EXPLORING THE WORLD OF PLANE SHAPES: A STUDY ON FOURTH-GRADE STUDENTS' COMPREHENSION OF MATHEMATICAL CONCEPTS

ABSTRACT


INTRODUCTION
Learning is teaching someone about an information or concept through experience [1].Mathematics learning emphasizes the process of finding knowledge.Students are directed to discover for themselves the various facts and concepts, as well as new values necessary for their lives, and the focus of learning is directed towards developing students' skills in processing knowledge, discovering, and developing the necessary facts, concepts, and values.Learning is an effort by teachers to organize the environment and provide learning facilities for students to learn it.
Mathematics is the queen of science in everyday life as well as in helping in other fields of science [2].Mathematics is not separated from life, either directly or indirectly.Mathematics has a vital role, both in science and in everyday life.In addition, mathematics is also one of the subjects that play a significant role in education.By learning mathematics, we will learn the critical, creative, and active reasoning that people desperately need to solve various problems [3] Mathematics is a fundamental science in life, so it makes mathematics mandatory learning at every level of education, namely elementary school, junior high school, senior high school, and even universities [4].Mathematics needs to be studied and understood by all students.Mathematics is taught from elementary school to college so students can achieve a goal [5].As is known that one of the objectives of mathematics subjects is explained in the Regulation of the Minister of National Education Number 22 of 2006 on Standard Content of Mathematics Subjects for all levels of primary and secondary education so that learners can understand mathematical concepts, explain the interrelationships between concepts and apply concepts or algorithms, flexible, accurate, efficient and precise in problem-solving.One of the success factors of students in mastering mathematical materials and achieving learning goals is the teacher's ability to carry out the learning process.Mathematics learning is still one of the lessons many students avoid because many still consider mathematics a complex subject.
Mathematics is a structured subject.In studying mathematics, we first understand easy matter and then complex matter.Learning mathematics requires understanding the concepts taught because mathematics is related to concepts in similar materials [6].These concepts will give birth to a theorem or formula that is expected to be applied, so the ability to use these concepts and theorems is needed.One of the basic skills that students must master in studying mathematics is understanding concepts.
The ability to understand mathematical concepts is an ability that needs to be considered in the process of learning mathematics.Understanding concepts in mathematics learning is an essential foundation for solving mathematical and everyday problems.understanding mathematical concepts is very important for students because mathematics concepts are related [7].Mathematics lessons emphasize understanding concepts, meaning that in studying mathematics, students must understand mathematical concepts first to solve problems and be able to apply the concepts in the real world.Understanding concepts is the ability of students to master some subject matter, where students not only know or remember several concepts but can reveal again in other forms that are easy to understand [8].
In fact, students' mathematical understanding needs to improve in the field.This concept follows the results of the 2015 TIMSS report from the International Association for the Evaluation of Educational Achievement [9], which shows that Indonesia is in the 44th position out of 56 participating countries with an average score of 397 out of 500.Thus, mathematics learning in Indonesia has not achieved satisfactory or good results.That the ability to understand mathematical concepts in flat quadrilateral building material is relatively low; this is seen from students still experiencing errors when solving problems [10].Indications of low ability to understand the concept are characterized by some symptoms, namely, some students have not been able to choose the appropriate procedure to solve the problem, students have not been able to apply the concepts that have been taught when given the story, students have difficulty in solving problems whose models are slightly different from examples and students do not understand in determining the known data on the story [11].The difficulty of understanding mathematics becomes a problem, especially in plane material.Grade IV elementary students need to understand plane material, for example, rectangular and triangular.
Students are said to have concept comprehension skills if all indicators of concept understanding are met.Researchers use indicators of understanding the concepts of [12], i.e., (a) Recertifying a concept, (b) Classifying objects according to certain traits (according to the concept), (c) Providing examples and non-examples of concepts, (d) Presenting concepts in the form of mathematical representations, (e) Developing the necessary terms and conditions of a concept, (f) Using, utilizing, and selecting specific procedures or operations, and (g) Applying concepts or algorithms in problem-solving.In everyday life, we do not escape with objects that are flat-shaped.For example, when we install ceramics/tiles in a square-shaped room, to avoid making mistakes in determining the number of ceramics/tiles needed, we will estimate the room area to know the number of ceramics/tiles needed.
Based on the exposition provided above on the importance of understanding mathematical concepts.Various studies have been conducted previously, including the integration of plane concepts and local wisdom as an alternative mathematical learning media in elementary schools [13], common mistakes made by students in understanding mathematical concepts related to planes [14], flipped classroom model regarding understanding of mathematical concepts [15], exploration of ethnomathematics at Cetho Temple with a focus on plane topics [16], exploration of effective teaching methods to enhance understanding of plane mathematical concepts [17].However, there has been no research on the creative mathematical abilities of elementary school students with the assistance of interactive multimedia.
This research analyzes students' mathematical understanding abilities in plane material.Previous research has used various media tools and classroom models to see the ability to understand mathematical concepts.Still, it has yet to focus on analyzing the ability to understand mathematical concepts.In this research, we analyze multimedia learning tools used as instruments to assist students in understanding mathematical concepts.

METHOD
The research employed qualitative research using descriptive methods.This research aimed to describe students' ability in plane material in grade IV.To understand mathematical concepts, the subjects of this study were students of grade IV MI Ar Rahmah Bengle Village Majalaya Subdistrict 2020/2021.The technique of selecting research subjects was purposive sampling.Purposive sampling is a technique of retrieving data from source subjects with specific considerations [18].The research subject is the subject or source of information intended for research by researchers [18].
Researchers provided instruments as a description test in determining high, medium, and low-skilled students.The test was a mathematical comprehension ability test on rectangular and triangular plane materials.Students' answers were scored on each question item to analyze their ability to understand mathematical concepts.The mathematical concept comprehension score data obtained was analyzed using the following percentage formula: (student score)/(ideal score) x 100%.
Based on the test results analysis, the researchers interviewed research subjects about their abilities to solve problems through semistructured interviews and documentation.Semistructured interviews were used to find more open problems, where sources were asked for their opinions and ideas, making it easier for researchers to dig up information.Furthermore, the researchers performed documentation for collecting written or unwritten data, such as picture documents.
The data analysis used in this study was data analysis by Miles and Huberman, consisting of three stages: data reduction, data presentation, and conclusion/verification.The first stage is data reduction, which is to group data, ranging from collecting student answers to determining the research subjects from high, medium, and low-ability test results and then conducting interviews on research subjects.The second stage is the presentation of data, namely by presenting the data of the question, the answers, and the results of interviews on each indicator of mathematical concept understanding ability of the research subject.The last conclusion is to describe the results of student understanding as measured from indicators of mathematical concept comprehension ability in rectangular and triangular materials based on high, medium, and low categories.

RESULTS AND DISCUSSION
The test of mathematical concept understanding obtained 47% (nine students) of highly skilled students (scored ≥ 80), four students of moderately-skilled students or 21% (scored ≥ 65 and < 80), and six students with low-skilled ability or 32% (< score 65).The results of this study are the results of the student's test on the mathematical concept comprehension ability test.The analysis of the work of students from each category (high, medium, and low) is as follows:

High Category of Mathematical Concept Comprehension Skills
The work of subject 1 (T) on problem number 1 can be seen in Figure 1 below.Subject 1 (T) could answer the problem correctly in problem number 4, which shows the indicator of applying concepts or algorithms in problem-solving.In question number 4, subject 1 (T) applied the concept of the rectangular area formula to find the area of Ani's book with the correct answer and write the unit area appropriately.
The results of the analysis of the ability to understand the mathematical concept of subject 1 (T) can be seen in Table 1 below.

Moderate Categories of Mathematical Concept Understanding Ability
The following is the work of subject 2 (S) on question number 1. Based on Figure 5, subject 2 (S) could reflect indicators of the ability to understand mathematical concepts and provide precise answers.Subject 2 (S) answered the question correctly, which indicated the indicator of restating the concept.In question number 1, subject 2 (S) answered the question briefly according to the concept studied in the triangle's area and circumference.Subject 2 (S) answered correctly and wrote the unit area and circumference of the triangle precisely.The work of subject 2 (S) in question number 2 can be seen in Figure In problem number 2, which shows the indicator develops the necessary conditions or sufficient conditions of a concept, subject 2 (S) could not answer the problem appropriately and apply the formula for finding the length of the rectangle.Subject 2 (S) did not understand the mathematical concept in indicator 2 and the intention of the problem.The work of subject 2 (S) on problem number 3 can be seen in Figure 7. Subject 2 (S) answered the question correctly, which shows the indicator of using, utilizing, and selecting a specific procedure or operation, although there were some errors.Subject 2 (S) chose a procedure for finding the length of the triangular base that is already known to be wide and high, but there were conceptual errors in the writing.Question number 2 asked the length of the triangular base, but subject 2 (S) wrote the area of the triangle asked.Although subject 2 (S) answered the question with the right formula and answer, subject 2 (S) did not understand indicator 3 because there were writing errors in the question problem.The work of subject 2 (S) on problem number 4 can be seen in Figure 8. Subject 2 (S) could answer the question correctly, which shows the indicator of applying concepts or algorithms in problem-solving.In question number 4, subject 2 (S) applied the concept of the rectangular area formula to find the area of Ani's book with the correct answer and write the unit of area correctly.However, subject 2 (S) wrote incompletely.The problem asked in the question was the area of the rectangle, but subject 2 (S) only wrote the rectangle when answering the question.
The results of the analysis of the ability to understand the mathematical concept of subject 2 (S) can be seen in Table 2.The researchers interviewed the subject about his answer to question number 3 related to the indicator of using, utilizing, and choosing a specific procedure or operation.
Here is an interview excerpt related to question number

Low Category of Mathematical Concept Comprehension Ability
The following are the work results of subject 3 (R) on problem number 1:    Judging from the category of ability to understand concepts, the fourth-grade students' concept understanding test results show three levels of understanding: high, medium, and low [8], [19].As mentioned in the above research results, Figure 13 describes the percentage of fourth-grade students' ability to understand mathematical concepts.Figure 13 shows the ability level to understand the mathematical concept of class IV.There are three categories: high category with 47% percentage, medium category with 21% percentage, and low category with 32% percentage.The classification of the level of understanding ability of the concept refers to Arikunto [8], [19], who states that the average value and standard deviation of research data can determine the categories of concept understanding capabilities, including high, medium, and low.The explanation of the three categories is: (1) The high category is the student who gets more than the average grades summed by the standard deviation, (2) The moderate category is the student who obtains a grade between high category grades and low category grades, and (3) Low categories are students who get grades less than the difference from the average grade with standard deviation.The guidelines for the test questions are adjusted to indicators of understanding concepts according to [12].The suspension guidelines used in the study refer to the modified chords according to Abraham.The category of achievement of the ability to understand mathematical concepts used in this study refers to Arikunto [8], [19].The analysis found 47% of nine high-skilled students (scored ≥ 80), 21% or four moderatelyskilled students (scored≥ 65 and < 80), and 32% or six low-skilled students (scored < 65).
Students with high and moderate categories met the indicators of stating concepts; using, utilizing, and selecting certain procedures or operations; and applying concepts or algorithms in problem-solving.However, there were errors.Students with low categories met the indicator of applying concepts or algorithms in problem-solving.Students with high, medium, and low categories cannot meet the indicators of developing the requirements and sufficient requirements of a concept because they were fixated on memorizing formulas and mimicking the solution of problems exemplified by teachers.This finding follows the research results which states that based on interviews with teachers, students cannot develop the necessary conditions because they are fixated on memorizing formulas [20].Students only imitate the completion of the same problem with the teacher.When given a different problem, students are still confused about how to solve it.Many students made mistakes in the calculation, so the answer was incorrect.
The grade IV student's concept understanding test results showed that all research subjects from the high, medium, and low categories could not work on the mathematical concept understanding test problem perfectly.Based on the interview results, researchers found problems in mathematics learning.The students have not mastered the indicators of understanding concepts.Some students can redefine a concept but were confused about recognizing objects by their nature.They had difficulty deciphering problems, especially problems in the form of stories, and could not model statements into mathematical form.This finding is in line with the opinion of [21], which states that some students have difficulty solving mathematics problems in the form of stories, understanding language, what is asked in questions, and calculations.
Interview results showed each subject experienced a different level of difficulty.This finding refers to the study's results [22], which state that students with high, medium, and low cognitive levels all have difficulty working on the problem of understanding mathematical concepts.The inaccuracy of students in working on test problems leads to students' errors in completing comprehension test questions.
Errors in the results of students' work when completing the test include errors in writing units of area or circumference, errors in the writing of what is asked, and errors during the calculation operation process so that the results of student answers are incorrect.These errors occurred because they were in a hurry and were less thorough, so they could not apply the right formula and experienced errors in calculating operations and solving mathematical concepts.This finding follows the results which states that the factors that cause mistakes made by students are less understanding of the intention of the problem, less careful in reading the problem, less thorough, too hasty in solving the problem, and not mastering the steps of the problem [23].In addition, high student mathematics anxiety is also a factor that causes student errors in working on concept comprehension test problems.Students with high mathematics anxiety experience errors in three aspects: (1) mistakes in writing mathematical symbols, (2) the meaning of mathematical models, and (3) inconsistency in the use of symbols [24].
Aside from the above mistakes, the student's psychology also affects their understanding of the concept.Psychological factors play an essential role in students studying mathematics.Anxiety is the most significant psychological factor because, as a result of anxiety, students are nervous about learning, have no interest in learning, and feel less confident [25].When that happens, students cannot understand mathematical concepts.Students become clueless and have difficulty learning the following material.Mathematics anxiety can cause students difficulties as well as a phobia of mathematics.Anxiety is the most significant psychological factor because, as a result of anxiety, students are nervous about learning, have no interest in learning, and feel less confident [26].

CONCLUSION
Based on the research and discussion, the analysis of the ability to understand the mathematical concept of students on plane materials in the fourth grade at MI Ar Rahmah Bengle Village, Majalaya Subdistrict, varies according to the level of understanding.There are high, medium, and low-skilled students.Students with high and medium categories met the indicators of stating concepts; using, utilizing, and selecting specific procedures or operations; and applying concepts or algorithms in problem-solving.However, there were errors.Students with low categories met the indicator of applying concepts or algorithms in problem-solving.Hence, improved teaching methods are needed to enhance students' mathematical understanding, particularly in plane materials.Further research is recommended to explore effective strategies for reducing mathematical anxiety and enhancing students' conceptual understanding.

Figure 1 .
Figure 1.Work Results of Subject 1 (T) on Problem Number 1 Subject 1 (T) could not reflect the indicator of the ability to understand mathematical concepts despite the correct answer.Subject 1(T) answered question number 1 correctly, which indicated the indicator restating the concept.Subject 1 answered the question briefly

Figure 2 .
Figure 2. Work result of Subject 1 (T) on Problem Number 2In problem number 2, which shows the indicator develops the necessary conditions or sufficient conditions of a subject concept, 1 (T) could not answer the problem appropriately and could not apply the formula to find the length of the rectangle.Subject 1 (T) needed help understanding the mathematical concept in indicator two and the intention of the problem.The work of subject 1 (T) on question number 3 can be seen in Figure3below.

Figure 3 .
Figure 3. Work Result of Subject 1 (T) on Problem Number 3Subject 1 (T) answered the question appropriately, which shows the indicator of using, utilizing, and selecting a specific procedure or operation.Subject 1 (T) chose a procedure for finding the length of the triangular base, which is already known to be wide and high.Subject 1 (T) answered the question correctly but needed to write the unit in solving the problem.

Figure 4 .
Figure 4. Work Result of Subject 1 (T) on Problem Number 4

Exploring
The World of Plane Shapes …. │ Andes Safarandes Asmara, et al I n d o n e s i a n J o u r n a l o f S c i e n c e a n d M a t h e m a t i c s E d u c a t i o n ( I J S M E ) | 289

Figure 5 .
Figure 5. Work Result of Subject 2 (S) on Problem Number 1

Figure 7 .
Figure 7. Work Result of Subject 2 (S) on Problem Number 3

Figure 8 .
Figure 8. Work Result of Subject 2 (S) on Problem Number 4

Figure 9 .Figure 10 .
Figure 9. Work Result of Subject 3 (R) on Problem Number 1Based on Figure9, subject 3 (R) could not reflect the indicator of the ability to understand mathematical concepts.Subject 3 (R) answered the question correctly, which indicated the indicator of restating the concept.In question number 1, subject 3 (R) answered the question briefly according to the concept studied in the triangle's area and circumference.Subject 3 (R) answered correctly and wrote the unit of the triangle circumference appropriately.However, subject 3 (R) encountered errors in calculating the area of the triangle, and the answer was incorrect.The result of subject 3 (R) work on problem number 2 can be seen in 10 below:

Figure 11 .
Figure 11.Work Result of Subject3 (R) on Problem Number 3 Subject 3 (R) could not answer the question correctly, which showed the indicator of using, utilizing, and selecting a specific procedure or operation.Subject 3 (R) could not choose a procedure for finding the length of the triangular base.Subject 3 (R) also experienced a conceptual error in the writing of the formula.Answer and formula errors occurred because subject 3 (R) did not understand the problem in indicator 3. The result of subject 3 (R) work on problem number 4 can be seen in Figure 12 below:

Figure 12 .
Figure 12.Work Result of Subject 3 (R) on Problem Number 4

Figure 13 .
Figure 13.The Percentage of Concept Understanding Ability Level

Exploring
The World of Plane Shapes …. │ Andes Safarandes Asmara, et al I n d o n e s i a n J o u r n a l o f S c i e n c e a n d M a t h e m a t i c s E d u c a t i o n ( I J S M E ) | 297

Table 1 .
Analysis of the Ability to Understand Mathematical Concepts of Subject 1 (T)

Table 1
Furthermore, the researcher interviewed the subject about his understanding of solving problem number 2 on developing a concept's necessary or sufficient conditions.Here is an interview with subject 1 (T) related to the answer to question number 2:After the interview related to question number 2, the researcher interviewed the subject about question number 3 related to the indicator of using, utilizing, and choosing specific procedures or operations.Here is an interview excerpt related to question number 3: shows the results of the analysis of the mathematical understanding ability of subject 1 (T) through the test.To support the test results analysis, the researcher interviewed the subject related to his understanding of solving problem number 1 on the indicator (restating the concept).Here is a snippet of the interview with subject 1 (T):P :Can you tell me what was asked?T : The question is the length of the triangle's base.P : Are you having trouble solving the problem?T : Yes, on the division count operation.Next, the researcher interviewed the subject related to problem number 4.Here is a snippet of the interview: P : Do you know what information is given?T : Information about the book.P : Can you tell me what was asked about it?T : What is asked is the rectangular area of the book.P : Do you know what formulas are used in solving problems?T : Formula of 2 x rectangular area (length + width).P : Are you having trouble solving problems?T : No, ma'am.

Table 2 .
The Analysis of the Ability to Understand Mathematical Concepts of Subject 2 (S) I n d o n e s i a n J o u r n a l o f S c i e n c e a n d M a t h e m a t i c s E d u c a t i o n ( I J S M E ) | 291

Table 2
shows the results of the mathematical understanding analysis of subject 2 (S) through the test.To support the test results analysis, researchers interviewed the subject about the answer to question number 1 on the indicator of restating the concept.Here is a snippet of the interview with subject 2 (S).Furthermore, the researcher interviewed on the subject related to understanding problem number 2 on the indicator of developing the necessary conditions or sufficient conditions of a concept.Here is an interview excerpt on subject 2 (S) related to the answer to question number 2: P : Can you tell me what was asked about it?S : Rectangular length, ma'am.P : Do you know how to find a rectangle if what it knows is its circumference and width?S : I can't, ma'am.P : Are you having trouble solving problems?S : Yes, ma'am.
Yes, ma'am.It was on the division operation. R: