How to cite:

La Ili. (2022). Analysis of Students' Misconceptions in Solving

Mathematics Problems on Flat Construction Materials. Journal

Eduvest. Vol 2(3): 475-483

E-ISSN:

2775-3727

Published by:

https://greenpublisher.id/

Eduvest – Journal of Universal Studies

Volume 2 Number 3, March, 2022

p- ISSN 2775-3735- e-ISSN 2775-3727

ANALYSIS OF STUDENTS' MISCONCEPTIONS IN

SOLVING MATHEMATICS PROBLEMS ON FLAT

CONSTRUCTION MATERIALS

La Ili

Halu Oleo University, Indonesia

Email: [email protected]

ARTICLE INFO ABSTRACT

Received:

Ferbuary,

2022

Revised:

March, 15

2022

Approved:

March, 16

2022

This study aims to find out the misconceptions experienced by

students in solving mathematical problems in the material of

quadrilaterals in the fourth grade of SD Negeri 2 Biwinapada.

This type of research is qualitative research. The subjects in this

study were 3 fourth-grade students at SD Negeri 2 Biwinapada.

Data collection techniques using tests and interviews. The data

analysis techniques used are data reduction, data presentation,

and drawing conclusions. The results showed that the

misconceptions experienced by students include: 1)

classificational misconceptions, namely a) not writing down

what is known and asked or other elements needed to answer

questions and b) errors in determining examples of rectangular

shapes which are square or square long. 2) Correlational

misconceptions, namely a) errors in representing the problem

in the form of pictures, b) errors in applying the area value in

the formula and c) making mistakes in applying the

relationship between the formula used and the problems

contained in the problem. 3) Theoretical misconceptions,

namely errors in writing quadrilateral units, namely area (cm)

and circumference (cm2).

KEYWORDS

Bagasse, Briquettes, Energy, Orange Peel

This work is licensed under a Creative Commons Attribution-

ShareAlike 4.0 International

La Ili

Analysis of Students' Misconceptions in Solving Mathematics Problems on Flat

Construction Materials 476

INTRODUCTION

Mathematics is a subject that has an important role in education. Based on the

Regulation of the Minister of National Education No. 22 of 2006 concerning Content

Standards for primary and secondary education units, mathematics needs to be taught to

students starting from elementary school to equip students with logical, analytical,

systematic, critical, and creative thinking skills as well as the ability to work together

(Siswono, 2018). In addition, mathematics is also the basis of science and technology.

Hence why it is necessary to be understood, taught, and mastered to make it applicable in

everyday life. Therefore, mathematics must be taught starting from basic education.

The Ministry of Education and Culture (2014) explains that there are various

abilities that must be mastered by students, one of which is problem-solving skills.

Problem-solving is one of the goals of learning mathematics (Amaliah, Fitri, Sutirna &

Rafiq, 2021). NCTM (2000) in Amaliah, Sutirna, & Zulkarnaen (2021), stated that

problem-solving means engaging in a task where the solution method is not known

beforehand. To find solutions, students must draw on their knowledge, and through this

process, they will develop new mathematical understandings. There are several steps that

can be taken to solve mathematical problems, Polya (1973) in Amaliah, Sutirna, &

Zulkarnaen (2021), namely (1) understanding the problem Please delete these words (2)

planning a solution (devising a plan), (3) implementing the plan and (4) checking back.

Students can be said to have good problem-solving skills if they are able to go

through all stages of problem-solving. However, there are still find students who have

misconceptions about solving mathematical problems. Abraham explained that students

are said to have understood a concept if they have met a criterion, namely understanding,

misconception, and not understanding. Meanwhile, misconceptions are things that are

often experienced by students. Therefore, it is important for teachers to know the

misconceptions experienced by students.

A teacher should teaching subjects from the ideas that the students already has as

a benchmark for preparing learning that can reduce misconceptions and increase the

concept of new ideas. That way, the teacher can help students not to experience

misconceptions about the lesson, especially the mathematics lesson on the geometry of

quadrilaterals, namely squares and rectangles. Suparno (2013) defines misconceptions as

understanding concepts that are not in accordance with scientific understanding or the

agreement of experts in the field (Ainiyah, 2015).

In this study, the researchers analyzed the types of misconceptions based on the

types proposed by Moh. Amien (Ainiyah, 2015), namely: 1) classificational

misconceptions, which are forms of misconceptions based on misclassification of facts

into organized charts, 2) correlational misconceptions, which are forms of misconceptions

based on errors regarding special events. interconnected, or observations consisting of

assumptions, especially in the form of the formulation of general principles, and 3)

theoretical misconceptions, which are forms of misconceptions based on errors in

studying facts or events in an organized system.

Based on the results of the initial test for fourth graders at SD Negeri 2

Biwinapada, there are some students who still have misconceptions in determining

formulas and performing operations to calculate the area and perimeter of a combined

square and rectangular shape. Furthermore, after interviewing the teacher, sometimes he

does not provide reinforcement for students if there is a misunderstanding in the

explanation. Therefore, misconceptions are a condition that must be handled because they

can hinder students' knowledge of mathematics, one of which is geometry material,

especially in rectangular flat shapes, namely squares and rectangles. Thus, it is necessary

Eduvest – Journal of Universal Studies

Volume 2 Number 3, March 2022

477 http://eduvest.greenvest.co.id

to analyze the misconceptions experienced by students. Hence, the researchers were

interested in conducting research with the title analysis of student misconceptions in

solving mathematical problems on the material of quadrilaterals (squares and rectangles)

in grade IV SD Negeri 2 Biwinapada.

RESEARCH METHOD

This research applied qualitative approach. According Bodgan & Taylor qualitative

research is one of the studies using descriptive data in the form of words or verbal and

observed behavior of each subject (Sujarweni, 2014). Thus, the data obtained from this

study were analyzed descriptively to determine the types of misconceptions experienced

by students in solving mathematical problems in rectangular shapes, namely squares and

rectangles. The subjects of this research were selected 3 fourth grade students of SD

Negeri 2 Biwinapada who represented each category of ability, namely high, medium,

and low, as well as students with good communication skills. This is done by researchers

because they want students to be able to give or convey ideas, ideas, or reasons. So that

researchers can identify more deeply the research subject. The instruments used in this

research were 1) a description test of 6 numbers consisting of rectangular shape material,

namely square and rectangular and 2) interviews. The data obtained were then analyzed

using qualitative data analysis, proposed by Miles and Huberman, namely data reduction,

data presentation and conclusion drawing (Rahimah, 2019). To compare the results of

students' work with interviews, researchers used triangulation techniques to analyze

students' misconceptions in solving mathematical problems on rectangular flat shapes,

namely squares and rectangles.

RESULT AND DISCUSSION

After the mathematical problem solving test on the rectangular flat shape

material, it can be seen that the results of the categorization of students' abilities are as

follows.

Table 1. Results of Students' Mathematical Problem Solving Ability Tests on

Quadrilateral Flat Shapes

Category

Student Value

Number of Students

Tall

51-100

Currently

33-50

Low

0-32

In order to describe students' misconceptions in solving students' mathematical

problems in each category, 1 student in the high category will be selected with the subject

code S-01, medium, subject code S-02, and low, subject code S-03.

Based on the test results, it can be seen that students with high abilities (S-01) are

able to solve questions well. Likewise, students with moderate abilities (S-02) are quite

good at answering test questions. Meanwhile, students with low abilities have not been

able to solve problems well. The types of misconceptions experienced by students are

described in the following table:

Analysis of Students' Misconceptions in Solving Mathematics Problems on Flat

Construction Materials 478

Table 2. Results of the Misconception Analysis of High Ability Students (S-01)

No.

Problem

Types of Misconception

Statements

Classification

Correlational

Theoretical

No misconceptions

Error in

assuming area

value as length

value

Error in applying

the formula for

area and perimeter

of rectangle

No theoretical

misconceptions

There are no

other numbers

that can be

used as length

values

No misconceptions

classificational

misconceptions

Error in applying

the formula for the

perimeter of a

rectangle

Error in

determining

the unit for the

perimeter of a

rectangle

Writing the

formula K = 2

× x (p × l),

because the

lamp distance

is 3 meters

No misconceptions

Errors in

determining the

value of the side

length of a

square

Error in applying

formulas &

representing

problems in the

form of pictures

No theoretical

misconceptions

There are

lengths and

lengths of

sides, so write

the formula L

= 2 (p × l)

Table 3. Results of the Misconception Analysis of Medium Ability Students (S-02)

No.

Problem

Types of Misconception

Statements

Classification

Correlational

Theoretical

Error in

determining the

example of a

rectangular shape

which is either a

square or a

rectangle

Error representing

the problem in the

form of a picture

No theoretical

misconceptions

The selected

image has been

seen in a book

No misconceptions

Not experiencing

classificational

misconceptions

Error applying the

formula for the area

of a square &

rectangle

Error

determining

the unit area

of a square &

Writing the

formula L = p × l,

because the area

of the shaded area

Eduvest – Journal of Universal Studies

Volume 2 Number 3, March 2022

479 http://eduvest.greenvest.co.id

rectangle

is in the rectangle

No misconceptions

Error in

determining the

value of the side

length of a

square

Error in applying

the formula for the

perimeter of a

square

Error writing

the unit for

the perimeter

of a square

Writing the

formula K= 4

(side + side),

because there are

two length values,

namely tape &

side

Does not

experience

classification

misconceptions

Errors in

representing

questions in the

form of pictures

Makes

mistakes in

writing the

unit area of

squares &

rectangles

writing the unit

area of squares &

rectangles Writes

the formula for

the area of the

garden, L = s×l×p,

because the pond

is made in a

garden

Table 4. Results of Low Ability Students' Conception Analysis (S-03)

No.

Problem

Types of Misconception

Statement

Classification

Correlational

Theoretical

Error determining

the example of a

quadrilateral

which is a square

or a rectangle

Error representing

the problem in the

form of a picture

Make a mistake in

identifying the

shape of a square or

rectangle based on

its properties

I don't

understand,

just just

answering

Made an error in

specifying the

length value as the

area value of the

rectangle

Error applying the

relationship between

the area formula and

the perimeter of a

rectangle

Error in

determining the

unit perimeter of a

rectangle

Write the

formula K=p +

l, because the

perimeter is the

sum of all sides

of the shape

Made an error in

determining the

value of the

length, width of a

rectangle and the

value of the side of

a square

Error applying the

formula for the area

of a square &

rectangle

Error determining

unit area of square

& rectangle

Do not

understand

how to work

on the problem

so that it is

answered

arbitrarily with

12+4+8+32=56

La Ili

Analysis of Students' Misconceptions in Solving Mathematics Problems on Flat

Construction Materials 480

Not experiencing

classificational

misconceptions

Error in applying the

formula for the

perimeter of a

rectangle

Error writing unit

perimeter of

rectangle

Write the

formula K= p

+ l, because the

perimeter is the

sum of all the

outer sides of

the plane

No misconceptions

Not experiencing

classification

misconceptions

Errors in applying

the formula for the

area of squares and

rectangles and

representing the

problem in the form

of pictures

Made a mistake in

writing the unit area

of a square &

rectangle

Write down the

answer

10+8+6=24,

because it's just

an answer

Discussion

There are several types of misconceptions experienced by groups with high,

medium, and low abilities in class IV SD Negeri 2 Biwinapada in solving problems

solving mathematical problems with rectangular flat material, namely:

1. Description of Classificational Misconceptions

Based on the analysis of the results of the tests and interviews, it showed that

students experienced classificational misconceptions in several indicators of

misconceptions on the material of rectangular flat shapes.

In the description question number 1, it relates to restating the concept of

quadrilaterals (squares and rectangles). There are several answers that have

misconceptions, namely S-16 and S-08 on the indicator making an error in determining

the example of a rectangular flat shape which is either a square or a rectangle. This is in

line with the opinion of Dedy & Sumiaty in (Fajari, 2020) states that students become

poor in context because they always imitate existing examples and do not understand the

construction of concepts from the results of their own thinking. This is supported by the

opinion of Gita et al (2018) which states that the misconceptions that occur can be caused

by the way of teaching and presenting pictures (Fajari, 2020).

In the description questions number 2, 3, 4, 5, and 6 related to the concept of area

and perimeter of quadrilaterals (square and rectangle). The three subjects experienced the

same misconception in answering, namely not writing down what was known and asked

in the question. This is, in line with the opinion (Darmila, 2015) which states that based

on the results of research conducted, students' conceptual errors are caused by several

things, namely students are wrong or even unable to write down known objects clearly

and completely and have difficulty interpreting the sentence questions into known objects

one by one. This is also supported by the opinion of Polya (2004) in (Rofi’ah, Ansori, &

Mawaddah, 2019) states that in understanding the problem, it begins with understanding

the language and terms in the problem and formulating what is known, then ensuring that

what is known is sufficient to determine what you want to get in the question.

Eduvest – Journal of Universal Studies

Volume 2 Number 3, March 2022

481 http://eduvest.greenvest.co.id

2. Description of the Correlational Misconception

Based on the analysis of test results and interviews, it was found that there were

correlational misconceptions in some of the description questions. From the results of the

analysis, it shows that the subjects of S-14 have correlational misconceptions which are

located in questions number 1, 2, 4, and 6. S-16 have correlational misconceptions which

are located in the description questions numbered 1, 3, 5 and 6. Meanwhile, S-03

experienced a correlational misconception which lies in the description questions number

1, 2, 3, 4, and 6

In the description problem number 1, it relates to the concept of quadrilaterals

(squares and rectangles). Subjects S-16 and S-08 experienced a misconception, namely an

error in representing the problem in the form of an image. This can be seen from the

answers of students who made mistakes in determining the shapes which are types of

squares and rectangles based on the existing images. This is in line with the results of

Fajari's research (2020), including that students are accustomed to getting up in a flat

position or building a horizontal space.

In the description problem number 2 is related to the concept of the relationship

between the area and the perimeter of a rectangle. Subject S-14 applies the formula K = 2

(area + width) and S-08 applies the formula K = p + l. So that S-14 and S-08 have

misconceptions, namely: students' mistakes in applying the area value in the formula and

applying the perimeter formula of a rectangle that is not in accordance with the concept of

the perimeter of a rectangle. This is in line with the opinion of Putra Jaeng & Sukyasa in

Hanifaturrocmah, Sary, and Azizah stating that they are said to have made a conceptual

error if they do not use the formula correctly and students are also unable to operate

multiplication, division and subtraction.

In the description problem number 3 it is related to the concept of the area of the

shaded flat shape. Subjects S-16 applied the formula L = length x area and S-8 applied

the formula 12 + 4 + 8 + 32. So they experienced misconceptions, namely students'

mistakes in applying the formula to solve problems. In the description problem number 4

is related to the concept of the perimeter of a rectangle. Subject S-14 applies the formula

K = 2 × x (p + l) and S-08 applies the formula K = p + l. So that they experience

misconceptions, namely students' mistakes in applying the formula for the perimeter of a

rectangle, namely K = 2 × x (p + l) and K (p + s). In question number 5 it is related to the

concept of the perimeter of a square. Subject S-16 applies the formula K = 4 (side + side).

So that there is a misconception, namely an error in applying the formula to solve the

problem. This is in line with the opinion of Putra Jaeng & Sukyasa which states that they

are said to have made a conceptual error if they do not use the formula correctly and

students are also unable to operate multiplication, division and subtraction.

(Faturrochmah, Sary, & Azizah, 2021).

In the description problem number 6, related to the relationship between the

formula for the area of a square and a rectangle, the three subjects experienced

misconceptions in applying the formula and illustrating the shape of the land which was

then made a fish pond in it. Students apply the formula for the area of the garden as L = 2

(p × l), L = p × l × s, and L = p + l + s. This is in line with the results of research by

Rahayu and Arfiansyah (2021) stating that the correlational misconceptions experienced

by students include students making mistakes in applying the relationship between the

formulas used and the problems contained in the questions, which include errors in

applying the perimeter formula of a rectangle, errors in applying the perimeter formula.

La Ili

Analysis of Students' Misconceptions in Solving Mathematics Problems on Flat

Construction Materials 482

the same as the formula for the area of a rectangle and errors in applying the formula for

the perimeter of a square. In addition, errors in representing the problem in the form of

images (Rahayu and Arfiansyah, 2021).

3. Description of Theoretical Misconceptions

Based on the results of data analysis, it was found that there were theoretical

misconceptions in some of the description questions. From the results of the data analysis,

it shows that the three subjects experienced theoretical misconceptions about the error

indicator in writing the perimeter unit of a rectangular shape. This is in line with the

opinion, Ningsih, (2016), understanding the concept is very important to be mastered by

students in dealing with variations in the form of problems in mathematics that are being

faced, the importance of understanding concepts is the basis in obtaining the expected

learning outcomes, while the use of concepts in mathematics is related to understand and

distinguish words, symbols and signs (Fauzi & Arisetyawan, 2020). This is also

supported by the results of research, Putra, Jaeng, & Sukyasa (2016) which states that one

of the mistakes is not writing down the unit area and perimeter of a flat shape

(Faturrochmah, Sary, & Azizah, 2021).

CONCLUSION

Based on the description and analysis of the data on the misconceptions of fourth

graders of SD Negeri 2 Biwinapada on the material of quadrilaterals (square and

rectangle) the results are obtained, namely students with high mathematical abilities

experience the least level of misconceptions when compared to students with moderate

and low mathematical abilities; students with moderate math abilities experienced the

most misconceptions from students with high math abilities, and students with low math

abilities experienced the most misconceptions compared to students with high and

moderate math abilities.

The misconceptions experienced by fourth grade students of SD Negeri 2

Biwinapada include: 1) Classificational misconceptions, namely: 1) not writing down

known and asked elements or other elements needed to answer questions and making

mistakes in determining examples of rectangular shapes. which is a square or a rectangle

2) Correlational misconceptions, namely errors in representing the problem in the form of

images, errors in applying the area value in the formula and making mistakes in applying

the relationship between the formula used and the problems contained in the problem. 3)

Theoretical misconceptions on the error indicator in writing the perimeter unit of a

rectangular flat shape, which is cm2 and the unit area of a rectangle, which is cm.

REFERENCES

Ainiyah, Lutfia Afifatul. (2015). Identifikasi Miskonsepsi Siswa Dalam Materi Geometri

Pada Pembelajaran Matematika Siswa Kelas VIII SMP Negeri 1 Punggelan. Journal

Student UNY, 3.

Amaliah, Fitri, Sutirna, &., & Rafiq, Zulkarnaen. (2021). Analisis Kemampuan

Pemecahan Masalah Matematis Siswa Pada Materi Segiempat dan Segitiga. AKSIO

MA: Jurnal Matematika Dan Pendidikan Matematika, 12(1), 10–20.

Darmila. (2015). Analisis Kesalahan Konsep Matematika Siswa dalam Penyelesaian Soal

Pemecahan Masalah Matematika di SD Negeri 30 Kendari. Universitas Halu Oleo.

Fajari, Urip Nurul. (2020). Analisis Miskonsepsi Siswa pada Materi Bangun Datar dan

Eduvest – Journal of Universal Studies

Volume 2 Number 3, March 2022

483 http://eduvest.greenvest.co.id

Bangun Ruang. Jurnal Kiprah, 8(2), 113–122.

https://doi.org/10.31629/kiprah.v8i2.2071

Faturrochmah, H., Sary, R. M., & Azizah, M. (2021). Kesalahan Siswa dalam

Mengerjakan Soal Materi Bangun Datar Berdasarkan Teori Nolting pada Siswa

Kelas IV Sekolah Dasar. Elementary School: Jurnal Pendidikan Dan Pembelajaran

Ke-SD-An, 8(2), 310–321.

Fauzi, Irfan, &., & Arisetyawan, Andika. (2020). Analisis Kesulitan Belajar Siswa pada

Materi Geometri di Sekolah Dasar. 11(1), 27–35.

Rahimah, Nonong. (2019). Pemecahan Masalah Matematika Siswa Pada Materi Bangun

Datar Segi Empat Berdasarkan Kemampuan Matematik ( Students ’ Mathematics

Problem Solving Ability On Rectangular ). THETA: Jurnal Pendidikan Matematika,

1(2).

Rofi’ah, N., Ansori, H., & Mawaddah, S. (2019). Analisis Kesalahan Siswa dalam

Menyelesaikan Soal Cerita Matematika Berdasarkan Langkah Penyelesaian Polya.

EDU-MAT: Jurnal Pendidikan Matematika, 7(2).

Siswono, Tatag Yuli Eko. (2018). Pembelajaran Matematika Berbasis Pengajuan dan

Pemcahan Masalah Fokus Pada Berpikir Kritis dan Kreatif. Bandung: PT Remaja

Rosdakarya.

Sujarweni, V. Wiratna. (2014). Metodologi Penelitian Lengkap, Praktis, dan Mudah

Dipahami. Yogyakarta: Pustaka Baru Press.