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Kalamatika: Jurnal Pendidikan Matematika

Volume 8, No. 1, April 2023, pages 1-10

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ANALYSIS OF STUDENT ERRORS IN SOLVING MINIMUM

COMPETENCY ASSESSMENT PROBLEMS BASED ON KASTOLAN

THEORY

Novita Anggraini1, Dwi Priyo Utomo 2, Rizal Dian Azmi 3

1University of Muhammadiyah Malang, Jl. Raya Tlogomas No.246, Babatan, Malang, Jawa Timur.

novialn29@email.com
2University of Muhammadiyah Malang, Jl. Raya Tlogomas No.246, Babatan, Malang, Jawa Timur.

dwi_priyo@umm.ac.id
3University of Muhammadiyah Malang, Jl. Raya Tlogomas No.246, Babatan, Malang, Jawa Timur.

rizaldian@umm.ac.id

ABSTRACT

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.

ARTICLE INFORMATION

Keywords Article History

Errors Analysis

Kastolan’s Theory

Asessment Competency Minimum

Submitted Nov 14, 2022

Revised May 1, 2023

Accepted May 2, 2023

Corresponding Author

Novita Anggraini

Universitas Muhammadiyah Malang

Jl. Raya Tlogomas No.246, Babatan, Tegalgondo, Kec. Lowokwaru, Malang, Jawa Timur

Email: novialn29@email.com

How to Cite

Anggraini, N., Utomo, D & P., & Azmi, R & D. (2023). Analysis of Student Errors in Solving Minimum

Competency Assessment Problems Based on Kastolan Theory. Kalamatika: Jurnal Pendidikan Matematika,

8(1), 1-9.

https://doi.org/10.22236/KALAMATIKA.vol8no1.2023pp1-10

http://creativecommons.org/licenses/by-sa/4.0/
http://creativecommons.org/licenses/by-sa/4.0/
http://creativecommons.org/licenses/by-sa/4.0/

2 KALAMATIKA, Volume 8, No. 1, April 2023, pages 1-10

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-

Anggraini, Utomo, & Azmi 3

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

4 KALAMATIKA, Volume 8, No. 1, April 2023, pages 1-10

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.

Table1. Kastolan Error Indicator

Types of Errors Indicator

Conceptual error Unable to interpret 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 long-

answer 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.

The data analysis technique involved data reduction, data presentation, and conclusion.

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

Anggraini, Utomo, & Azmi 5

AKM problems using Kastolan theory is presented in this section. In the implementation,

researchers analyzed the student's answers. Table 2 presents the percentage of students errors.

Table2. Student Error Percentage

Error Type The Errors in Each Problem Sum Percentage
Problem 1 Problem 2 Problem 3
Conceptual 18 22 44 84

Procedural 10 13 44 67

Technical 36 27 44 107

Conceptual Error

Table 2 shows that the percentage of conceptual errors is 23.3%. Further analysis

revealed that most conceptual errors occurred in Problem 3, where students had difficulties

entering the values from the length of the parallel sides. For instance, Subject S1 made

conceptual errors in all three indicators of conceptual errors in Problem 1, as illustrated in

Figure 1.

Figure 1. An Example of Conceptual Error

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

6 KALAMATIKA, Volume 8, No. 1, April 2023, pages 1-10

Most students only looked for one of the parallel side lengths in a trapezoid. Figure 2

represents one of the students’ procedural errors.

Figure 1 An Example of Procedural Error

Based on the answer sheet of S3 students, one of the errors made was not being able to

solve the problems until the final stage. The student only did the problem until entering the

value into the trapezoidal area formula. The solution to Problem 3 should require three stages:

finding the value of the parallel side obtained from the area of the trapezoid, looking for the

hypotenuse of the triangle, and looking for the circumference of the trapezoid. However, S3

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 displays one

of the students’ answers with technical errors.

Procedural errors

due to inequality of

steps and

questionable

questions and

settlement

not until the final

stage

It can be seen

that the student

is wrong in

performing the

count operation

Figure 2. An Example of Technical Error

Anggraini, Utomo, & Azmi 7

Figure 3 shows that S6 students made technical errors where students were wrong

when calculating , which should have been, but S6

students wrote . Another error made by S6 students was in moving . S6 student moved ,

which should . It can be seen from students making errors in counting. Technical errors are

the most common among students and are caused by factors such as carelessness during the

calculation process, hasty or incomplete answers, and the consequences of previous errors.

The results of this study revealed that most students made technical errors. This finding

contrasts the research of Ayuningsih et al. (2020), where technical errors are the least.

Technical errors are caused by students lacking accuracy in solving problems and not

checking the results of their work, resulting in incomplete solutions. This finding is consistent

with the study conducted by Raharti and Yunianta (2020), which identified several factors

contributing to technical errors, such as students' lack of carefulness in calculating and

checking their answers, the tendency to rush through problem-solving, and inattention to

details. External factors could also influence these technical errors, such as time constraints

imposed during the problem-solving process.

CONCLUSION

This study found that students made errors in three types of errors: conceptual errors

(23.3%), procedural errors (27.9%), and technical errors (44.5%). Conceptual errors were

indicated by students' inability to interpret the problem, choose the formula accurately, and

apply the formula accurately. Procedural errors were marked by students' failure to solve the

problem until the final stage. Errors in the calculation process indicated technical errors.

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.

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