Mathematical Engagement When Solving Mathematical Problem With Brawijaya Temple Context Based on Mathematical Ability Level

Received : 08-09-2020 Revised : 15-09-2020 Accepted : 17-09-2020 Online : 03-10-2020 This research to describe the mathematical engagement of seventh grade junior high school students in problems solving with the theme of Brawijaya Temple with high, medium, and low levels of mathematical ability. This type of research is qualitative research using an exploratory approach. The students used were 6 grade VII students of Junior High School 1 Karangrejo who were students working on problem solving and interviewing. The results showed: (1) mathematical engagement of highly skilled students in problems solving with the theme of Brawijaya Temple, namely students having the engagement of “get the job”, (2) mathematical engagement of students with moderate abilities in problems solving with the theme of Brawijaya Temple, namely students having engagement is “I am really into this”, (3) Mathematical engagement of students with low abilities in problems solving with the theme of Brawijaya Temple is that students have “pseudo-engagement”. Keyword:


B. METHODS
This type of research is a qualitative study using an exploratory approach. According to Sugiyono (2016) qualitative research is research based on the philosophy of postpositivism which is used to examine the conditions of natural objects, where the researcher is a key instrument, data collection techniques are carried out in triangulation (combined), data analysis is qualitative, and qualitative research results emphasize more. Meaning rather than generalization (Sugiyono, 2016). This research was conducted in June 2020 at Junior High School 1 Karangrejo, Tulungagung. The students involved in this study were 6 students of class VII-A. The 6 students were taken by using purposive sampling technique, which is based on the students mathematical abilities (high, medium, low) on the results of the students UTS scores. The instrument uses worksheets and interview guidelines. Each level consists of 2 students for worksheets and interviews conducted individually as a data collection technique.
Data were collected through student worksheets that have been done. The worksheets are in the form of essay questions as many as 2 points which aim to measure the extent to which students ability to solve math problems if given questions related to the circumference and area in the context of Brawijaya Temple seen from the students answers. Researchers also conducted interviews with each student, aiming to dig deeper into the structure of student engagement in problems solving. The researcher also recorded the entire interview process using a voice recorder and made a transcript of the interview results. The data analysis carried out were: data reduction, display data, and verification. The word engagement is commonly used to show meanings such as commitment, agency, and reciprocity, which makes the concept synonymous with self-participation in several activities (De Vito, 2016). According to Gunuc (2014), student engagement as the time allocated by students for educational activities, contributing to the desired results and as the quality of their efforts. Furthermore, the mathematical understanding according to Indonesia Dictionary, means concerned with mathematics, is mathematical, and very definite and precise. According to Watson and Gest (2012), engagement in mathematics includes covering awareness of all objects, intelligent details, viewing equations and relationships, focusing on properties, and viewing properties such as definitions or axioms. There is no specific definition for mathematical engagement, but some references use the term mathematical engagement, which means engagement in mathematics, among others Ingram (2011), Patahuddin (2018. Mathematical engagement is considered as student engagement in mathematics activities in the classroom and their commitment to learning mathematics content (Ingram, 2011).
To measure students mathematical engagement in learning, it can refer to several aspects of students mathematical engagement according to Goldin (2011) namely as follows: (1) Purpose/motivation drive; (2) Behavior; (3) Emotions beginning to end; (4) External expression; (5) The meaning of emotions; (6) Metta-affect; (7) Thoughts; (8) Interaction of beliefs and values; (9) The interaction between personality traits, self-identity towards mathematics, with motivation orientation; (10) Interaction to all aspects with problem solving and heuristics. The structure of engagement is used to describe patterns in student engagement during group mathematics activities (Goldin et al., 2011), are in the following table. Check this out Students wish to get prizes in obtaining the final result, so as to increase interest in the given assignment. 4 I am really into this Students want to be involved in work on assignments, because they are interested in mathematics or problem solving. 5 Don't disrespect me Students desire to meet the perceived challenges of existing mathematical ideas. 6 Stay out of trouble Students wish to avoid interactions that can cause conflict or make friends difficult, so they prefer to solve it themselves. 7 It's not fair Students wish to correct perceived injustices in group problems, for example the level of participation by others. 8 Let me teach you Students desire to help others to problems solving. 9 Pseudo-engagement Students desire to appear to be good to teachers or peers by being involved while avoiding genuine participation. Source: Goldin (2011) To find out student engagement, it is important to problems solving in mathematics learning, because the problem solving process will make student understanding better (Sapitri, Utami & Mariyam, 2019). Troubleshooting introduced by Bransford and Stein (1993) is IDEAL problem solving, which is a problem solving model that is able to improve thinking skills and improve skills in the problem solving process. The presentation of the categories of problem solving steps is used as a reference to describe the students mathematical problem solving abilities in completing worksheets. The ability and inability of students to solve these problems are categorized into three abilities including good, adequate, and lacking. Descriptions of the table are expected to describe the ability to solve mathematical problems that are sequential and structured according to the steps of Bransford & Stein in the worksheet. The description of the results of students mathematical problem solving abilities in this study is used as an evaluation to see the extent of the improvement in students mathematical problem solving abilities.

C. RESULT AND DISCUSSION
In the results and discussion will explain about the mathematical engagement of students in solving student problems with high, medium and low abilities. The results of the research and discussion are described in several subsections as follows:

Description of Student Engagement with High Ability in Solving Mathematical
Problems Problem solving is very important in learning mathematics, because the problem solving process will make student understanding better (Sapitri, 2019). To find out the description of the results of the spelling of the worksheet of students with high abilities in problems solving in the context of Brawijaya Temple can be seen in the following Table 3. Each student tries to provide the information provided in his own language.
Define goals Students are able to complete by determining what is being asked in the question.

Explore possible strategies
Students are able to write down the problem solving strategies /steps used. Next, describe them using their own sentences.

Anticipate
Students are able to find the method used to solve the problem so that they can solve it with the final result correctly.
Look back and learn Students review the answers so that they can make conclusions on the last question.
Furthermore, during the interview session, students were able to explain what the steps of working on the questions were from the first step to completion and found the correct results.

P
: "Can you tell us how you did the worksheets?" ST : "Yes, sis" P : "Please explain for problem 1 first, okay?" ST : "For problem 1, the first one was asked to write down known information, then I wrote the base of the temple in a square shape measuring 6x6m; temple height 10m; around the temple will be installed paving 2m wide from the temple; and the paving that will be installed is in the shape of a 10x20cm rectangle. Then what was asked was how much paving was needed to cover the entire edge of the temple. Then the finishing steps I used included calculating the area of the base of the temple to be installed with paving; then knowing the area of the whole; then calculate the paving area; and the latter divides the area of the temple base with the paving area. Then I did it according to my steps and found the answer. And I believe I wrote the answer correctly. P : "Okay, then move on to the second problem" ST :"From problem number 2 it is known that a 1m high iron pole will be used as a guardrail; distance between poles 2m; chain length for connecting 2.5m; and in the middle of the fence is a door 2m wide. then the question is how many poles are needed and the length of the chain required? Furthermore, the finishing steps that I use start from calculating the circumference of the temple which will be given a guardrail; counting the number of poles by dividing the circumference by the distance; to calculate the length of the chain by multiplying it. Then do it according to the steps I chose earlier and find the answer. And I am sure of the answer. P : "Why did you use that step?" ST : "Because I think using that step can make it easier for me to do it" To find out the validity of data about the engagement of highly skilled students in problems solving can be compared in the following Table 4: Students are able to explain how they do it until they find the right results Look back and learn Students review their answers so they can make conclusions The student explains that he is able to make conclusions on the last question.
Mathematical engagement of high-skilled students at the stage of identifying the problem, students are able to get through it, namely by reading and understanding the problems given.
Next write down what is known in the problem. Students try to provide information appropriately and are able to complete it in their own language. At the stage of determining the goals students are able to determine what is being asked in the questions. Judging from the answer, students can gather information appropriately and be able to convey it in their own language. In this case, students feel motivated and become active participants (Febrilia & Nissa, 2019). At the stage of exploring possible strategies, students plan well and clearly. At the stage of overcoming the results and acting students are able to get the correct answer. Students are also very enthusiastic about explaining their feelings when working on worksheets. This is in accordance with the opinion Watson (2007), student engagement can be seen from the ability of students to identify the properties of mathematical objects.
Based on the stages of solving students' mathematical problems in solving mathematical problems according to Bransford & Stein, high-skilled subjects can fulfill all stages of problem solving including, identifying, setting goals, exploring possible strategies, overcoming results and acting, and seeing and learning. Based on the description above, the engagement that occurs in high-ability students is get the done.

Description of Student Engagement with Medium Ability in Solving Mathematical Problem
Problem solving is very important in learning mathematics, because the problem solving process will make student understanding better (Sapitri, 2019). To find out a description of the results of the spelling of the Worksheet of Students with moderate abilities in problems solving in the context of Brawijaya Temple can be seen in the following Table 5. Define goals Students are able to determine what is being asked in the questions by using their own sentences.

Exploring possible strategies
Students are able to write down the problem solving strategies/steps used. Next, describe them using their own sentences.

Anticipate
Students are able to problems solving using the steps to solve them coherently, but the results are not correct.
Look back and learn -Students are not able to complete this stage, so they cannot display the results of the answers to the existing questions.
At the time of the interview session, students were able to explain what the steps of working with the questions were from the first step to the finish, but the results obtained were not correct.

P
: "Can you tell us how you did the worksheets?" SS : "Yes" P : "Please explain for problem 1 first, okay?" SS : "For problem 1, it is known that the base of the temple is a square shape with a size of 6x6m; temple height 10m; paving will be installed around the temple; rectangular paving with paving size 10x20cm. Then asked how much paving is needed to cover the edge of the temple. Continue to be calculated using the steps " P : "Okay, then move on to the second problem" SS :"From problem number 2, it is known that the iron pole is 1m high; distance between poles 2m; chain link length 2m. It asks how many poles are required and the length of the chain required. Then calculated using steps and find the answer " P : "Why did you use that step?" SS : "Because it's easier for me to understand" . To find out the validity of data about the engagement of students with moderate abilities in problems solving, it can be compared in the following Table 6: Students are able to complete the questions that have been given but the final result is wrong Students are able to explain the process until they find the final result even though the answer is wrong Look back and learn Students are not able to complete this stage, so they do not provide final conclusions.
Students are unable to explain the final conclusion The mathematical engagement of the subject students is at the stage of identifying the problem, the subject is able to get through it, namely by reading and writing the known elements. In accordance with the opinion Abidin (2015), that reading is defined as a complex information processing process. And understand the context of the problem that must be resolved with the information needed to solve the problem. At the stage of determining the objectives, the subject is able to determine what is being asked in the question. Judging from the answer, students can gather information appropriately by using systematic reasoning so that they are able to convey it in their own language. In accordance with the opinion Salmina & Khairun Nisa (2018), namely the ability to connect problems into an idea or idea so that it can solve mathematical problems. At the stage of exploring possible strategies, the subject is able to write down steps that will be used in problem solving. At the stage of overcoming the results and acting the subject is able to solve the questions that have been given but the final result is still not correct. The subject was also a little confused in explaining his feelings while working on the worksheets.
Based on the stages of solving students mathematical problems in solving mathematical problems according to Bransford & Stein, medium-capable subjects can fulfill four stages of problem solving, including identifying, setting goals, exploring possible strategies, overcoming results and acting. And not being able to get past the problem solving stage of coping with the results and acting, because the subject did not provide an answer to the last question. Based on the description above, the engagement that occurs in students with moderate abilities is I am really into this.

Description of Student Engagement with Low Ability in Solving Mathematical Problem
Problem solving is very important in learning mathematics, because the problem solving process will make student understanding better (Sapitri, 2019). To find out a description of the results of the spelling of the worksheet of students with low abilities in problems solving in the context of Brawijaya Temple can be seen in the following Table 7. Students choose the information that is known in the questions, and dig up the information appropriately as an initial attempt to solve the problem.

Define goals
Students are able to determine what is being asked in the questions by using their own sentences.

Explore possible strategies
Students write down the problem solving steps that will be used when solving the problem but the steps used are wrong.

Anticipate
Students do not complete the questions using predetermined completion steps, and student work has not been completed and has not found the final result of completion. Look back and learn -Students are not able to complete this stage, so they cannot display the results of the answers to the existing questions.
At the time of the interview session, the students were unable to explain what the steps of working on the questions were from the first to the finish, it can be seen from the following interview excerpt.

P
: "Can you tell us how you did the worksheets?" SR : "I can't sis because I don't understand" To find out the validity of data about the engagement of students with moderate abilities in problems solving, it can be compared in the following table. Students are unable to explain the final conclusion Mathematical engagement of low-ability students at the stage of identifying problems, students are able to get through it, namely by reading and writing what is known but cannot explain it at the time of the interview. At the goal-setting stage, students are able to determine what is being asked in the question, but cannot explain it. Here, students are able to tell their motivation and purpose in doing the worksheets, but in explaining it, students are not excited. This corresponds to Appleton, Christenson, and Furlong (2008), that students who are not involved in learning tend to be apathetic, not excited, chat with friends, and not focus or even sleep during the lesson. At the stage of exploring possible strategies, students are able to write down the steps that will be used in problem solving but cannot explain the steps. At the stage of overcoming the results and acting students are not able to solve the questions that have been given and cannot display the final results. For the seeing and learning stage students are unable to pass it, because in the answer sheet students cannot answer it because they do not do it. This corresponds toKartiwi, the difficulty of learning mathematics is because students are less able to apply mathematical concepts in real life so that this learning is less meaningful for students.
Based on the stages of solving students mathematical problems in solving mathematical problems according to Bransford & Stein, low-ability students can fulfill two stages of problem solving, including identifying, determining goals. Meanwhile, to explore possible strategies, overcome the results and act, students are not able to solve them. Based on the description above, the engagement that occurs in students with moderate abilities is pseudoengagement.

D. CONCLUSION AND SUGGESTIONS
Based on the results of the analysis, it can be concluded that the mathematical engagement of students with high, medium and low ability levels in problems solving in the worksheet, namely: (1) Mathematical engagement of high-skilled students has good problem-solving abilities so that they can fulfill the 5 stages of problem solving, namely identifying problems, setting goals, exploring possible strategies, coping with results and acting, and seeing and learning. Student engagement in problem solving, namely "get the job done"; (2) The mathematical engagement of moderate-capable students has sufficient problem-solving abilities because it can fulfill the 3 stages of problem solving, namely identifying problems, determining goals, exploring possible strategies. Student engagement that occurs in students with moderate abilities is that "I am really into this"; (3) Mathematical engagement of lowability students have less problem-solving abilities because they can fulfill the 2 stages of problem solving, namely identifying problems, determining goals. The engagement that occurs in low-ability students is "pseudo-engagement". And suggestion for future research, this research works on worksheets individually, and it is recommended for further research in groups. and activate the different types of angagement in this study.