ANALYSIS OF STUDENT ERRORS IN SOLVING MINIMUM COMPETENCY ASSESSMENT PROBLEMS BASED ON KASTOLAN THEORY

In studying geometry, it is common for students to make various errors when working on word problems. Although some students understand the example problems, they may be confused and make errors when presented with different questions. This study employed a qualitative descriptive approach to examine the types and causes of errors made by Grade 8 students from a junior high school in Pronojiwo, Indonesia. The study involved 40 students, with six students selected for interviews. Data were collected using descriptions and interviews. The research employed three procedural stages: preparation, implementation, and data analysis. Data analysis involved data reduction, data encoding, and conclusions. The analysis revealed that 23.3% of students made conceptual errors, 27% made procedural errors, and 44.5% made technical errors. The factors contributing to these errors included students' lack of focus on reading the questions, limited understanding of the material, haste in completing the questions, insufficient knowledge of the problems in the questions, and carelessness in checking their answers.


INTRODUCTION
Mathematics is considered a crucial subject because it is the foundation of science and technology, with arithmetic and logical reasoning being its core components (Yeh et al., 2019).Therefore, mathematics learning should be designed to engage students and encourage mathematical thinking, problem-solving, and attainment of learning objectives (Muhammad Fajri, 2017;Sukmawati & Amelia, 2020).Mathematical learning aims to develop students' mathematical communication skills and reasoning abilities (Habsah, 2017), which have multifaceted implications for mathematics education (Sukirwan et al., 2018).In this context, the ultimate goal of mathematics education is to foster students' abilities in mathematical communication, reasoning, and problem-solving.
Although one of the objectives of learning mathematics is problem-solving, some students find it difficult to solve mathematical problems (Hidajat, 2018).Mathematical errors refer to those pervasive errors that students make based on the difficulties they have experienced when dealing with mathematical problems (Iswara et al., 2022).Errors made by students in doing problems result in the low acquisition of learning outcomes for each student when participating in the mathematics learning process (Fitry et al., 2022).Error is a deviation from a correct and structured answer (Mubarok et al., 2017).Systematic and consistent errors result from students' lack of mastery and perception of the material studied (Melisari et al., 2020).Meanwhile, incidental errors are caused by not being careful in understanding the meaning of the problems, calculating, and haste when doing them (Rangkuti, 2020).
Student errors when doing math problems lead to low literacy ability of numeracy in Indonesia (Fitry et al., 2022), as confirmed by the results of the 2018 PISA test, where Indonesia was ranked 72 out of 77 countries (Fazzilah et al., 2020).The difficulty of students in doing Higher Order Thinking Skills (HOTS) problems in the National Exam (UN) is one of the consequences of the lack of ability to think critically and reason (Sani, 2021).This resulted in the enactment of a Minimum Competency Assessment (known as AKM) by the Ministry of Education and Culture to improve literacy and numeracy in Indonesia (Yusuf & Ratnaningsih, 2022).Ratna Sari (2021)) in her research, stated that numeracy skills in doing AKM questions are relatively low.This statement is also supported by Arofa & Ismail (2022) revealed that many students have low numeracy skills.They found that out of 36 students, 23 were with low-level numeracy ability, 12 were with medium-level numeracy ability, and one had high-level numeracy ability.
One approach to evaluating students' problem-solving errors is by applying various theoretical frameworks, such as the Kastolan theory.This theory identifies three types of errors that students may make when solving problems: conceptual, procedural, and technical errors (Ulfa & Kartini, 2021).Utilizing the Kastolan theory can assist researchers in pinpointing the specific nature and location of students' errors when working on AKM problems.
This study differs from the research conducted by Raharti & Yunianta (2020) in several ways.First, this study utilized plane geometry as the subject matter, while the previous research focused on the System of Linear Equations in Two Variables (SLETV).Second, this study only selected a few subjects who made the most errors in the interviews.In contrast, the previous study included several subjects based on their math scores and willingness to participate in the research.Finally, in the previous study, scaffolding was provided to the research subjects, while this study did not provide any scaffolding.
Based on the information provided by a mathematics teacher at one of the junior high schools, students often make various errors when solving geometry word problems.Although some students comprehended the sample problems, they were confused when solving different problems.Consequently, they made errors while solving the problem.However, the exact location of students' errors in solving geometry word problems remains unknown to the teachers.
Hence, it is necessary to conduct a study on the errors made by students to evaluate them and help teachers address the difficulties students face while solving problems and achieving the objectives of learning mathematics.The research question of this present study is 'What are the percentage of errors and the causes of errors according to the type of error?
This study aimed to provide a descriptive analysis of the percentage and causes of errors based on the Kastolan theory.

METHODS
This research is a descriptive study using a qualitative approach that aims to determine student error types.The research subjects were 40 Year 8 students selected to participate in AKM, with six as representatives for the interviews.The six students were those who made the most errors.The error analysis was done by referring to the Kastolan error stages.The errors were identified by looking at students' steps to solve the problems.The indicators of errors that the researchers developed corresponded to Kastolan's analysis, as seen in Table 1.The data analysis technique involved data reduction, data presentation, and conclusion.

Types of Errors Indicator
The data reduction stages included: 1) The researchers collected the data in the implementation procedure, 2) The data was the student's answers, 3) The research results of the student's test were scored based on the answer key, the researchers removed the students with high scores because this study focused on student errors, 4) the results of the interviews were simplified.Data was then presented in narrative form; the data presented was the reduced data, containing information about student errors.Conclusions were drawn by concluding the data obtained and the data analyzed in the study.

RESULT AND DISCUSSION
The presentation of results of research on the errors made by students in solving the AKM problems using Kastolan theory is presented in this section.In the implementation, researchers analyzed the student's answers.

Conceptual Error
Table 2 shows that the percentage of conceptual errors is 23.3%.Based on the answer sheet of the S1 student, one of the errors made was an error in choosing the formula.The student was less thorough when reading the problem.In Problem 1, the question was the area of the semicircle paper cap; students could do the problem using the formula .However, S1 students use the formula of tube surface area, resulting in an incorrect solution.
Conceptual errors occur when students misinterpret the question, inaccurately write, or incorrectly apply formulas.Factors contributing to conceptual errors include a lack of focus on reading the questions, inadequate understanding of the material, and feeling rushed to complete the problems.

Procedural Errors
The percentage of students' procedural errors is 27.9%.In Problem 3, most students made procedural errors, with indicators of being unable to solve the problem in the final stage.

Conceptually incorrect because you can't choose the formula and apply the formula correctly
Most students only looked for one of the parallel side lengths in a trapezoid.Figure 2 represents one of the students' procedural errors.students only found the value from the parallel side and were unsuccessful, resulting in incorrect answers.Students make errors when they are unable to do until the final stage.The factor causing students to make procedural errors is that students are too hasty in doing the questions and do not understand the problems.

Technical Errors
The percentage of students' technical errors is 44.5%.The analysis of students' answers shows that many students made technical errors in Problem 3. Figure 3  Factors contributing to these errors included lack of focus on reading the questions, lack of understanding of the material, haste in completing the questions, lack of familiarity with the problems in the questions, and failure to check answers carefully.
the problem/use a term, concept, and principle Unable to select formulas/properties accurately Unable to apply formulas/properties accurately Procedural errors Inequality of steps of resolution with the question in question Unable to solve the problem until the final stage Technical errors Error on count operation Error in moving count or number operations from one step to another Source : (Ulfa & Kartini, 2021) Data collection was done through tests and interviews.The test consists of three longanswer problems.The indicators in the questions were as follows: 1) Given an illustration of making a hat, students determine the area of a semicircle, 2) Given an illustration of making an ideal house, students determine the area of the ideal house land, 3) Given an illustration of the land for the house, students determine the circumference of the land.Interviews were conducted every day after the students took the test.The interview subjects were selected based on those who made the most error on each error indicator.The interview guide used the constraints of the error indicator.The test questions and interviews used have been validated by the mathematics education lecturer, with the results of the test questions being suitable for use.

Figure 1 .
Figure 1.An Example of Conceptual Error

Figure 1
Figure 1 An Example of Procedural Error Figure 2.An Example of Technical Error Table 2 presents the percentage of students errors.