroom are general educational, mathematical, and the mathematic educational (Daher, 2021). The latter value focused on the gains related to its teaching (Aisyah, Saad, & Dollah, 2013;Aisyah, Saad, & Dollah, 2013). When students comprehend and appreciate value in mathematics, they will engage more in the learning process and hence, their mathematics achievements increase (Kalogeropoulos & Clarkson, 2019;Lam, 2012). Therefore, it shows the need for the educational system to highlight the internalization of values in mathematics education by providing significance (Aisyah, Saad, & Dollah, 2013;Aisyah, Saad, & Dollah, 2013).
Mathematics educational values are classified into five complementary pairs: (1) formalistic versus activist view, (2) instrumental versus relational understanding, (3) relevance versus theoretical nature of mathematics in teaching and learning, (4) accessibility versus specialism of its knowledge, and (5) the utilization of this specific skill as part of a process, as opposed to a tool (Daher, 2021). The prior study shows that the dominant values provided by the teachers in mathematics classroom activities are activist, relevance, theoretical, and reasoning, which were implemented and planned in the teaching process, while the instrumental and accessibility type were applied but not planned (Aisyah, Saad, & Dollah, 2013;Aisyah, Saad, & Dollah, 2013).
In order to gain mathematics educational values, a proper approach needs to be implemented in the instruction, one of which is through solving mathematical problem (Zhang, 2019). Furthermore, problem solving enhances students' training, in order to implement knowledge, and discover solutions, thus, producing meaningful comprehension (Anggo, 2011).
In mathematics, the ability to understand, reason, and connect mathematics is included in the value of mathematics education (Gaspard, Dicke, Flunger, Brisson, Hafner, & Trautwein, 2015). The fact shows that the values of mathematics education have not been fully integrated in mathematics learning, as a result, it affects the quality of the learning process (Aisyah, Saad, & Dollah, 2013). The researcher's initial observations in the implementation of mathematics learning in one of the schools carried out by prospective mathematics teachers, showed that prospective mathematics teachers had not applied the values of mathematics education in learning. Therefore we need a learning activity that can provide a stimulus so that the values of mathematics education can emerge.
Based on the description above, this study aimed to comprehend which mathematics educational values would occur during the learning process by utilizing problem-solving approach for high school students of SMAN 1 Indralaya. ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442

METHODS
This study was a qualitativedescriptive study aiming to describe mathematics educational values occurring when implementing the mathematics problem solving instruction. The study consisted of two phases, preliminary and field research as shown in Figure 1. In order to control variability of the sample, the research subjects of this study were selected through three steps of selection, namely above average academic competences, teacher's recommendation especially on student's behavior and cooperative manner, as well as student availability. There six students of class X IPA 3 SMAN 1 Indralaya that determined as sample. Two higher competent students are ER and SWN, two moderate competent students are AJ and KE, and two lower competent students are PW and AT.  Being able to show the correlation between the concepts or principles of creating schemes or structures for use in the description of a more general problem. 3 Relevant Knowledge The ability to apply the mathematical ideas and principles in solving daily challenges. 4 Theoretical Knowledge The student was proficient in utilizing these concepts and philosophies to resolve problems.

Specialties
Being able to answer enrichment or non-routine questions. 6 Reasoning The capability to create linkages with facts, in order to draw conclusions.
The focus of this research was on the six mathematical education values that dominantly occur in mathematics classroom, which are activist, relational understanding, relevant knowledge, theoretical knowledge, specialties and reasoning. At the preliminary stage, the researchers construct theoretical framework to be implemented in field research. This construction produces Indicators of Mathematics Educational Values in Finishing the Problem-Solving Exercise as shown in Table 1.
Lastly on the preliminary stage, the researchers designed student worksheet and all instruments needed to collect the data. The worksheet was designed based on the problem-solving Other research instruments were observation sheet, mathematics test, and interview guidelines. All the data collected from these processes were then analyzed through the data reduction and then compared to the existing theory and prior relevant research in order to derive complete, deeper, and meaningful conclusion.

RESULTS AND DISCUSSION
This research analyzed the occurrence of mathematic educational values during the mathematics instruction, utilizing problem-solving approaches for student of Grade X IPA 3, of SMAN 1 Indralaya, illustrated by an exercise, consisting of two tests.

Activist
The activist indicator occurs when a subject actively engages during the learning process (Hui Nong & Adnan, 2017;Aisyah, Saad, & Dollah, 2013;Daher, 2021). The occurrence was determined by the observation conducted by the observer. Table 2 shows, that 4 of 6 students were identified as active students. Based on the observation (Figure 2), the subject ER was the most active participant in the group discussion due to the response administered towards the questions of others that did not understand the point of the discussion. Furthermore, this subject was not afraid of asking the teacher about the difficulties or things that were not clearly understood.
The occurrence of active indicators was shown on a dialogue between the participants while performing the exercises in the LKPD below: From the dialogue above, it shows that the subject was actively involved in the group discussion, ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442 The student is answering question(s) from their friends which haven't understood.
The student is asking teacher about things they haven't understand.  Table 2 we can see that subject PW and MSY did not show any significant engagement in the classroom activity, which seems to affect their performances in relevant knowledge and specialized values. Students who are actively participated in a variety of mathematics learning activities scored higher mathematics achievements (Fung, Tan, & Chen, 2018). Students may have incentive to overcome learning challenges, and at the same time have interest and enjoy the given tasks (Bazelais, Lemay, & Tenzin, 2016;Orsini C, 2015). On the other hand, sometimes being not active in a class discussion doesn't necessarily mean that the student is lack of mathematical understanding (Kiwanuka, Damme, Noortgate, & Reynolds, 2020). As a counter example, the subjects AJ and KE showed significant engagement in the class activity, but failed to perform in reasoning. Hence, further research needs to be conducted in response to this phenomenon.

The Relational Understanding Values
The indicator of relational understanding occurs when students are able to show the correlation between the concepts or principles of creating schemes or structures for use in the description of a more general problem (Şahin & Özpinar, 2020;Aisyah, Saad, & Dollah, 2013;Daher, 2021). The result showed that all subjects were able to exhibit this value. For example, the subject AJ. When AJ's answers the question number 2, the subject was able to make an example, using variable x, y, and z. The subject subsequently created an equation from the information gained 2098| from the question. However, during the process, the answer was searched for by performing trial and error, and a correct answer was selected. Meanwhile, the following was the content of the subject's answer sheet as shown in Figure 3.  This showed the difficulties faced by the subject while making the third equation, thus the solution was sought by performing trial and error or logics. In addition, the following admission was made by the subject during the interview. This was because the subject was confused through the process of creating the third equation. Hence, a trial and error was conducted (Keleş & Yazgan, 2021).

Relevant Knowledge
In answering the written test, relevant knowledge appears when a subject is able to apply the mathematical ideas and principles in solving daily challenges (Aisyah & Dollah, 2014;Aisyah N., 2016;Bishop A., 2008;Dollah, 2007), for example, the subject KE in solving mathematical problem. This involved the elimination and substitution of previous result through the use of a mathematical model personally created to enhance the ease of calculation. In addition, the subject made an example of motorcycle, car, and van as variables of x, y, and z, as seen in the Figure 4..  Figure 4, the substitution and elimination were used to determine the score. Previously, the variables of motorcycle, car, and van were changed into x, y, and z, followed by the creation of the mathematical model. The following is a part of the interview with the subject is as follows: Based on the interview, the subject was capable of describing the way of answering the questions correctly; therefore, the subject understood how to solve the problem using mathematical concepts and principles in real contexts (Shinariko, Saputri, Hartono, & Araiku, 2020). Problems that require students to connect mathematical knowledge and real word problem have an effect on students' problem solving abilities The subject made an example by using variables The subject made a mathematical model The subject used the elimination and subtitution to get the score of x, y, and z ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442

Theoretical Knowledge
The indicator of theoretical knowledge occurs when students are proficient in utilizing all concepts and philosophies needed to resolve problems (Aisyah, Saad, & Dollah, 2013;Daher, 2021;Hui Nong & Adnan, 2017). For example, in the answer sheet of question number 2, the subject MSY answered the question through the creation of an example and the remodeling of previous equation, using prior information. Figure 5 shows the answer sheet of the subject.  Figure 5, the subject provided an example which was changed into variables of x, y, and z followed by the creation of a mathematical model from the information obtained in the question. However, in finishing the equation, the data were supported by the result of the equation, although the answers were wrong and the substitution was not yet possible. The following is the part of the interview with the subject as follows: Based on the dialogue, the subject reported that, during the process of completing this example, the strategy ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442 of the subject was making a simpler alternative equation in order to enhance the ease of substitution or elimination in order to obtain the right answer (López, Férez, & López, 2021). In obtaining the solutions to the problems, sometimes students have different strategies, one of which is by simplifying the calculation process, but still getting logical answers (Yansen, Putri, Zulkardi, & Fatimmah, 2019).

Specialties
The specialties occur when students are able to answer enrichment or non-routine questions (Aisyah, Saad, & Dollah, 2013;Hui Nong & Adnan, 2017). The instance that this indicator occurred in the answer sheet of the subject SWN was shown in Figure 6, indicating the ability to answer questions in a real context, utilizing the appropriate steps, and obtaining the right answer. This was conducted with thorough and precise calculation in order to enable the subject to solve the problem. Figure 6 shows that despite of minor error in writing some letters, the subject was capable of solving the problem correctly, using the steps of three-variable linear equation system learned previously, by connecting the available information (Araiku, Parta, & Rahardjo, 2019). This was initiated by writing out the information, creating example by making some variables followed with a mathematical model, and conducting elimination and substitution. This was also supported by the result of the interview, in which the adopted method while answering the question from the beginning to the end was described without any confusion. Based on the interview, the subject tried to describe the origin of the equation derived in order to answer the question. Subsequently, the steps taken were also described.

SWN
: When the first and second equation are excluded (write the answer), eliminate x and z, then substitute it (write the answer).
The part of the dialogue shows that the subject eliminated and then substituted the score obtained in answering the question in the exercise. Finding out the relevant information from the problem and then determining the variables to be able to make a mathematical model correctly is important to find solutions to the questions (Saputri & Zulkardi, 2020).

Reasoning
The last mathematics educational value is reasoning (Aisyah, Saad, & Dollah, 2013). Reasoning appears when students are able to create linkages with facts in order to draw conclusions. For example, the subject AJ's solution on problem number 1 as shown in Figure 7 below. The final answer offered by the subject was correct although the calculation was incorrect during the substitution. Hence, the reasoning is considered done incorrectly (Araiku, ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442 Based on the interview, the subject realized the mistake made and only recollected the answer learned previously. ISSN 2089-8703 (Print) Volume 10, No. 4, 2021, 2093-2106ISSN 2442 International