Daya Matematis : Jurnal Inovasi Pendidikan Matematika

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Daya Matematis : Jurnal Inovasi Pendidikan Matematika

Volume, 10 Nomor 2 July 2022 Hal. 98-106 p-ISSN:2541-4232 dan e-ISSN: 2354-7146

ANALYSIS OF MATHEMATICAL PROBLEM-SOLVING ABILITY BASED ON SELF-EFFICACY AND SELF-CONFIDENCE OF CLASS VIII JUNIOR

HIGH SCHOOL STUDENTS

Aida Ar Rahmah ¹, Slamet Soro ²

1 Mathematics Education, Faculty of Teacher Training and Education University of Muhammadiyah Prof. Dr. HAMKA

Email: [email protected]

2 Mathematics Education, Faculty of Teacher Training and Education University of Muhammadiyah Prof. Dr. HAMKA

Email: [email protected]

Abstract

This study aims to describe students' mathematical problem-solving ability of Junior High School in terms of students' self-efficacy (SE) and self-confidence (SC). This typr of research is descriptive qualitative. This research was conducted in class VIII at one of Junior High Schools in Jakarta. Subjects in this research based on the result of questionnaire selected 3 students who had SE and SC from high, medium and low. The research's instruments are SE and SC questionnaires, mathematical problem-solving ability tests , and interviews . The test and non-test instruments were validated by expert validators before being tested for validity and reliability. The data analysis techniques uses the Miles and Huberman model for data reduction, data presentation, and drawing conclusions.

Triangulation techniques were used to test the validity of the research data. The results of this research indicate that students with high SE and SC had the best mathematical problem-solving abilities compared to students with medium to low SE and SC. Students with high SE and SC fulfill 4 indicators of problem-solving ability with maximum scores. Students with medium to low SE and SC only met 3 indicators of problem-solving ability Keywords: Mathematical Problem-Solving Ability; Self-Efficacy; Self-Confidence; Junior High School

INTRODUCTION

At this time, the achievements of Indonesian students are still not optimal and are still far behind from other countries . According to the 2015 PISA survey in research (Dewi & Minarti, 2018) that student scores in Indonesia are very low. Study (Wahyudi & Anugraheni, 2017) stated that Indonesia was ranked 70th, meaning that the ability to solving math problems in Indonesia is classified as poor or low. According to NCTM, problem solving ability is one of the mathematical skills . In the mathematics curriculum, problem solving skills are closely related to the characteristics of mathematics, including higher order thinking. In Permendiknas RI No.

22 Year 2006 (Depdiknas, 2006) , explains that the learning process of mathematics has a goal, namely problem solving , including understanding problems, developing strategies, solving problems and explaining solutions.

According to Polya (Wahyudi & Anugraheni, 2017) Problem solving is defined as an effort or process of finding solutions to problems challenging . According to Hudoyo (Purnama &

Mertika, 2018) that problem solving is a process from someone in solving problems until the problem is solved . From the opinions of some of these experts , it is concluded that mathematical problem solving ability is a person's ability to solve mathematical problems by understanding what is known and asked, using planning strategies in determining the settlement formula to obtain problem solving solutions. According to Polya (Jatisunda, 2017) There are four indicators in the problem solving process including : (1) understanding the problem (

(Received:15-4-2022; Reviewed: 17-4-2022; Revised: 24-05-2022; Accepted: 22-06-2022; Published: 29-07-2022)

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Daya Matematis: Jurnal Inovasi Pendidikan Matematika, Vol. 10 No. 2 July 2022

understanding ), (2) planning a strategy (strategy), (3) solving the problem (solve), and (4) evaluating (look back).

In addition to problem-solving abilities, the success of the learning process in schools is also supported by psychological aspects related to student attitudes in the learning process. Based on the fifth point of the Minister of National Education RI No. 22 Year 2006 (Depdiknas, 2006) regarding strengthening psychological aspects in learning mathematics . One aspect that has a significant impact on the success of the learning process is self-efficacy and self-confidence.

According to Bandura (Jatisunda, 2017) that SE is defined as one's belief in one's ability to complete a task in order to achieve a certain result. Research (Utami & Wutsqa, 2017) states that SE in mathematics learning is defined as students' beliefs about the ability to solve mathematical problems. According to Bandura (Alifia & Rakhmawati, 2018) There are three indicators used to measure SE including : (1) Magnitude , which measures how students overcome their difficulties , (2) Strength , namely students' confidence in overcoming their difficulties and completing tasks , and (3) Generally , namely confidence in themselves in maintaining their abilities. SE in this study is SE mathematical, namely students' self-confidence about knowledge and ability in solving mathematical problems.

In research (Marasabessy, 2020) explained that SE has a function as a tool for student success in completing assignments, as well as solving problem solving problems. This study uses indicators SE according to Bandura. In line with previous research , namely by (Amalia et al., 2018) ; (Agumuharram & Soro, 2021) ; (Indahsari et al., 2019) ; (Nurseha & Apiati, 2019) ; (Zakiyah et al., 2018) ; (Zamnah, 2019) that SE and problem solving ability have a positive relationship. Students with high SE have been able to achieve all indicator of problem solving ability to the maximum . Meanwhile, SE currently and low has not reached the maximum of the four indicators . It is concluded that SE plays an important role in everything, especially in the learning process in solving mathematical problems.

In the learning process, SC including important aspects. SC is a psychological aspect that includes self-confidence in the form of abilities and skills to achieve what they want (Guidance, 2019) . According to (Wardhana & Lutfianto, 2018) SC is a person's confidence in his ability to apply mathematics in his life. Mathematical confidence is confidence in students about their knowledge and ability to solve mathematical problems. According to Lauster (Dewi & Minarti, 2018) The indicators to measure SC are: (1) self -confidence in their abilities, ( 2) making decisions independently , (3) positive self - concept , and (4) being able to opinion . This study uses the SC indicator according to Lauster.

According to previous research conducted by (Fauziah et al., 2018) ; (Nurojab & Sari, 2019) ; (Saputri, 2019) that SC and problem solving ability have a positive relationship. It is said that students with high SC have been able to achieve the four indicators of problem solving ability to the maximum . While students with Medium and low SC have not reached the maximum of the four indicators of problem solving ability. From the previous research, there is a difference, namely there is no research that discusses mathematical problem solving abilities from the SE and SC aspects simultaneously on the material of building space. While the renewal in this research is on the selected variables, the subject and the place where this research is conducted .So this research was conducted with the title Analysis of Mathematical Problem-Solving Ability of Junior High School Students From Self-Efficacy Aspects and Self-Confidence of Students ” with indicators that have been selected from several sources.

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Daya Matematis: Jurnal Inovasi Pendidikan Matematika, Vol. 10 No. 2 July 2022 METHODS

This type of research is a qualitative research that aims to describe students' mathematical problem solving abilities from the SE and SC aspects of junior high school students. This research was conducted in class VIII of SMP Negeri in Jakarta for the academic year 2021/2022. In taking the subject, the researcher uses a purposive sampling technique , namely the researcher determines the research subject with considerations such as establishing special characteristics that are in accordance with the research objectives. Subjects in the study were selected as many as 3 students with SE and SC categories of high, medium, and low. This study uses test and non-test instruments, namely: (1) a test of mathematical problem-solving skills on the flat-sided geometry material, (2) SE and SC questionnaires , (3) interview guidelines. The test and non-test instruments were validated by lecturers and subject teachers before being tested for validity and reliability. This study uses triangulation techniques to test the validity of research data with different techniques, namely questionnaires, tests and interviews.

The research began by filling out a questionnaire via Google Form to all eighth grade students.

SE Questionnaire adapted from (Imaroh et al., 2021) which consisted of 30 statements. The SC questionnaire was adapted from (Dewi & Minarti, 2018) which consisted of 20 statements. The questionnaire uses a Likert scale with 4 choices of scale. Based on the results of the questionnaire, students were categorized into 3 categories, namely students with high SE and SC , students with moderate SE and SC , and students with low SE and SC . Determination of categories, according to table 1 calculation of intervals on the mean ( X ) and standard deviation (SD). (Guidance, 2019). The selected subjects will be given a mathematical problem solving ability test based on the Polya indicator. Data analysis techniques using the Miles and Huberman model to analyze data (Nugrahani, 2014) include: (1) data reduction, that students are grouped into three categories obtained from the results of the questionnaire to be interviewed, (2) data presentation, in the form of pictures of the subject's answers to be described, (3) drawing conclusions.

RESULTS AND DISCUSSION SE and SC Student Results

The number of students who have filled out the questionnaire is 37 students. Researchers categorize into 3 categories, namely high SE , medium SE, and low SE which can be seen in table 2. In table 3, the researcher also categorizes students into high SC , medium SC and low SC.

Table 2 . Student SE Data

Category SE Total students Percentage

Tall 4 11%

Currently 30 81%

Low 3 8%

Table 3 . Student SC Data

SC Category Total students Percentage

Tall 4 4%

Currently 31 84%

Low 2 5%

Based on table 2, it is found that there are 4 students with high SE, 30 students with moderate

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SE , and 3 students with low SE. For SC , students who have high SC are 4 students, moderate SC is 31 students, and low SC is 2 students. Researchers used purposive sampling and subject recommendations by mathematics teachers to select 3 subjects from each SE and SC categories who would be identified more deeply about mathematical problem solving abilities.

Results of Students' Mathematical Problem Solving Ability

There are four indicators of mathematical problem solving ability that are measured, namely:

understand, strategy, solve and look back . Data on students' mathematical problem solving abilities were obtained from the test results of 2 description questions. Questions are given to 3 selected students. The data on the results of students' mathematical problem solving abilities on the flat-sided geometry based on SE and SC categories can be seen in table 4 and the achievement of each indicator can be seen in table 5.

Table 4 . Mathematical Problem Solving Ability Data by Category SE and SC Subject

Code

Questionnaire

Category Test Score No.

Question

Indicator Category Problem

solving skill

SE SC 1 2 3 4

RP Tall Tall 27 1 3 4 4 3 Capable

2 2 4 4 3 Capable ZL Currently Currently 17

1 2 4 4 0 Not

enough

2 2 4 2 0 Not

enough

MZ Low Low 9

1 2 0 1 0 Not

enough

2 0 4 2 0 Not

enough Table 5. Achievement of each Indicator of Mathematical Problem Solving Ability

Indicator Total score Percentage

Understand 11 20%

Strategy 20 37%

Solve 17 32%

Look Back 6 11%

a. RP Subjects with High SE and High SC

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The following will describe the mathematical problem solving abilities of RP in Figure 1 below.

Figure 1. Answers of RP Subjects at No. 1 and No. 2

First indicator is understand , the RP writes down the known elements and is asked in full so that they get the maximum score at No. 1, but at No. 2 RP is incomplete in writing known elements. During the interview, the RP can re- explain the information on each question completely, and understand the purpose of the question. In the second indicator, namely strategy , the RP writes down the correct formula concept completely so that it gets the maximum score on both questions. RP has good ability because it is able to determine how to solve it by writing procedures and choosing the right formula concept. This was proven at the time of the interview RP feels confident, confident and able to explain sequentially the concepts used .

In the third indicator, namely solve , the RP is able to write a complete solution with the correct calculation so that it gets the maximum score on both questions . This was proven during the interview , the RP explained that he was confident with the chosen strategy and the results obtained were correct. Furthermore , the last indicator is look back . RP is able to evaluate and draw conclusions appropriately. This was proven during the interview , the RP said that he always checked the answers. RP looks very confident and confident in explaining the process to the conclusions obtained. Based on the results of the answers and interviews on the two questions, the RP fulfilled the four indicators optimally. Therefore, RP has excellent problem solving abilities

b. ZL Subjects with Medium SE and Medium SC

The following will describe ZL's mathematical problem solving abilities in Figure 3 below.

understand (3)

strategy (4)

solve (4)

look back (3)

understand (2)

strategy (4)

solve (4)

look back (3)

understand (2)

strategy (4)

solve (4) look back

(0)

understand (2)

strategy (4) solve

(2)

look back (0)

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Figure 2. Subject ZL's Answer at No. 1 and No. 2

The first indicator is understand , ZL writes known and asked but is incomplete. During the interview , ZL was not completely able to re-explain the information on each question. The researcher asked ZL "is there any other information?", then ZL answered "no". ZL It is said that they understand the problem quite well , but they are not careful enough. In the second indicator, namely strategy , ZL is good enough to be able to make a good strategy by writing the correct formula concept. According to the results of the interview, ZL looks already convinced with the concept of building space used.

In the third indicator, namely solve , ZL was able to write the solution with the correct result at No. 1, but wrote the solution with the wrong calculation in No. 2. When interviewed , the researcher asked "are you sure and confident with the steps and results you get?", then ZL answered "I'm still not sure and lack confidence, because I finished the questions in a hurry".

Furthermore, on the last indicator , namely look back , ZL did not write a conclusion on No. 1 and No.2 . During the interview , the researcher asked ZL “Did you check the answers? and why not write a conclusion?”, then ZL answered “I didn't do an examination and didn't write a conclusion so that there was enough time”. According to the results of answers and interviews, that ZL only met 3 indicators with a less than maximum score and the 4th indicator was not met. ZL is less thorough in solving problems, and is unable to evaluate the answers. Therefore, ZL has poor problem solving abilities.

c. MZ Subjects with Low SE and Low SC

The following will describe the mathematical problem solving ability of MZ in Figure 2 below.

Figure 3. Answers of MZ Subjects at No. 1 and No. 2

The first indicator is understand , MZ is not complete in writing the information No. 1. During the interview , MZ did not explain the information but only reread the questions. The researcher asked MZ "What kind of space does it appear from the question?", then MZ answered "No. 1 I don't know and No. 2 is in the form of blocks and pyramids”. MZ said that they did not understand the questions well and when interviewed they looked very unsure and lacked

understand (0)

strategy (4)

solve (2) look back

(0) understand

(2)

strategy (0) solve

(1) look back

(0)

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confidence . In the second indicator, namely strategy , MZ wrote the correct formula concept only in No.2 only. During the interview, the researcher asked NR “What concept do you use?”, then MZ answered “for No. 1 I worked on trial and error and for No. 2 I use the concept of a combined volume of a rectangular pyramid and a block.”

In the third indicator, namely solve , MZ was able to write a solution with incorrect calculations on both questions, and for No. 1 MZ has not been completed completely. When interviewed , the researcher asked "why No. 1 is not completed?”, then NR replied “I have not finished working because I have no ideas and I gave up”. Furthermore, on the last indicator , namely look back , NR did not write conclusions on the two questions. During the interview , the researcher asked NR “Are the calculations correct? and why not write a conclusion?”, then ZL answered “I didn't have time to check the calculations and didn't write the conclusion because the time was not enough”. MZ also explained that he found it difficult to do the questions, felt very unsure and very insecure. According to the results of the answers and interviews, it was explained that MZ only met 2 indicators with a score that was less than the maximum, namely the understand indicator , and solve at No.1 and the strategy indicator , and solve at No. 2.

Therefore, MZ has very poor problem solving skills.

Discussion

Research (Sa'adah et al., 2021) explains that SE and SC have an influence on students in the process of solving mathematical problems. Students who have high SE and SC have met the four indicators of problem solving ability. Based on research (Imaroh et al., 2021) says students who have high SE tend to have excellent problem solving skills. Research (Purnama & Mertika, 2018) also states that students who have high SC will have good problem solving skills. So that with both being in the high category, students will have excellent problem solving skills and will increase.

Meanwhile , students with moderate to low SE and SC still did not meet the four indicators. On research (Aisyah et al., 2018) and (Ulya & Hidayah, 2016) stated that students with moderate SE and moderate SC were able to meet 3 indicators and some indicators were still not optimal, so students' problem solving abilities were not good. Study (Resmiati & Hamdan, 2019) and (Ramdan et al., 2018) explained that the lower SE and SC students, then the problem solving ability of students is not good and must be improved.

CONCLUSION

According to the results of the analysis that has been discussed, it can be concluded that:

1. Students who have SE and high category SC , able to achieve all indicators of mathematical problem solving ability to the fullest,

2. Students who have SE and SC in the medium category, only able to achieve 3 indicators with less than maximum scores, namely the indicators of understand , strategy , solve , 3. Students who have SE and low category SC , only able to achieve 2 indicators with less

than maximum scores, namely the understand indicator , and solve at No.1 and the strategy indicator , and solve at No. 2.

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