HOW DOES PROBLEM-SOLVING METHOD AFFECT STUDENTS’ SELF-CONFIDENCE AND MATHEMATICAL UNDERSTANDING?

Received: June 18, 2020 Accepted: July 30, 2020 Published: July 31, 2020 This study aimed to determine the effects of problem-solving method on students’ self-confidence and mathematical understanding in learning. This study used quantitative and qualitative methods. The research followed the process of quantitative calculation from instruments about mathematical understanding and described students’ self-confidence, analyzed using Rasch with the WinSteps application. This research was conducted at SMPN 30 Jakarta with class VIII students as the research population. Based on this population, 34 students were selected as the sample with a cluster random sampling technique. Based on the data obtained, it was known that there is a significant effect of problem-solving methods on mathematical understanding. Meanwhile, Rasch data analysis showed a high category for the relationship between understanding and self-confidence of students by 60%. This proved that the effect of the problem-solving method on self-confidence and mathematical understanding is directly proportional.

Penelitian ini bertujuan untuk mengetahui pengaruh metode pemecahan masalah terhadap kepercayaan diri siswa dan pemahaman matematika dalam pembelajaran. Penelitian ini menggunakan metode kuantitatif dan kualitatif. Penelitian ini mengikuti proses perhitungan kuantitatif dari instrumen tentang pemahaman matematika dan menggambarkan kepercayaan diri siswa, dianalisis menggunakan Rasch dengan aplikasi WinSteps. Penelitian ini dilakukan di SMP Negeri 30 Jakarta dengan populasi siswa kelas VII. Sampel 34 siswa dipilih menggunakan teknik cluster sampling. Berdasarkan data yang diperoleh, diketahui bahwa pengaruh metode pemecahan masalah dengan kemampuan untuk memahami konsep matematika termasuk dalam kategori tinggi. Sementara itu, analisis data Rasch menunjukkan kategori tinggi untuk hubungan pemahaman dan percaya diri siswa sebesar 60%. Ini membuktikan bahwa efek dari metode pemecahan masalah pada kepercayaan diri siswa dan pemahaman konsep matematika berbanding lurus. │Putri Dorojatun Rahayuningdewi and Ayu Faradillah 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 ) | 167 mathematical communication skills and self-confidence. Furthermore, Andrayani's research developed this research topic by examining the effect of problem-solving strategies according to Wankat and Oreovicz on students' ability to understand mathematical concepts and self-regulated learning. In this research, the researchers are interested in researching about the effect of the problem-solving method on students' selfconfidence and understanding of mathematical concepts. The purpose of this study is to find out how the problem-solving method can affect self-confidence and understanding of mathematical concepts of students in junior high school.

METHOD
This research was conducted in SMPN 30 North Jakarta with all VII grade students as the research population. Samples were taken randomly using a cluster random sampling technique so that one class was determined as an experimental class, which was VII-C of the 2019/2020 school year. The method was a quantitative and qualitative approach, where the quantitative method was used in the first stage of the study by calculating normality, homogeneity, t-test, and effect size. The second stage used qualitative method based on the results of the analysis of the Rasch model. Rasch analysis is a statistical technique that is commonly used to analyze both test data and Likert survey data to construct and evaluate question item banks [8]. The Rasch model produced a fit statistical analysis that provided information to the researchers whether the data obtained ideally illustrated that people who had high ability provided patterns of answers to items according to their level of difficulty. Data were analyzed using WinSteps software to produce consistent Rasch output [9]. For calibration that was conducted between respondents and test questions, student responses to the complaint response from the raw score then entered into the logit interval value using Rasch modeling [10]. It was then exported as an excel file.
To easily understand the research methodology, the researchers describe it using a flowchart. The research instrument used was in the form of student worksheets of conceptual understanding with 7 questions. Further, the questionnaire on students' confidence with a scale of 25 questions to determine students' confidence was analyzed with the Rasch model.
The instruments about understanding mathematical concepts had several indicators such as restate a concept, classify objects according to the concept, give examples and nonexamples from concept, present concepts in various forms of mathematical representation, a necessary condition, a sufficient concept to use, utilize, and choose certain procedures or operation. It was followed by applying the concepts or algorithms solution to the problem [11]. The test questions that chosen were examined and fulfilled the requirement to be good questions according to its validity, reliability, difficulty, and differentiator for each question. Here, the example of questions on the instrument had an indicator of finding a concept according to information and experience that already known before. The question shows how the ability of students' mathematical concepts on the indicator of rediscovering a concept is a valid item with a moderate level of difficulty and good differentiation. This problem is able to measure students in a previously unknown concept based on previously known knowledge and experience. [12] Identify things that are relevant to a concept Andri has 10 marbles while Anis has 5 pet cats. Based on this statement, can a comparison be made between Andri's marbles and Anis's cat, if there is any comparison? If not, please explain the reason.
The question that shows how the ability of students' mathematical concepts on the indicator of identifying things that are relevant to a concept is a valid item with a moderate level of difficulty and good differentiation. This problem is able to measure students in identifying concepts in the right way. [12] Furthermore, to measure students' self-confidence, the researchers used a questionnaire taken from Gabriella's research [13].  In Table 2, the indicators of self-confidence questionnaire were believing in your potential, have an independent mindset, have a positive concept of yourself, and brave to express your opinion. There were 25 statements in which 14 of those were positive and 11 of those were negative. There were four choices of answers including SA, A, D, and SD. The researchers used the questionnaire above because it was the questionnaire by Gabriella that had been tested for its validity and reliability.

RESULTS AND DISCUSSION
This study collected data in two ways, including quantitative and qualitative methods. The researchers used the problem-solving method in providing treatment to the experimental class that was used as a sample and then examined how the problem-solving method was used to understanding mathematical concepts by giving 7 questions. Then, based on the results of these questions, the researchers collected quantitative data by conducting tests of normality, homogeneity, t-test, and effect size to find out how influential the method was given. Furthermore, the researchers also examined the extent of the effect of the problem-solving method on students' self-confidence by spreading 25 self-confidence questionnaires. Then, the results were analyzed qualitatively using the RASCH model analysis assistance.  Table 3 shows that the data was normally distributed and homogeneous. Effect size result was fairly in the high category so it can be concluded that the problem-solving method affects conceptual understanding.
The researchers described the results of this study by showing the result answers of one of the students who scored high, medium, and low on the problem of the ability to understand mathematical concepts and compares the results on the student's selfconfidence questionnaire with student scores on the matter of understanding mathematical concepts.
The results of the students' post-test can be seen in Table 4 below. Very Low 0 Table 4 shows the students' posttest results following the problem-solving method. Problem-solving is the ability of students to determine how to solve a mathematical problem for which the solution is unknown yet [14]. Problem-solving can affect students' understanding of mathematical concepts, leading them to be more enthusiastic in learning mathematics. A study conducted by Andrayani explained that there was an increase in students' understanding of mathematical concepts by using the problem-solving method [7]. The entire learning process in the problem-solving method can help students to be more independent and believe in their intellectual skills. The problem-solving method can also provide more meaningful learning and create proactive learning processes so that students can understand the concepts and solve problems well.

Analysis of Students' Mathematical Conceptual Understanding
In this part, the researchers presented two problems with moderate and high difficulty level. The researchers chose problems with those levels of difficulty to measure the degree of understanding of students' mathematical concepts. This can be seen from the exercises with medium and high difficulty levels that can train students to creatively solve problems and improve conceptual understanding for the better. Meanwhile, all students can solve easy problems, so those questions cannot be used to measure the level of each student's mathematical conceptual understanding.

Medium level
This problem can measure the ability of students to apply concepts that can solve problems with appropriate steps [12]. The student wrote down the problem that was known correctly and used the appropriate algorithm. This can measure students' understanding of the problems they know and use the right steps to solve them. Father will distribute a total of Rp 240,000.00 to Amir and Budi with a ratio of 3 : 5. Determine the amount of money received by Amir and Budi ?
Apply concepts or algorithms for solving a problem

High Level
This problem can measure the ability of students to apply concepts that can solve problems with appropriate steps [12]. The student wrote down the problem that was known correctly and used the appropriate algorithm. This can measure students' understanding of the problems they know and use the right steps to solve them. Table 5 shows examples of problems with medium and high levels of difficulty. Then, with these questions, three answers of students with different scores were selected to find out the students' mathematical conceptual understanding with the given problems. So, the estimated time needed for 25 fish to spend one bag of food is 5 days.
As we can see, the student wrote the information they know from the question. Then, the student wrote the concept they used to solve the problem by making a proportion inverse formula of . After writing the formula that was used for solving the problem, the student calculated the value of x, which was = (12)(10) 25 . The value of x that was calculated by the student was 4.8 and then rounded to 5 days. We could conclude that the student obtained the correct conclusion through a good answering process with complete algorithms and correct answers. It proves that the student has a good comprehension of mathematical concepts. The data can be explained based on research that had been done by Harry that students who have good conceptual understanding skills can solve the problem correctly according to the specified indicators. [15], [ So, the estimated time needed for 25 fish to spend one bag of food is 4 days.
As we can see, the student wrote the information they knew from the question. Then, the student wrote the concept they used to solve the problem by making a proportion inverse formula of . After writing the formula that used for solving the problem, the student calculated the value of x which was = (12)(10) 25 . The value of x calculated by the student was 4.8 and then rounded to 4 days. We can conclude that the student used the right process but have the wrong conclusion. Therefore, the answer they calculated was wrong. It proves that the student has a medium comprehension of mathematical concepts. [ As we know, the student writes the information they know from the question. Unfortunately, the student used the wrong concept to solve this problem. The student

Indonesian Journal of Science and Mathematics Education
Putri . The student calculated the value of x using that formula and obtained the result of 30 days. We can conclude that the student got the wrong process and algorithms. In the end, the student got the wrong conclusion about the concept that was used. Therefore, the answer they got was wrong because of not comprehending the concept. This proves that the student has a low comprehension of mathematical concepts. [15]- [16] Based on the analysis of the data above, the author emphasizes the importance of learning activities in mathematics learning so that students' understanding of mathematical concepts becomes good and resulting in good learning outcomes. Learning activities are processed and very fundamental elements in the implementation of each type and level of education [17]. So, the money received by Amir is Rp120,000 and the money received by Budi is Rp 200,000 As we can see, the student wrote the information they know from the question. Then, the student wrote the concept they used to solve the problem, which was Amir = The student calculated that Amir had Rp 120.000 and Budi had Rp 200.000. We can conclude that the student used the right process but have the wrong conclusion. Therefore, the answer calculated was wrong. It proves that the student has a medium comprehension of mathematical concepts. So, the money received by Amir is Rp144,000 and the money received by Budi is Rp 400,000 As we can see, the student wrote the information they know from the question Then, the student wrote the concept they used to solve the problem, which was Amir = The student calculated that Amir had Rp144.000 and Budi had Rp400.000. We can conclude that the student used the wrong process and algorithms. In the end, the student got the wrong conclusion about the concept that was used. Therefore, the answer they got was wrong because of not comprehending the concept. It proves that the student has a low comprehension of mathematical concepts. [15]- [16] Analysis of the data above shows the influence of problem-solving on understanding mathematical concepts. The ability to solve problems is needed by students in understanding concepts, relationships between concepts, and other fields. Good problem solving generally builds a problem representation to facilitate understanding [18]. Students who have the ability to understand high mathematical concepts must have better performance than those who have low understanding abilities of the mathematical concept. The higher the ability of students to understand mathematical concepts, the higher the mathematics learning achievement.

Analysis of Students' Self-Confidence
The self-confidence questionnaire was given to students during their participation in mathematics learning, aiming to obtain a picture of students' self confidence towards understanding mathematical concepts. In filling out the questionnaire, students were asked to choose one of the answer choices according to their self-description. The results of students' self-confidence in each indicator was shown in Table 8 below.  Table 8 shows the indicator of believe in your ability by 75%, acts independently in making a decision by 69%, have a positive self-concept by 64%, and brave to express an opinion by 79%. All percentages on self-confidence indicators show high criteria. Therefore, it indicates that students have good self-confidence for each indicator. Based on the self-confidence questionnaire, the researchers conducted an analysis using the RASCH model as presented in the Figure 2 below.  Figure 2 shows that the percentage of students who have high conceptual understanding and high confidence is 60% with a total of 9 students; students who have medium conceptual understanding and medium confidence is 46.16% with a total of 6 students, and students who have low conceptual understanding and low confidence is 50% with a total of 3 students. It can be concluded that students' understanding of concepts and self-confidence is directly proportional. This shows that students' good understanding of mathematical concepts also affects students' confidence.
The picture above shows that a good understanding of mathematical concepts also affects students' self-confidence. Self-confidence is essential for students to succeed in learning mathematics [19]. In learning mathematics, the self-confidence of each student is very important because it can build an optimistic attitude during learning. Students' confidence will help improve the ability to understand students' mathematical concepts so that students can determine the best course of action and can solve problems well. With confidence, students will be more motivated and prefer to learn mathematics. Selfconfidence must be increased because it is crucial and affects the ability to understand the concept even though the effect is not too large [20]. In increasing students' self-confidence and mathematical conceptual understanding, there are many influential factors. One of them is the learning methods carried out by the teacher. Therefore, to develop students' confidence and conceptual understanding in the mathematics learning, the researchers used problem-solving method to increase self-confidence and students' mathematical conceptual understanding. Table 9 describe the process that researchers taken during research process The syntax problem-solving of "defining the problem" affects the statement on the selfconfidence questionnaire of I am sure can solve the problem well. 20% of students strongly agree, 68% of students agree, and 12% of students disagree on the statement. This shows that students are confident in their abilities and they are confident that they can do the given questions well. [21]- [24] The syntax problem-solving of "defining the problem" affects the matter of conceptual understanding, in which Rafa notes that 60% of his classmates are women and he concludes that the ratio of women to men is 3 : 5. Is the conclusion correct? Please explain. With the indicator of identifying a concept in the right way, 73.52% of students answered correctly and 26.48% of students answered incorrectly.
The results obtained indicate that the problem-solving method affects students' understanding of concepts. [25]- [27] Planning a problem The syntax problem-solving of "planning a problem" affects the statement on the selfconfidence questionnaire that I can plan something without asking for help and consideration from friends. That means students are able to diagnose the problem themselves without the help of others. As many as 40% of students strongly agree, 40% of students agree and 20% of students disagree on the statement. This shows that by diagnosing problems students can take on their responsibilities and so as not to depend on others. [21]- [24] The syntax problem-solving of "planning a problem" affects the matter of conceptual understanding, in which in addition to Amir's house, there is a plot of land in the form of a long square. Amir's father plans to plant various types of medicines. The circumference of the land is 40 m, and the ratio of the length and width is 3: 2. Determine the length and width. With the indicator of ability to link various concepts, 67.64% of students answered correctly and 32.36% of students answered incorrectly. The results prove that students with carefully planned problems are able to relate the influence of various concepts well. [25]- [27] Implementing strategy The syntax of problem-solving "implementing strategy" affects the statement on the self-confidence questionnaire of I dare to express my opinion in front of the class. 28% of students strongly agree, 40% of students agree, and 32% of students disagree. This shows the need for self-confidence. [21]- [24] The syntax problem-solving of "implementing strategy" affects the matter of understanding the concept, in which a contractor estimates that a bridge will be completed within 24 days if done by 30 workers. After the work went on for 10 days, the work was stopped for 4 days for some reason. Determine the number of workers that must be added so that the bridge is completed on time. With the indicator of ability to apply concepts or algorithms to solve problems, 88.23% of students answered correctly, and 11.77% of students answered incorrectly. The results prove that the problem-solving method affects students' understanding of concepts. [25]- [27] Checking again The syntax problem-solving of "checking back" affects the statement on the selfconfidence questionnaire of I am always looking for the best way. 12% of students strongly agree, 48% of students agree, The syntax problem-solving of "checking back" affects the problem of understanding concepts with the indicator of identifying things that are relevant to a concept in the right way., where the students re-examine the answers generated precisely. [25]- [27] ( I J S M E ) and 40% of students disagree. It shows that students have to recheck their answers carefully. [21]- [24]

CONCLUSION
The results of the analysis above indicate that problem-solving method was able to affect the students' self-confidence and mathematical conceptual understanding with high effectiveness (0.917). Besides, students who have a high understanding of mathematical concept also have high self-confidence, so that self-confidence is directly proportional to conceptual understanding. Students who have a high conceptual understanding with a high self-confidence was amounted to 60%. This proven that the problem-solving method affects students' confidence and understanding of mathematical concepts.