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Analysis of The Difficulty of VIIIth Grade Junior High School Students in

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ICRIEMS 6

Journal of Physics: Conference Series 1397 (2019) 012086

IOP Publishing

doi:10.1088/1742-6596/1397/1/012086

1

Analysis of The Difficulty of VIIIth Grade Junior High School

Students in Circle Material Reviewed from The Mathematics

Connection Ability

Indra Kusuma Wijayanti1, a) and Agus Maman Abadi2, b)

1Mathematics Education Department of Graduate School, Yogyakarta State

University, Indonesia

2Mathematics Education Department, Yogyakarta State University, Indonesia

a) indrakusumawijayanti@gmail.com ; indrakusuma.2018@student.uny.ac.id

b) agusmaman@uny.ac.id

Abstract. This study aims to analyze the difficulty of VIIIth grade junior high school students

in circle material reviewed from mathematical connection ability. The method used in this

research is descriptive qualitative with a case study approach. The subjects in this study were 23

eight grade in one of the junior high schools in Temanggung. Data collection is done by tests

and interviews. The instrument used in this study are 3 questions about the material related to

the Circle and interview guide to know where the students’ difficulties are. The results of data

analysis showed students varied mathematical connection skills; some students belong to the

high category while others are in the medium or low category. However, student’s ability to

connect inter-mathematical concepts and apply mathematical concepts in solving daily problems

are in the low category with 43.47% and 53.26%. The low mathematical connection ability of

students is indicated by the low percentage of students who give correct answers, the low

percentage on each indicator of mathematical connections, and errors made by students.

Mistakes made by students show the difficulties experienced by students. The difficulty that is

generally expressed by students is the difficulty of understanding the problem and the difficulty

of determining the formula or theorem used to solve the problem.

1. Introduction

Education is an important basis for the progress of a nation because through education we can see the

development of human resources and the management of natural resources. Education is an important

aspect to improve the economy of a country [1-3]. Based on these facts, the Indonesian government has

been working to improve the quality of education in Indonesia. Education quality improvement can be

done through several efforts, one of them is improving the quality of the teacher, complete educational

facilities and infrastructure, increase the allocation of education funds and the implementation of

continuous education evaluations. Government efforts to improve the quality of education in Indonesia

change the paradigm and old mindset about education. Education cannot be seen only as a 'transfer of

knowledge', but more than that, education must be understood as a way to prepare students to face many

challenges in real life [4]. Shute & Becker [5] explained that in facing the challenges of the current era,

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humans are required to have collaborative abilities, think critically and creatively and be able to

communicate effectively.

Organizations that focus on developing current learning namely the Partnership for 21st Century

Skills [6] reveal that skills that must be possessed by humans to improve their economy, workability

and readiness as citizens are, 1) critical thinking and self-evaluation; 2) solving complex,

multidisciplinary, and open-minded problems; 3) creative; 4) communicate and collaborate with people

across cultures, geographies and languages; and 5) utilizing innovative knowledge, information and

opportunities.

Based on the opinions of Partnership for 21st Century Skills organization that is engaged in ability

development to face the times in 21th centuries, this is in accordance with the statement National Council

Teacher of Mathematics [7] which states the general purpose of learning mathematics is to develop the

ability of students in mathematical communication, mathematical reasoning, mathematical problem

solving, mathematical connections, and mathematical representation. Based on the learning purpose

formulated by NCTM, it is seen that the purpose of implementing mathematics learning is to develop

effective and mathematical abilities. Mathematical abilities include problem-solving ability, reasoning,

mathematical connection, representation, and mathematical communication.

Mathematics school has an important role for students to reach the standard of mathematical

abilities. The material in mathematics learning consists of many things, both related to everyday life,

related to other subjects, as well as related to topics in mathematics. The ability to solve mathematical

problems related to these three things is known as mathematical connection skills [7] Linto, Elniati, &

Rizal [8] explained that mathematical connection ability is the ability to solve mathematical problems

related to previous material. Furthermore, Kennedy Tipps & Johnson [9] stated that mathematical

connections are abilities that direct students and teachers to find mathematics related to everyday life,

associating between mathematical concepts and topics.

According to Sugiman [10], mathematical connection ability is a strategic ability that becomes a

mathematics learning goal. Mathematical connection ability is an important thing but students who

master mathematical concepts are not smart by themselves in connecting mathematics [10]. Without a

mathematical connection, students should learn and remember too many separate concepts and

mathematical procedures [7]. The idea of mathematical connections has been examined by W.A.

Brownell since 1930, but at that time the idea of mathematical connections was limited to arithmetic

[11]. Lembke and Reys [11] said that in research found that students are often able to make a list of

mathematical concepts related to real problems, but only a few students were able to explain why the

concept was used in the application. This shows that many students are good at solving mathematical

problems but not all understand how the relationship between concepts.

The importance of connections in mathematics learning has not been balanced by the mathematical

connection abilities possessed by the student. Basically, the student’s mathematical connection ability

is still low, this can be seen from the OECD report regarding the results of the PISA 2009 relating to

student’s ability to solve questions that require a mathematical connection process, only 5.4% or about

95% of students participating in the activity have not been able to associate problems with

concepts/principles, associate with other fields of study, or with daily life [12].

To improve student’s mathematical connection skills, we need to know what is the problem of

students in solving problems related to mathematical connections. It is important to know the aspects of

the mathematical connection skills that make it difficult for students. So, the cause can be shown and it

is expected to get a solution. The aim of this study is to analysis the mathematical connection ability of

grade VIIIth students on Circle material.

2. Method

This research is a qualitative study with a case study approach. The case study design is used to obtain

an in-depth understanding of the situation and meaning for those involved in the form of descriptive,

holistic and intensive analysis. The cases studied are limited by time and activity, the researcher collects

information completely using various procedures for collecting data based on the specified time. The

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selection of research subjects in this study was carried out intentionally (purposeful) or not randomly to

collect the desired data. The subjects of this study were 23 students of grade VIIIth at one of the Junior

High Schools in Temanggung Regency. The process of implementing this study follows the process of

case study research according to Yin [13] as follows: (1) define and design research, researchers conduct

a study of the theories development or concepts to determine cases and design protocols for data

collection; (2) preparing, collecting, and analyzing data, researchers prepare, collect and analyze data

based on research protocols that have been previously designed; (3) analyze and conclude, in a single

case, the results of the study are used to check back on the concepts or theories that have been built in

the first stage of the study.

Data was collected using essay tests and short interviews to know where the students’ difficulties

are in which the subjects of the study were asked to write down the steps of their answers in solving the

problem. In the interview, the students were asked about the steps they used to solve the given problem

and where did they find difficulties in solving it. The test is given consists of 3 questions. These three

questions were developed to measure mathematical connection skills which included aspects: (1)

connections between topics in mathematics that link material in a particular topic to material in other

topics, (2) connections between mathematics material in daily life, (3) connections between mathematics

material with other science fields. The indicator of mathematical connection in this research is applying

the relationship between concepts in mathematics and applying mathematics concepts to solve the real

problem. These two indicators are intended to measure aspects 1 and 2, while the third aspect is indicated

by giving questions that link mathematics to other science fields. The language originally used was

Bahasa, but the researcher translated it into English for the convenience of the readers. By using student

responses, the researcher will classify student’s mathematical connection abilities and identify students’

difficulties in solving problems related to mathematical connections. Criteria for student’s mathematical

connection ability is done by calculating the test results score of mathematical connection ability. Then

it is changed to the percentage of learning success rate, furthermore, the category of learning success

rates is carried out to determine the level of student’s mathematical connection abilities. The category

of student learning success rates is a five-scale categorization based on modifications from Suharsimi

Arikunto [14] described in Table 1 below.

Table 1. Categories of Mathematical Connection Capabilities

Range of Score Mathematical Connection Ability Tests

Category

84 < 𝑠𝑘𝑜𝑟 ≤ 100

Very High

69 < 𝑠𝑘𝑜𝑟 ≤ 84

High

59 < 𝑠𝑘𝑜𝑟 ≤ 69

Enough

44 < 𝑠𝑘𝑜𝑟 ≤ 59

Low

0 < 𝑠𝑘𝑜𝑟 ≤ 44

Very Low

Identification of student difficulties types observed from mistakes made by students in answering

test items. To maintain the credibility of the data obtained, the test was carried out with the format of

the test exercise [4]. Precisely, it is done as the final test of the material and the results are used by their

teacher as a component for the semester assessment. By doing this, students do the best to answer the

test and the answers they give reflect their true abilities. To prevent students from cheating, researchers

asked the teacher for help to supervise the exam. To maintain objectivity while examining and analyzing

student answers, researchers ignored student identity, gender, and abilities.

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3. Result and Discussion

The test questions in this research consisted of three description questions given to 23 students and

worked within 40 minutes. The indicator of mathematical connection in this study consists of two

indicators. Indicator 1 applies the relationship between concepts in mathematics. Indicator 2 applies

mathematical concepts to solve real problems. Then the data is processed and analyzed based on the

assessment rubric. The average test results in this study were 53.8. The results of tests on students

mathematical connection skills can be seen in Table 2 below

Table 2. Results of the Mathematical Connection Ability Test

Indicator

Total Score

Percentage(%)

Category

Indicator 1

150

43.47

Low

Indicator 2

98

53.26

Low

Based on Table 2, it can be seen that student’s mathematical connection ability in the indicator of

applying the relationship between concepts or topics in mathematics is classified as low with a score of

150 or 43.47% of the total score of 345. If the percentage was converted into a score produces an average

score of 43.47 so that it falls into the low category. While the indicators applying mathematical concepts

to solve real problems are classified as low with a score of 98 or 53.26% from a total score of 184. If

the percentage was converted into a score produces an average score of 53.26 so that it falls into the low

category.

1. Student Mathematical Connection Ability according to Indicator 1

The first indicator of mathematical connection ability is applying relationships between

concepts in mathematics. This ability is seen from the accuracy of students in using the

interrelationships between concepts in mathematics to answer what is asked in the question. The

following are presented bar charts resulting from the categorization of student’s mathematical

connection abilities according to indicator 1.

Diagram 1. Categories of Mathematical Connection Abilities in Applying Relations

Between Concepts in Mathematics

Based on diagram 1, it can be seen that students' mathematical connection ability in applying

the relationship between concepts in mathematics is in a very low category of seven students or

0

1

2

3

4

5

6

7

8

Very High High Enough Low Very Low

Student Mathematical Connection Ability

according to Indicator 1 Categories

The number of student according to the category

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30% of 23 students, in the low and enough categories each of them is 6 students or 26% of 23

students, in the high category as many as 3 students or by 13% of 23 students, and in the very

high category there was only one student.

2. Student Mathematical Connection Ability according to Indicator 2

The second indicator of mathematical connection ability is applying mathematical concepts to

solve real problems. This ability is seen from the ability of students to modeling real-world

problems into mathematical problems and student’s ability to use concepts in circle material to

solve problems related to everyday life. The following are presented bar charts resulting from

the categorization of students' mathematical connection abilities according to indicator 2.

Diagram 2. Categories of Mathematical Connection Ability in Applying Relations

Between Concepts in Mathematics

Based on Diagram 2, it can be seen that students mathematical connection ability in applying

deep mathematical concepts are in a very low category of 4 students or 17% of 23 students, in

the low category as many as 7 students or 30% of 23 students, enough categories are 2 students

or by 8% of 23 students, in the high category as many as 4 students or by 17% of 23 students,

and in the very high category there were only 6 students or 26% of 23 students.

Identification of Students Difficulties in Solving Mathematical Connection Problems

Identification of students’ difficulties in solving mathematical connection problems seen from the

mistakes made by students in answering questions. The following is the data on the number of students

who answered the questions and did not answer the questions, and the number of correct answers, the

data is presented in the table below.

Table 3. Percentage of Students that Answering Questions, Not Answering Questions and

Correct Answers

Question 1

Question 2

Question 3

Average

n

%

n

%

n

%

n

Answer

23

100

23

100

10

43

82

No Answer

0

0

0

0

13

57

18

Correct Answer

13

57

0

0

0

0

18

0

1

2

3

4

5

6

7

8

Very High High Enough Low Very Low

Student Mathematical Connection Ability

according to Indicator 2 Categories

The number of student according to the category

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Based on the table above, it can be seen that the average percentage of correct student answers is

18% of the three questions given to 23 students. That is, the percentage of students answered correctly

was lower than the average number of students answered correctly. The difficulties of students in this

study can be seen from the mistakes made by students on each question.

The Mistakes Made by Students on Question Number 1

The number 1 question is shown as follows.

Figure 1. Question number 1

In question number 1 students are expected to be able to understand problems in daily life related

to mathematics, then students connect between mathematical topics related to the square area and circle

area. In point b, students are expected to be able to represent approved results of mathematics to

determine the remaining money they have. Based on the results of the analysis it is known that 1 student

can answer correctly and give the right reasons for point a, 9 students can answer correctly and give

wrong reasons, 6 students were able to answer correctly but did not write down the reasons, and 7 other

students answered incorrectly. In general, students can model real-world problems into mathematical

problems. However, there are still some student mistakes in answering question number 1 point a, among

others students are not careful enough so that they only count square area and area of a circle, whereas

to find out the land area, students should reduce the area of a square by the area of a circle. That is,

students know the mathematical concepts, but cannot apply them to find solutions. The following is an

example of student’s answers to questions number 1 points a.

Figure 2. Example Incorrectly Calculation

Another mistake made by students is students miscalculating the multiplication operation as seen

in the picture above. The results of the analysis on question number 1 point b are known as 13 students

answered correctly and 10 students answered incorrectly. The following is one example of student

answers.

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Figure 3. Student can not represent the result of problem-solving

The mistake made by students are errors in the calculation process of multiplication operations.

Besides, in the process of working students are not coherent and students have not been able to draw

conclude so that they do not represent the results of problem-solving.

The Mistakes Made by Students on Question Number 2

Here is question number 2 which contains an indicator connecting mathematical material to other

fields.

Figure 4. Question Number 2

Problem number 2 shows the relation of mathematics with other fields that is physics and

astronomy, more precisely the material around the circle with a matter of straight motion and the solar

system. The relationship between mathematical topics is shown in question number 2 point b that is the

relationship between the material around the circle as a distance (point a) and calculation of speed. Based

on the results of the analysis there were 19 students answered correctly but could not write down the

reasons for number 2 points a and 4 other students answered incorrectly. The following is an example

of student’s answers to questions number 2 points a.

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Figure 5. Students mistake to apply the formula

The mistake made by students based on the picture above is that students do not know the formula

around the circle. Another error is that students are not able to distinguish the concept of the diameter

and radius of the circle as shown in the following figure.

Figure 6. Wrong Concept

In question number 2 point b, none of the subjects answered the question correctly or it could be said

that the related mathematical indicator linking mathematical topics was not fulfilled. This is seen from

23 students, none of them got a score on question number 2 points b. The following is one example of

student answers.

Figure 7. The mistake in question understanding

The mistake made by students is that students do not understand the question and speed material,

students do not pay attention to the unit intended by the question maker. In the results of this study, there

was one student who considered the desired speed unit, which is km/hr, but due to miscalculations, this

student failed to score. All students have tried to solve the problem even though it has not been maximal.

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This is seen from no students who get the correct final answer. This fact shows that students have not

been able to work on a circle problem that is associated with the concept of speed.

The Mistakes Made by Students on Question Number 3

As for question 3 which contains an indicator associating the concept of the Pythagorean Theorem,

arc length and around flat shown in the following picture.

Figure 8. Question Number 3

In question number 3, none of the subjects answered the question correctly or the mathematical

connection indicator was not fulfilled. This was seen from 23 students, only 1 student was able to apply

the relationship between the Pythagorean theorem and the arc length. The following is the student’s

answer.

Figure 9. Students can connect concepts

However, the student cannot get the right result. Meanwhile, 22 other students answered by writing

a mathematical symbol but only showed students not understanding. This shows that the mathematical

connection indicators related to connecting material between mathematical topics are still low. In

addition to the results of the tests, researchers conducted interviews with several students who were the

subjects of the study. Based on the results of the interview related to question number 3 where none of

the students were able to answer the questions correctly, the subject had difficulty finding a concept that

had to be associated with the concept of arc length and circumference to solve the problem. This is in

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line with the results of the study of Lestari [15] and Pratiwi [16] each of which revealed that the lowest

ability of students in the ability to connect between topics. This is in line with Kusmayadi [17] who

argues that most students do not know and do not understand which material has to do with the material

to be studied. The low level of connection ability between mathematical topics compared to real-world

connections is partly due to a large number of mathematical topics that must be associated with problem-

solving so that it requires broader thinking.

In question number 2 there were no students who were able to solve the problem correctly overall.

Subjects have difficulty understanding questions because students are still confused and have not

interpreted the sentence presented. This can be seen from the inability of students to write down the

reasons why they should know the distance of the satellite from the center of the earth and the unit of

velocity if it is known the time. This fact is in line with the results of Muncarno’s research [18] which

states that students have difficulty understanding questions because students are not careful in reading

and understanding sentences about things that are known, asked and how to solve the problem correctly.

Research on analyzing student difficulties in mathematical connection skills in the material of the

Pythagorean Theorem [16] shows that students cannot apply concepts that have been studied previously

with the Pythagorean Theorem concept, so students have difficulty in solving problems. Students have

difficulty understanding questions because students are still confused and have not been able to interpret

the sentences presented. Besides, students forget the material of the Pythagorean Theorem. Students are

also confused in choosing concepts that must be used in solving problems.

In general, the results of this study indicate that the mathematical connection ability of VIIIth grade

junior high school students on the Circle material is low. However, students can be modeling real-world

problems into mathematical problems. This shows mathematical connection ability on indicators

applying mathematical concepts in solving real-world problems is better than connections between

mathematical topics. However, the mistakes made by students in this research when solving

mathematical problems were incorrect formula selection and incorrect calculation in number operations.

This is in line with the statement of Budiyono [19] the types of mistakes students make in completing

math problems are conceptual errors, including (1) error determining theorem or formula to answer the

problem, (2) formula uses that are not by applicable prerequisite conditions. The difficulty experienced

by students in solving story problems is process skills. Difficulties in mathematical process skills in this

study mostly occur when students carry out count operations. This shows the low mathematical

connection ability.

4. Conclusion

Based on the results of this research, the mathematical connection ability is classified as low, this is

indicated by the low percentage of students who give correct answers, the low percentage on each

indicator of mathematical connections, and errors made by students. The most common mistake found

in this research is a misunderstanding. The misunderstanding occurs when students fail to identify 'what

is asked' and 'what is given' from the test problem. Students have difficulty understanding questions

because they have not been able to interpret the sentences presented. Students difficulties in applying

mathematical concepts in solving mathematical problems because students have not been able to

determine precisely the use of formulas or theorems in solving mathematical problems. Besides, in the

study [20] revealed that the most errors were misconceptions of concepts followed by miscalculations.

In this study, students had difficulty solving mathematical problems because of calculation errors.

This research is limited to the categorization ability mathematical connection that has not gotten a

proper solution to the above problems. Future research is expected to get a solution to overcome the low

mathematical connection ability. Also, the data distribution in this study is still limited to one school

only, so that it does not represent the overall data. Subsequent research can be developed in the wider

domain for the same levels or different levels.

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References

[1] Hanushek E A and Woessmann L 2012 J Econ Growth. 17 267

[2] Kruss G, Simon M, Petersen I and Gastrow M 2015 International Journal of Educational

Development 43 22

[3] Papaioannou E and Ciccone A 2009 Review of Economics and Statistics. 91 66

[4] Hadi S, Retnawati H, Munadi S, Apino E and Wulandari N F 2018 Problems of Education in the

21st Century 76 520

[5] Shute V J and Becker B J 2010 Innovative Assessment for the 21 Century: Supporting Educational

Needs (New York: Springer)

[6] Partnership for 21 Century Skills 2008 21 Century Skills, Education & Competitiveness: A

Resource and Policy Guide (New York: ERIC Clearinghouse on Urban Education)

[7] NCTM. 2000. Principles and Standards for School Mathematics. United States of America : The

National Council of Teachers of Mathematics, Inc.

[8] Linto, Rendya L, Elniati S and Rizal 2012 Jurnal Pendidikan Matematika 1 83

[9] Tipss S, Johnson A and Kennedy L M 2008 Guiding Children's Learning of Mathematics, 12th

Edition (USA: Wadsworth)

[10] Sugiman 2008 Pythagoras 4 56.

[11] Bergeson, T 2000 Teaching and Learning Mathematics: Using Research to Shift From the

“Yesterday” Mind to the “Tommorow” Mind [online www.k12.wa.us ]

[12] Kartikasari A and Widjajanti D B 2017 J. Phsy Conf Ser 812 012097

[13] Yin R K 2011 Qualitative Research from Start to Finish (New York: Guilford Publication Inc)

[14] Arikunto S 2012 Dasar-Dasar Evaluasi Pendidikan (Jakarta: Bumi Aksara)

[15] Lestari K E 2013 Implementasi Brain-Based Learning untuk Meningkatkan Kemampuan Koneksi

dan Kemampuan Berpikir Kritis Matematis Siswa Sekolah Menengah Pertama (Tesis SPS

UPI Bandung: tidak diterbitkan)

[16] Warih P D, Parta I N and Rahardjo S 2016 Proc. KNPM I Universitas Muhammadiyah Surakarta

ISSN 2502-6526

[17] Kusmayadi 2011 Pembelajaran Matematika Realistik untuk Meningkatkan Kemampuan

Komunikasi dan Pemecahan Masalah Matematis Siswa SMP (Tesis SPS UPI Bandung: tidak

diterbitkan)

[18] Muncarno 2008 Penerapan Model Penyelesaian Soal Cerita Dengan Langkah-Langkah

Pemecahan Masalah Untuk Meningkatkan Prestasi Belajar Matematika Siswa Kelas I SMP

(Lampung: LPMP Universitas Lampung)

[19] Budiyono 2008 Jurnal Penelitian Pendidikan. 11

[20] Agustyaningrum N, Abadi A M, Sari R N and Mahmudi A 2018 J. Phys.: Conf. Ser. 1097 012118