33 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Analysis of Students’ Errors in Solving Concept Understanding Problems On Integral Matter Faradiba Jabnabillah Mathematics of Department, Batam Institute of Technology Email: Faradibanabillah@gmail.com Abstract The ability to understand students' concepts is very important to be applied to learning mathematics. When students cannot understand the concept well, students cannot solve the problem correctly. This is the reason the researcher conducted this research. The purpose of this research is to describe the percentage of students' errors in solving the problem of understanding the concept of integral matter. The subjects in this study were class XII students, totaling 8 students. Data collection techniques used were observation and tests to see student errors in answering questions of understanding the concept. This study uses a quantitative approach with a descriptive type of research. The data analysis technique used the percentage of students' ability assessment in solving problems. The results obtained in this study are the indicator of error reading about the questions gets a percentage of 62.5%, then the percentage of errors in understanding the questions gets a value of 50%, the percentage of transformation errors gets a value of 75%, then on the percentage of error processing skills gets a score of 62.5% and the percentage of errors in writing the final answer also obtained the same results as the percentage of process skills errors, which was 62.5%. This is because most students do not understand the integral concept so they do not understand in determining the formula and applying it. the percentage of transformation errors gets a value of 75%, then the percentage of process skills errors gets a value of 62.5%, and the percentage of errors in writing the final answer also gets the same result as the percentage of process skills errors that is 62.5%. This is because most students do not understand the integral concept so they do not understand in determining the formula and applying it. the percentage of transformation errors gets a value of 75%, then the percentage of process skills errors gets a value of 62.5%, and the percentage of errors in writing the final answer also gets the same result as the percentage of process skills errors that is 62.5%. This is because most students do not understand the integral concept so they do not understand in determining the formula and applying it. Keywords: Student Errors, Concept Understanding INTRODUCTION Mathematics is a basic science that has an important role in the development of science and technology. Mathematics is also a science that is identical to formulas and calculations (Manalu et al., 2019) so it is always used to solve problems in everyday life that we always encounter (Sholihah & Mahmudi, 2015). Not only that, but mathematics can also develop students' thinking patterns (Surat, 2016). Therefore, mathematics lessons are very important to learn mailto:Faradibanabillah@gmail.com 34 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ (Wiliawanto et al., 2019). Learning mathematics is an exact science that requires more understanding than memorization (Suswigi & Zanthy, 2019). One of the mathematical sciences that requires understanding is integral. Integral is the concept of continuous addition in mathematics with its inverse differential, that's why to be able to understand the integral concept, students have to understand the derivative concept (Hartono & Noto, 2017). In its application, integrals are often found in the fields of physics and engineering as well as other fields (Ghozi & Hilmansyah, 2018). Mathematics is always synonymous with concepts and students will always be required to understand concepts in mathematics (Andriani et al., 2017). Understanding the concept means explaining the relationship between concepts and applying concepts flexibly, accurately, efficiently, and precisely in a problem (Maharani et al., 2013). Instilling mathematical concepts to students can be done by providing various activities such as watching videos, discussing, conducting question and answer activities, and Mastery of concepts in mathematics can be used to solve real problems. When solving problems in mathematics, skills such as interpreting problems into mathematical models, arithmetic skills, concept mastery skills, and others so that students do not make mistakes in doing math problems (Rachman & Saripudin, 2020). This is the reason the understanding of the concept is closely related to student errors in solving problems. If the student is wrong in solving the problem, it indicates that the student is not good at understanding mathematical concepts. This is in line with the statement (Yuliani et al., 2018) that one of the problems that often arise in learning mathematics is the low ability of students to solve mathematical problems in the form of questions that emphasize understanding concepts in a particular subject. (Damayanti et al., 2017). However, achieving an understanding of concepts in mathematics is not an easy thing because the ability to understand mathematical concepts of each student is different, one of which is in the integral matter. Therefore, to determine the right method in solving integral problems, the problem must be identified first (Saparwadi, 2015) then determine the most appropriate procedure or method to be used in identifying the solution to the problem to be worked on (Kesumawati, 2008). In reality on the ground, in solving integral questions students cannot yet understand concepts well (Ario & Asra, 2018). This statement is reinforced by (Fitriani & Yuliani, 2016) that the cause of the problem of students' lack of understanding of mathematical concepts is that students do not think about the concepts that have been studied so that the concepts learned do not last long, and students are reluctant to understand the practice questions first in doing the questions and assume that the problem is difficult to do. So there are many mistakes in solving math problems. The statement above is by the results of observations at SMK N 4 Batam where the majority of students still make many mistakes in solving math problems related to understanding concepts, this data is obtained from the results of students' daily tests in mathematics. This is the reason the researchers researched this school. This study refers to Newman's analysis which divides errors into several factors, namely (1) reading errors, (2) comprehension errors, (3) transformation errors, (4) transformation errors. process skills (process skills error), and (5) writing error of the final answer (encoding error) (Karnasih, 2015). (Jha, 2012; Singh et al., 35 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ 2010) describe several indicators that cause students to make mistakes in solving problems in the form of descriptions based on the Newman procedure which is described in Table 1 below: Table 1 Factors and Indicators that Cause Student Errors Factors Causing Student Errors Indicator Reading error • Students are not able to interpret the meaning of each word, term, or symbol in the problem Comprehension error • Students do not understand what information is known in the problem completely Transformation error • Students are not able to make mathematical models from the information obtained • Students do not know the formula used to solve the problem Process skills error • Students do not know the procedures or steps used to solve the problem correctly Encoding error • Students are not able to find the final result of the problem based on the procedures or steps that have been used • Students cannot show the final answer of solving the problem correctly According to (Juliana & Zanthy, 2020) a student who already has an understanding of the concept has several indicators, namely: 1) defining the concept in writing; 2) defining and identifying examples and non-examples; 3) classifying certain objects based on certain properties according to the concept; 4) presenting concepts in various forms of mathematical representation; 5) use, utilize and choose certain procedures or operations. Previous research on student errors in solving math problems was conducted by (Agnesti & Amelia, 2020; Aulia & Kartini, 2021; Manalu & Zanthy, 2020; Septiahani et al., 2020) Meanwhile, other research related to concept understanding was carried out by (Kurniadi et al., 2020; Munasiah, 2021; Radiusman, 2020; Wijaya et al., 2018) Meanwhile, research on student errors in understanding mathematical concepts was carried out by (Az Zahra, 2019; Halawa & Oktaviani, 2021). The difference with this research is in the data analysis technique used, besides that there are also differences in the material, place, and subject under study. The purpose of this study is to describe the percentage of students' errors in solving the problem of understanding concepts in the integral matter. RESEARCH METHOD This study uses a quantitative approach with a descriptive type of research that aims to describe the percentage of students' errors in solving problems of understanding mathematical concepts on integral matter. This research was conducted at SMK N 4 Batam. The subjects in this study were students in class XII with a total of 8 students. The determination of research subjects using the purposive sampling technique by selecting subjects based on data from daily tests 36 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ on the previous material that meets predetermined criteria based on the teacher's considerations, namely students who have problems in understanding mathematical concepts. Data collection techniques using tests and observations. The test is carried out by giving students a question of understanding the concept. While the observations were made based on the teacher's explanation of the conditions of learning mathematics in the classroom and based on the data on the daily test scores of students' mathematics given by the teacher. The test research instrument consists of 5 questions in the form of a description of integral matter which refers to the test questions for the ability to understand mathematical concepts. As for this research, it refers to the concept of understanding indicators by (Juliana & Zanthy, 2020) which are described in Table 2 below. Table 2 Questions and Indicators of Concept Understanding Ability in Integral Matter No About Question Points Indicators of Ability to Understand Mathematical Concepts 1 Result of ∫ 𝑎𝑥𝑛 𝑑𝑥 is … Define the concept in writing 2 If 𝑓 ′(𝑥) = 4𝑥 + 1 then specify!𝐹(𝑥) Give examples and non-examples of a concept 3 Determine the result of the following integral function∫(3𝑥 − 8)𝑑𝑥 Classify certain objects based on certain properties according to the concept 4 Determine the result of the integral function ∫ 2 𝑡3 𝑑𝑡 Presenting concepts in various forms of mathematical representation 5 Determine the result of the following integral function using the substitution integral technique∫(2𝑥 + 3)4𝑑𝑥 Using, utilizing, and selecting certain procedures or operations After obtaining student answers, the student's errors were analyzed quantitatively and student errors were determined based on the scoring criteria that moved from 4 to 1, which is described in Table 3 below. Table 3 Scoring Criteria for Concept Understanding Indicators Category Score Appropriate 4 Less precise 3 Incorrect 2 No answer 1 After determining the score on each student's answer, then look for the percentage of assessment of the results of student answers. The percentage of assessment is as follows: P = 𝑛 𝑀 × 100% 37 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Question 1 Question 2 Question 3 Question 4 Question 5 62.5% Description: P: the percentage of students' ability to solve problems based on indicators 𝑛 : student answers on each of the assessment criteria 𝑀: the number of students. RESULTS AND DISCUSSION In general, students' ability to understand mathematical concepts is low. This can be seen from the table of the percentage of student answers based on the indicators of the ability to understand the concepts below. Table 4 Student Answer Results Based on Concept Understanding Indicators No Question Concept Understanding Indicator Assessment Criteria (%) 4 3 2 1 1 Define the concept in writing 12.5 25 62.5 0 2 Give examples and non-examples of a concept 0 12.5 62.5 25 3 Classify certain objects based on certain properties according to the concept 12.5 25 50 12.5 4 Presenting concepts in various forms of mathematical representation 0 12.5 75 12.5 5 Using, utilizing and selecting certain procedures or operations 0 12.5 62.5 25 Based on the results shown in Table 4, the students' conceptual understanding ability in solving integral problems for all indicators is still low. The highest percentage was obtained from assessment criteria 2 by obtaining a score of 50% and above on each question, which means that more than half the number of incorrect students (wrong) in solving the problem of understanding the concept. Meanwhile, students who are right in answering the question of understanding the concept get the least percentage on each question. The analysis of student errors shown in the concept understanding indicator with assessment criteria 2, namely the student is not right (wrong) in solving the problem is illustrated by the pie chart in Figure 1 below. Figure 1 Percentage of Student Errors in Each Question 62.5% 62.5% 50% 75% 38 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Meanwhile, in the test of student work descriptions using the Newman procedure, various types of errors were made by students on the problem of understanding the concepts given, namely as follows: Reading Error Figure 2 Example of Reading Error Figure 2 is the student's answer to question number 1 which is an indicator of understanding the concept, namely defining the concept in writing with the percentage obtained which is 62.5%. In this question, students were asked to write down the concept of integral, but the student's answer showed that the student did not write the concept correctly, the student did not add +C when writing the integral formula, besides that the way of writing was also wrong. This explanation is in line with (Rahimah, 2012) that one of the dominant mistakes made by students in solving integral problems is not adding a constant C to the results of indeterminate integration. This shows that students are not able to interpret the meaning of each word, term, or symbol in the problem. According to (Halawa & Oktaviani, 2021) reading errors can take the form of a student's inability to write symbols, notations, or numbers that are known in the questions. (Amalia et al., 2018) added that reading errors could be seen from students who did not write down the meaning of the questions asked and could not explain in writing. Comprehension Error Figure 3 Example of Comprehension Error Figure 3 shows the student's error in understanding what information is known in the problem completely. The problem being worked on is question number 3 with an indicator of concept understanding, namely classifying certain objects based on certain properties according to the concept and obtaining a percentage of 50%. In these questions, students do not understand the information 39 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ contained in the questions, students do not use integral concepts in answering questions so that the results of students' answers with the commands in the questions do not match. This shows that students' errors in answering questions occur because the process of interpreting the information given into mathematical expressions is not appropriate (Delisda & Sofyan, 2014; C. Rahmawati & Zhanty, 2019). Students are considered to have misunderstood the question if they are not able to understand what is being asked (Widodo, 2013). Transformation Error Figure 4 Example of Transformation Error Figure 4 shows the student's error in stating the formula in question number 4 with an indicator of concept understanding, namely presenting concepts in various forms of mathematical representations that get a percentage of 75%. In this question, it shows that students do not change their shape 2 𝑡3 into the form Students directly integrate the function, but the formula 2. 𝑡−3 used incorrectly. Students make mistakes in transforming the information they know in the problem into the correct mathematical model (D. Rahmawati & Permata, 2018). So from this, it can be concluded that students do not know the right formula to be applied to the problem. This is by research conducted by (Hutajulu et al., 2019) that students write answers that do not match the formulas that have been studied. Students have not been able to analyze the questions in the questions, and this has an impact on student answers that are made modest (Nadz & Haq, 2013). Process Skill Error Figure 5 Example of Process Skill Error 40 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Figure 5 is a student error who does not know the steps that will be used to solve the problem correctly. This error is taken from question number 2 with an indicator of concept understanding, namely providing examples and not examples of a concept with a percentage of 62.5%. Where in this problem students are not able to find the value of F(x) from the function f'(x) by using the integral method. Students are not able to do the steps exactly according to the request on the question. According to (Juliana & Zanthy, 2020) process skill errors can be seen from students who make computational errors, namely students doing wrong calculations in solving problems. This is in line with the statement of (Aulia & Kartini, 2021) that the process error made by students is that students have not been able to manipulate problems into the form of mathematical models and students are wrong in calculations. (Arifani et al., 2016) added that processing errors lie in the fourth largest order which indicates that students have not been able to apply the correct rules in solving mathematical problems. Encoding Error Figure 6 Example of Encoding Error Figure 6 is a student error who cannot show the final answer to solving the problem correctly. This error is taken from question number 5 with indicators of concept understanding, namely using, utilizing, and choosing certain procedures or operations with a percentage of 62.5%. Where in the question students are asked to integrate a function by way of substitution, but based on the student's answer, the final result is wrong because the student immediately squares the function and integrates it without first substituting the question. This shows that students do not understand the concept of integral substitution. According to (Wijaya et al., 2018) the error in writing the final answer is the inability of students to interpret and validate mathematical solutions. (Septiahani et al., 2020) added one form of writing error in the final answer, namely students could not show the final answer to solving the problem correctly and by the conclusion. This statement is reinforced by (Lestari et al., 2016) who say that errors in writing the final answer are one of the types of errors that often occur in students when solving problems. 41 Mathematics Education Journals Vol. 6 No. 1 February 2022 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ CONCLUSION Based on the results of research and discussion regarding the analysis of student errors in solving concept understanding problems on the integral matter, the indicator for reading errors in the questions obtained a percentage of 62.5%, then the percentage of errors in understanding questions obtained a value of 50%, the percentage of transformation errors obtained a value of 75%, then the percentage of process skill errors gets a value of 62.5%, and the percentage of errors in writing the final answer also gets the same result as the percentage of process skills errors that is 62.5%. So it can be concluded that the most mistakes made by students are the transformation errors with a percentage of 75%. This is because most students do not understand the integral concept so they do not understand in determining the formula and applying it. Students are also in a hurry to solve problems without thinking about concepts and formulas correctly so students are wrong in solving problems. Therefore, teachers play an important role in providing a conceptual understanding of integral matter and also other materials in learning mathematics to students. Teachers can not only see the final results of student answers in completing the material but the process of answering questions must also be considered by the teacher so that teachers can understand the extent to which students' conceptual understanding abilities are. 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