Volume 9 Nomor 2 July 2021 Hal. 124-131 p-ISSN:2541-4232 dan e-ISSN: 2354-7146
Analysis of Students' Mathematical Problem Solving Ability in Solving HOTS Problems in terms of Mathematical Resilience
Fitria Dwi Nurjanah1, Hella Jusra2
1,2 Universitas Muhammadiyah Prof.Dr.Hamka
Email: [email protected] , [email protected]
©2021–Daya matematis: Jurnal inovasi pendidikan matematika. This article open acces by licenci CC BY-NC-4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
Abstract
This research purposed to describe students' mathematical problem solving abilities in solving HOTS questions based on mathematical resilience. This type of research is descriptive qualitative research with the subjects of this study were class VII students, totaling 218 students who were selected by purposive sampling. The research subjects were grouped into 3 categories based on mathematical resilience, namely high, medium and low. The instrument used is a mathematical resilience questionnaire, a written test of mathematical problem solving ability, and interview. The results of this study indicate that from 218 students there are 22 students with low mathematical resilience category, 156 students with medium mathematical resilience category, and 40 students with high mathematical resilience category. Some students are in the category of moderate mathematical resilience. And each high, medium and low category has different mathematical problem solving abilities in solving HOTS questions.
Keywords: students mathematical problem solving, HOTS, mathematical resilience
INTRODUCTION
The main goal of learning mathematics is to make students have a higher level of thinking and personality processes in order to gain a deeper level of understanding when learning mathematics (Sumadi et al., 2020). For most students mathematics is not a simple subject. The quality of mathematics learning needs to be improved so that students have the ability to master their knowledge. One of the mathematical abilities is the ability to solve mathematical problems that make it easier for students to find solutions to various problems in everyday life. Problem solving ability is a student's potential to find solutions, solve problems and apply mathematics in everyday life (Andayani & Lathifah, 2019).
Problem solving steps according to Polya are understanding the problem, making plans, implementing plans and re-examining (Polya, 1973). If students know the steps of problem solving then they have the ability to find the right solution.
One of the problems related to mathematical problem solving skills is that most students have difficulty when they have not fully developed problem solving skills. Especially when students study material from mathematics books in the 2013 curriculum, there are many questions based on HOTS (Haryani, 2013). HOTS (Higher Order Thinking Skills) is a higher order thinking skill that includes analysis, evaluation and creativity. HOTS questions are questions that have characteristics to measure higher- order thinking skills which include critical thinking skills and creative thinking can be classified by analysis, evaluation and creativity, and HOTS questions are sourced from contextual problems that can train students to not only remember or understand knowledge and concepts only but can also connect problems with the real world (Widana, 2017). The HOTS questions given to students not only focus on problem solving, but also require students to solve problems and make students analyze critically, creatively and collaboratively (Kurniawan et al., 2019). From this, the HOTS question is a technique or tool that can measure a person's higher-order thinking skills including the ability to think creatively and think critically based on complex or non-routine problems. Students' abilities in solving HOTS questions
(Received:25-03-2021; Reviewed: 2-05-2021; Revised: 27-05-2021; Accepted: 9-05-2021; Published: 5-07-2021)
are different, meaning that students' higher-order thinking skills are also different. However, HOTS questions can make students more active and able to develop critical, creative and systematic thinking in the learning process.
However, in solving HOTS questions, it is certainly different for each student, one of which is depending on the student's mathematical resilience. Where each student has different difficulties in solving HOTS questions. When faced with this situation students will show a negative or positive attitude when learning mathematics. Such as not doing the questions, giving up easily, uncomfortable, afraid and avoiding learning mathematics. Resilience is a quality attitude towards learning mathematics which includes full confidence in the success achieved through hard work and perseverance in the face of difficulties (Ansori, 2020). Mathematical resilience is a student's attitude that affects the achievement of mathematics learning in solving various mathematical problems which is carried out through adaptation even though students are in challenging situations.
Research conducted by Rahmatiya and Miatun found that students with high mathematical resilience have confidence in solving problems while students with mathematical resilience are less careful in solving and often give up when facing difficult problems (Rahmmatiya & Miatun, 2020). From the results of the study, it can be said that if a student has high mathematical resilience, then learning mathematics is not a problem, but as a challenge for him to solve mathematical problems in various ways such as learning experiences, thinking highly and creatively. Meanwhile, a student with moderate or low mathematical resilience considers that learning mathematics is a difficulty faced, so that it becomes a problem in solving mathematical problems.
Based on the description above that each student will face various challenges in solving math problems and students will show a quality attitude towards learning mathematics through surviving and developing strategies in responding to obstacles. This attitude characterizes students in terms of mathematical resilience. The purpose of this study is to describe students' mathematical problem solving abilities in solving HOTS questions based on students' mathematical resilience classified with high, medium and low levels of mathematical resilience.
METHODS
This type of research uses descriptive qualitative research methods to describe students' mathematical problem solving abilities in solving HOTS questions based on students' mathematical resilience. The sample in this study was class VII students, totaling 218 students who were selected by purposive sampling. Purposive sampling technique was used to focus researchers on grouping students' mathematical resilience, so that 2 research subjects were selected for each high, medium, and low group.
The instruments used in the study were students' mathematical resilience questionnaires, students' mathematical problem solving abilities in solving HOTS questions, and interviews. In this study, students were first asked to fill out a mathematical resilience questionnaire, the questionnaire was adapted from the four-factor principal-axis factor analysis of the mathematical resilience scale (Wilder et al., 2013) which consisted of 36 statements. Then each student takes a mathematical problem solving ability test based on indicators of mathematical problem solving ability in the form of a description of 8 HOTS questions with comparative material and social arithmetic. The data collected was scored using Rasch modeling to determine students' mathematical resilience which can be classified into high, medium, and low groups. Furthermore, two research subjects were selected from each category, namely high, medium, and low based on mathematical resilience, and continued with semi-structured interviews on research subjects regarding the mathematical problem solving ability test completed by students. It aims to clarify information with the required data related to students' mathematical problem solving abilities in solving HOTS questions in terms of mathematical resilience.
RESULTS AND DISCUSSION
used to determine the level of students' mathematical resilience and written tests are used to determine students' mathematical problem solving abilities in solving HOTS questions. This mathematical resilience questionnaire is based on 4 factors that influence students' mathematical resilience in learning mathematics, namely grades, struggle, growth and resilience (Wilder et al., 2013). Such as the attitude of students in facing several obstacles in learning mathematics that have gone through hard work, cooperation and perseverance in facing difficulties. Then focused on 4 factors that affect students' mathematical resilience as a measure of students' mathematical resilience in learning mathematics, namely:
1. Value
Grades are based on students' perceptions of the importance of mathematics in their lives and the world.
If students view mathematics as very valuable, the more motivated they are to learn and the more likely they are to survive in the face of adversity. The percentage of student scores can be seen in Figure 1.
Figure 1. Percentage of Value Indicators
Based on Figure 1 above, it states that from 218 respondents and 9 statements for the first indicator about students' perceptions of the importance of mathematics in their lives and the world, 1% stated strongly disagree and the largest 55% agreed.
2. Struggle
Struggle is determined by students' perceptions of believing that struggles in mathematics are commonplace for their peer group or for all who study mathematics will have a stronger tolerance and endurance in the face of setbacks. The percentage of student struggle can be seen in Figure 2.
Figure 2. Percentage of Struggle Indicators 3. Growth
Growth is based on students' perceptions of the belief that mathematical knowledge is not fixed and can evolve. Even though students are born without the ability to learn. The percentage of student struggle can be seen in Figure 3.
Figure 3. Percentage of Growth Indicators
Based on Figure 3 above, it is stated that of the 218 respondents and 9 statements for the third indicator about students' perceptions of the belief in mathematical knowledge that is not fixed and can develop, 3% stated strongly disagree and many agreed at 47%.
4. Durability
Resilience is determined by students' perceptions of psychological resilience which includes exposure to significant threats followed by positive responses associated with learning mathematics. Thus, this factor combines two components, namely several experiences with obstacles and positive responses.
The percentage of student resilience can be seen in Figure 4
Figure 4. Percentage of Resilience Indicators
Based on Figure 4 above, it is stated that of 218 respondents and 8 statements for the first indicator about students' perceptions of psychological resilience to significant threats followed by positive responses related to learning mathematics, as many as 64% agree, 6% disagree and no one chooses. strongly disagree.
Overall, based on the results of the mathematical resilience questionnaire, there are 22 students with low mathematical resilience categories, 156 students with moderate mathematical resilience categories and 40 students with high mathematical resilience categories. Based on the results of filling in the mathematical resilience of students, most of them are in the medium category. However, in this study, it was focused on the results of students' mathematical problem solving abilities in solving HOTS questions based on mathematical resilience for 6 students consisting of 2 students in each high, medium and low category. The selected research subjects were S1 and S2 who had low mathematical resilience, S3 and S4 had moderate mathematical resilience, while S5 and S6 had high mathematical resilience.
Below will be presented the results of students' mathematical problem solving abilities in solving HOTS questions in terms of mathematical resilience.
Picture. 5 Results of Writing Test Answers for S1 Students
From the results of mathematical resilience scoring shows that undergraduate students are included in low mathematical resilience. Students' enthusiasm for learning mathematics is still lacking and less interested in mathematics. Which makes it difficult for students to accept and understand mathematical problems. However, if students are confused about the material being studied, they will find the answers on the internet or with the help of their friends. Students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed students could write down the information obtained from the problem and when interviewed students were able to reveal the information contained in the problem. For indicators of planning, it shows that students make inappropriate plans, where students do not write down the formula to be used, the solutions they get do not lead to the right solution and students are less able to express the plans they make. For indicators of carrying out the plan, it shows that students can solve problems, but do not write down in detail the completion steps and lead to wrong answers. And for the re-examination indicator, it shows that students immediately ended without re-examining the solution, did not write down the conclusions and did not prove the answers they got.
Picture. 6 Postgraduate Student Answers Writing Test Results
From the results of the mathematical resilience scoring shows that the master's degree students are included in the low mathematical resilience. Students' enthusiasm for learning mathematics is quite good and students are interested in mathematics. This makes it easier for students to accept and understand mathematical problems. If students are confused about the material being studied, they will find the answers themselves or ask for help from their closest family members. Students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed students could write down the information obtained from the problem. For indicators of planning, it shows that students make plans that lead to the right solution, but students do not write down the formula that will be used. For indicators of running a plan, it shows that students can solve problems correctly, and write in detail the steps of completion, and students can convince themselves that the solutions are completed according to the plan. The re-examination indicator shows that students are able to re-examine the answers obtained and write conclusions. However, on the results of the written test, students cannot prove that the answer obtained is correct, and after the interview the student can prove the answer is correct by saying "In order for the trader to cover his loss on the 2nd sale of cattle, the trader adds a loss of Rp. first cow. So the sale of the second cow is Rp. 10,810,000.00".
Picture. 7 Results of Writing Tests for Doctoral Students
From the results of the mathematical resilience scoring shows that the doctoral students are included in the moderate mathematical resilience. Students' enthusiasm for learning mathematics is quite good and students are interested in mathematics. This makes it easier for students to accept and understand mathematical problems. If students are confused about the material being studied, they will find the answers themselves or ask for help from a tutoring teacher. Students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed students did not write down the information obtained from the problem, even though from the results of the interviews students were able to reveal the information contained in the problem. For indicators of planning, it shows that students design solutions that lead to the right solution and do not write down the formula that will be used. The indicators for running the plan show that students can solve problems incorrectly or do not write down how to calculate correctly, even though the student's answers are correct. And for the re-examination indicator shows that students are less able to re-examine the answers obtained, students immediately end without writing conclusions and do not prove the answers they get are correct.
Picture. 8 Results of the S4 Student's Answer Writing Test
From the results of mathematical resilience scoring shows that S4 students are included in moderate mathematical resilience. Students' enthusiasm for learning mathematics is very good and students are very interested in mathematics. If students experience confusion about the material being studied, they will find the answers themselves or through learning videos on YouTube. Students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed that students could write down the information obtained from the problem. For indicators of planning, it shows that students design solutions that lead to the right solution and write down the formula that will be used. For indicators of carrying out the plan, it shows that in solving the problem students write in detail the steps of completion, but there are errors in calculations that make students' answers wrong. However, at the time of the interview, students can point out where the error is in the calculation of this question by saying "I calculated the selling price of the 1st cow to be Rp.
9,000,000.00 with a loss of Rp. 810,000.00. Then for the selling price of the 2nd cow to cover the loss.
is Rp. 10,000,000.00 + Rp. 810,000.00 = Rp. 10,810,000.00. And my obstacle in solving this math problem is that I am not careful enough even though I already understand this problem". And for the re- examination indicator, it shows that students are less able to re-examine the answers obtained and cannot prove the answers, even though students write the conclusions of the problem.
Picture. 9 Results of the S5 Students' Answer Writing Test
From the results of mathematical resilience scoring shows that S5 students are included in high mathematical resilience. Students' enthusiasm for learning mathematics is quite good and students are interested in mathematics. Students do not like to ask questions to the teacher, but students prefer to respond to questions from the teacher. If there are questions that are not understood, students will ask for help with tutoring teachers or look at learning on the internet. Students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed students could write down the information obtained from the problem and students were able to reveal the information contained in the problem. For indicators of planning, it shows that students write down the formula that will be used and the solutions they get lead to the right solution. For indicators running the plan shows that students can not solve the problem. However, during the interview, the student said, “I was a bit confused when I continued with this calculation, so I could only write the formula. And I'm not sure about the solution that I will make later, so I don't solve this problem." And for the re-checking indicator, it shows that students are not able to re-check the answers.
Picture. 10 Results of the S6 Student's Answer Writing Test
From the results of mathematical resilience shows that S6 students are included in high mathematical resilience. Students' enthusiasm for learning mathematics is very good and students are very interested in mathematics. If students experience confusion about the material being studied, they will find the answers themselves or through learning videos on YouTube. The students' mathematical problem solving ability in solving HOTS questions revealed that the indicator of understanding the problem showed students could not write down the information contained in the problem, even though from the results of the interviews students were able to reveal the information contained in the problem. For indicators of planning, it shows that students design solutions that lead to inappropriate solutions, and students do not write down the formulas that will be used. The running indicator shows that the students wrote the completion steps incorrectly. From the results of interviews there are obstacles experienced by students, namely students experience confusion in solving these problems. And for the re- examination indicator, it shows that the student immediately ends the completion without re-examining the solution, does not write down the conclusion and does not prove the answer he got.
CONCLUSIONS AND SUGGESTIONS
The results of this study indicate that from 218 students there are 22 students with low mathematical resilience categories, 156 students with moderate mathematical resilience categories and 40 students with high mathematical resilience categories. Most of the students are in the medium mathematical resilience category, and each high, medium and low category has different mathematical problem solving abilities in solving HOTS questions, namely (1) Low mathematical resilience indicates that undergraduate and postgraduate students have the same problem solving abilities students' mathematical problems in solving HOTS questions, namely students are able to meet the indicators of understanding the problem which means students understand the problem by showing the information contained in the problem. (2) On the mathematical resilience which is showing that S3 and S4 students do not have the same mathematical problem solving ability of students in solving HOTS questions, but has a difference,
namely S3 students fulfill the indicators of carrying out the plan incorrectly or not writing the calculation method correctly, even though the answer student is correct. While S4 students fulfill the indicators of carrying out the plan by writing in detail the completion steps, but there are errors in calculations that make students' answers wrong. (3) High mathematical resilience shows that S5 and S6 students do not have the same mathematical problem-solving abilities in solving HOTS questions, but they have a difference, namely S5 students fulfill the indicators of planning by writing the formula to be used and the solutions they get lead to completion. appropriate, while S6 students meet the indicators of planning by designing solutions that lead to inappropriate solutions, and students do not write down the formula to be used.
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