Forms Of Mathematical Representation Research Articles

Analysis of Ability to Understand Mathematical Concepts Class Students XI in Geometric Transformation Materials

The low ability of students to understand mathematical concepts is proven by the majority of students not being able to reformulate the solution to the problem given. This research aims to describe students' ability to understand mathematical concepts for each indicator so that it is known which indicators students experience problems with. The method used in this research is descriptive qualitative. The instruments in this research are test and interview instruments. The research subjects were 26 students of class XI Science 1 SMAN 5 Sukabumi City. Data were analyzed using data reduction, data presentation, and drawing conclusions. In data reduction, researchers summarize the data and classify the data. Based on the results of data analysis, it was concluded that students with high and medium abilities had excellent concept understanding abilities in restating a concept, classifying objects according to the concept, and presenting concepts in various forms of mathematical representation. while students with low abilities are in the good category. Highly capable students are able to restate the concepts they have learned and apply concepts or problem solving algorithms very well. Meanwhile, students with medium and low ability are in the sufficient category. In linking various concepts, high, medium and low ability students have quite good ability to understand mathematical concepts.

Analisis Kesulitan Memahami Konsep Matematis Ditinjau dari Kemampuan Metakognisi Siswa Pada Siswa Kelas X SMA Negeri 1 Sibolga

This research aims to understand how difficulties in understanding mathematical concepts are related to the metacognitive abilities of class X students at SMA Negeri 1 Sibolga for the 2023/2024 academic year. The research method used in this study is descriptive qualitative. The research subjects consisted of 32 students of class X MIA 2. Data collection was carried out through the use of questionnaires and tests as research instruments. The results of the research show that students with very high metacognitive abilities are able to fulfill all indicators completely, such as restating the concepts studied, classifying objects based on the requirements that form the concept, identifying the properties of operations or concepts, applying concepts logically, providing examples or are not examples of concepts that have been studied, and present concepts in various forms of mathematical representation. Students with high metacognitive abilities are only able to fulfill five of the six existing indicators. Meanwhile, students with moderate metacognitive abilities can only fulfill one indicator, namely providing examples or non-examples of the concepts they have studied

Analysis of Students' Mathematical Understanding in Gradient Material Linear Function Graphics Class IX UPTD SMP Negeri 3 Pematang Siantar

This research aims to find out how to analyze students' mathematical understanding of gradient materials for linear function graphs for Class IX 7 UPTD SMP Negeri 3 Pematang Siantar. The research method used in this research is a qualitative method with descriptive data analysis. The subjects in this research are all students in class IX 7 of SMP Negeri 3 Pematang Siantar in the 2023/2024 academic year. The number of subjects in this research was 30 students. The instrument used in this research is a mathematical understanding test in the form of a description using 3 indicators, namely restating concepts that have been studied, presenting concepts in various forms of mathematical representation, applying concepts or problem-solving algorithms. These 3 indicators are used in 6 questions. Based on the data analysis carried out, the overall mathematical understanding ability of students is at a medium level, namely with a percentage of 47.8%. The indicators used are 1) restating mathematical concepts, 2) presenting mathematical representations, 3) applying concepts or problem-solving algorithms. Based on the previous explanation, it can be concluded that the mathematical understanding of students in class IX 7 UPTD SMP Negeri 3 Pematang Siantar as a whole is at a medium level.

Analisis Pemahaman Konsep dalam Menyelesaikan Soal Geometri Dimensi Tiga Pada Peserta Didik SMK di Kota Makassar

This type of research is descriptive research. This study aims to determine the understanding of concepts in solving three-dimensional geometry problems in class XI students of SMK Muhammadiyah 3 Makassar. The population in this study were all students of class XI SMK Muhammadiyah 3 Makassar. Furthermore, selecting samples with Cluster Random Sampling technique. The selected sample in this study is class XI Accounting Department. From this sample, interviews will be continued with 9 students consisting of 3 students in the high category, 3 students in the medium category, and 3 students in the low category. The instruments in this study in the form of concept understanding tests and interview guidelines used to determine the understanding of concepts in solving three-dimensional geometry problems in class XI students of SMK Muhammadiyah 3 Makassar. The data analysis technique in this study is descriptive statistical analysis with the aim of describing the understanding of mathematical concepts of students in class XI SMK Muhammadiyah 3 Makassar. Based on the results of data analysis and discussion that has been stated, the conclusion in this study is the understanding of concepts in solving geometry problems of three dimensions in class XI students of SMK Muhammadiyah 3 Makassar is on the indicators: (1) Concept understanding on indicator I, namely giving examples and not examples of a concept by 91%, (2) Concept understanding on indicator II, namely presenting concepts in various forms of mathematical representation by 53%, and (3) Concept understanding on indicator III, namely applying concepts or algorithms in problem solving by 57%.

The Students’ Representative Processes in Solving Mathematical Word Problems

Representation in mathematics is essential as a basis for students to be able to understand and apply mathematical ideas. This study aims to describe how students produce different representations in solving word problems. In solving word problems, students make verbal–written representations, image representations, and symbol representations. This research uses a qualitative descriptive study involving 75 fifth-grade students at one of the private schools in Makassar, Indonesia. Setting and Participants: two subjects were chosen from 75 participants based on the completion of word problems that resulted in different representations, including verbal–written representations, picture representations, and symbol representations. The instruments used were word problems and interview sheets, although some other students only used one or two forms of mathematical representation. The results of this study indicate that, from the different representations produced that include verbal–written representations, image representations, and symbol representations, students carry out the process of translation, integration, solution, and evaluation until finding answers. In addition, other findings were students’ ‘mathematical literacy which immensely helped the students’ representation process in solving word problems. three forms of representation were found to be produced by students: verbal–written, image representation, and symbol representation. Furthermore, the three forms of representation were created through carrying out four representation processes, namely the processes of translation, integration, solution, and evaluation.

ANALISIS KEMAMPUAN PEMAHAMAN KONSEP PECAHAN PADA SISWA SMP

This study aims to determine the ability to understand the concept of fractions in grade VII students of SMP Kristen Kusu-Kusu Sereh Ambon. The type of research used is qualitative descriptive research. This research was carried out at SMP Kristen Kusu-Kusu Sereh Ambon, with the data source being class VII-1 students totaling 20 students, and the research subjects selected to be interviewed were three students. Researchers describe students' ability to understand fractional concepts by looking at the results of student answers and interviews. The results of this student's test refer to the question instructions and the student's accuracy in answering. The accuracy of the student's answers is adjusted to the assessment criteria for the test questions and the scoring criteria for the ability to understand fractional concepts with four indicators, namely indicators of the ability to provide examples and non-examples, indicators of the ability to present concepts in various forms of mathematical representation, indicators of the ability to use, utilize and select specific procedures or operations and indicators of the ability to apply concepts or algorithms in problem-solving. Based on the results of the fractional concept comprehension ability test and student interviews, one student met three indicators of concept understanding ability, namely indicators of the ability to provide examples and non-examples, the ability to present concepts in various forms of mathematical representation, and the ability to apply concepts or algorithms in problem-solving, and two students who met one indicator of concept understanding ability, namely indicators of ability to provide an example and non-example.

Multiple representations (MR) based instructional approach in support of physics identity and physics teachers' identity development: Design considerations

In this paper, we describe the intervention and the context of implementation of a multiple representations (MR)-based instructional approach as a classroom practice in an first-year thermodynamics course for preservice physics teachers at an Indonesian university. We argue that the implementation of this approach will contribute to the enhancement of students’ conceptual understanding and problem-solving skills. By enhancing those two aspects, we intend to contribute to their development of physics identity and physics teacher identity. We illustrate how this MR approach is applied in the classroom and describe how the relationship between the aspects of this approach interacts with physics identity and physics teacher identity. During lessons the teacher used real-life examples and students were encouraged to use different representations when they solved problems in small groups. The students realized that learning physics could involve many representations and might increase their interest to physics. However, we found some situations that did not match our expectations. For instance, most of the students were more interested when the problems were in the form of mathematical representation. In addition, we found that some students were inactive in the class. Therefore, it is necessary to think as educators about how to provide a positive learning experience to stimulate the development of student's identity. This work exemplifies how physics educators can stimulate physics and physics teacher identity formation in their physics courses as a preparation for future physics teachers.

PENINGKATAN KEMAMPUAN PEMAHAMAN KONSEP MATEMATIKA MENGGUNAKAN MODEL PROBLEM BASED LEARNING PADA MATERI POLA BILANGAN DI KELAS VIII SMP NEGERI 3 WERTAMRIAN KABUPATEN KEPULAUAN TANIMBAR

This study aims to determine the learning design of speech pattern material for class VIII students of SMP Negeri 3 Wertamrrian using a problem based learning model and determine students' ability to understand mathematical concepts through number patterns after using a problem-based learning model for class VIII students of SMP Negeri 3 Wertamrrian. This research was conducted at SMP Negeri 3 Wertamrian, Tanimbar Islands Regency in November 2022. This type of research is a qualitative research using a research design. Data collection methods used are research documentation, written tests and interviews. The data analysis technique used is data reduction, data presentation and conclusions or verification. The results of the study design research using a problem based learning (PBL) model on Bialngan Pattern material in class VIII of SMP Negeri 3 Wertamrian are as follows: (a) In the first and second meeting learning, the researcher reviewed the material related to the learning objectives to be achieved. (b) The researcher gave 2 problems to students, namely 1 problem at the first meeting and 1 problem at the second meeting. Then ask students to check the sentences or questions contained in the problem that they have not understood. (c) Researchers divide students into groups to solve problems. (d) Researchers assist students in solving the problems given by providing the supports that have been provided in the HLT that the researchers designed. (e) Researchers provide opportunities for group representatives to present each problem that has been discussed. (f) Researchers together with students discuss and check the results of the discussions that have been presented and evaluate the learning process that occurs. (2) The ability to understand mathematical concepts of class VIII SMP Negeri 3 Wertamrian on number pattern material after following the mathematics learning process using PBL is as follows: (a) In problem 1, students have a more dominant concept understanding ability in indicators 1, 3 and 4, namely restating each concept, presenting the concept in various forms of mathematical representation and using, utilizing and selecting certain procedures or operations in solving problems. (b) In problem 2, students have more dominant concept understanding skills in indicators 1, 3 and 4, namely restating each concept, presenting concepts in various forms of mathematical representation and using, utilizing, and choosing certain procedures or operations in solving problems.

Matrix Concept Understanding Ability: A Quantitative Descriptive Study on Grade XI Vocational High School Students

Understanding and completing a basic mathematical concept is often faced by students. This problem is fundamental to mathematical ability. This ability is part of the competency to understand mathematical concepts. Therefore, this study was conducted to describe the students' ability to understand matrix concepts. This study is a quantitative descriptive, be held on grade XI students from Multi Media I of a vocational high school at Kefamenanu. The number of participants in this study was 26 students. The instrument used is a test of the ability to understand the concept of the matrix and interviews. The results of this study indicate that the ability to understand the matrix concept of grade XI Multi Media I students is in the medium category with a percentage of 56.6%, with details of 7 students in the high category, 13 students in the medium category, and 6 students in the low category. There are 96% of students can restate a concept, 46% of students can classify objects according to the concept, 57% of students can give examples and non-examples of concepts, 61% of students can present concepts in various forms of mathematical representation, and 23% of students can use, utilize and select settlement procedures.

ANALISIS KEMAMPUAN PEMAHAMAN KONSEP MATEMATIKA MATERI PELUANG

The purpose of this study in general is to determine the ability of students of SMP Sunan Giri Malang in understanding mathematical concepts. The specific objectives in this study, including: 1). Describing students' ability in understanding concepts on opportunity material, 2) Describing students' abilities in understanding concepts when solving problems. This research belongs to the type of qualitative descriptive research. Qualitative descriptive research was used to analyze the ability of eighth grade students of SMP Sunan Giri Malang in understanding the concept of opportunity. Data was collected through the methods of observation, tests, interviews and documentation. Furthermore, the data were analyzed descriptively qualitatively sequentially based on the question indicators, as follows; 1) Restate a concept, 2). Giving examples and not examples of a concept, 3). Presenting concepts in various forms of mathematical representation, 4). Grouping objects according to the properties, 5). Apply a concept or algorithm to problem solving. The results showed that the ability of class VIII students of SMP Sunan Giri Malang on the overall opportunity material got the following percentages: high ability category 47%, medium ability category 35% and low ability category 23%.

Pengaruh Model Pembelajaran Kooperatif Tipe Think Pair Share Berbantuan LKPD Terhadap Pemahaman Operasi Bentuk Aljabar Pada Siswa Kelas VII SMPN 13 Mataram Tahun 2021/2022

Success in learning mathematics can be seen from understanding students' initial mathematical concepts, but a low average score is an indication of difficulties in understanding mathematical concepts related to algebraic operations. This study aims to determine the effect of cooperative learning models Think Pair Share (TPS) type assisted by student worksheets (LKPD) on students' understanding of algebraic operations. The research design used was Pre-Experimental Design (Non Design) in the form of One-Group Pretest-Posttest Design. The population in this study was all class VII, while the selected sample was class VIIA as the control class and class VIIB as the experimental class. Data on the ability to understand different concepts were taken using a pretest-posttest instrument in the form of essay questions. Before further analyzing the results of the pretest-posttest, the two classes were first tested for normality and homogeneity. The results of the hypothesis test show that = 0.441 < = 1.96 which means Ho is accepted, so that there is a difference between understanding the operation of algebraic forms in the experimental and control classes or in other words there is no effect of the TPS type cooperative learning model assisted by LKPD on understanding the operation of the form. algebra to students. This indicates that learning with the TPS type cooperative learning model assisted by LKPD allows students to achieve conceptual understanding where indicators are to restate concepts, classify objects according to certain properties, state concepts in various forms of mathematical representation, use, utilize and choose procedures. or certain operations and apply concepts

DECISION MAKING IN POLICY LEARNING MODEL THROUGH STUDENT MATHEMATICS REPRESENTATION ABILITY TEST IN LEARNING TWO VARIABLE LINEAR EQUATIONS

This study aims to make decisions about learning model policies by exploring students' mathematical representations in learning mathematics. The benefit of the ability to represent mathematics is that it facilitates problem-solving. Students need to train and develop things related to mathematical representation in a lesson. The form of mathematical representation used is a visual representation, making mathematical models, and using words in problem-solving. From the results of the study, it was found that the students' mathematical representation skills were linear equations of two variables, namely students as the first subject in the very capable category of students fulfilling complete and very good mathematical representations. Students with moderate academic ability in the second subject and meeting the mathematical representation ability were quite good, while students in the third subject with existing indicators had incomplete results and did not meet the mathematical representation.

ANALISIS PEMAHAMAN MATEMATIS SISWA DITINJAU DARI MOTIVASI BELAJAR PADA PEMBELAJARAN TATAP MUKA (PTM) TERBATAS

This study aims to analyze students' mathematical understanding in terms of learning motivation in limited face-to-face learning. This type of research is qualitative research. Subjects were taken using a learning motivation questionnaire and a mathematical ability test. Students who meet the indicators of learning motivation and the characteristics of the category of mathematical ability are determined as subjects and then given a mathematical understanding test and then interviewed. The data were then analyzed using the Miles and Huberman model. The results of data analysis show that students who have high learning motivation meet three indicators of mathematical understanding, namely the ability to classify objects according to certain properties (according to the concept), the ability to present concepts in various forms of mathematical representation and the ability to use, utilize and choose procedures or certain operations. However, students have problems in using and utilizing certain perating procedures. Subjects with moderate learning motivation only met two indicators of mathematical understanding, namely the ability to classify objects according to certain properties (according to the concept) and the ability to use, utilize and choose certain procedures or operations. However, students who are motivated to learn are having problems using and utilizing certain operating procedures. Subjects with low learning motivation fulfill one indicator of mathematical understanding, namely the ability to classify objects according to certain characteristics (according to the concept). Even though students do not work on the questions correctly, students still try to solve the questions given. It is recommended that teachers pay attention to students' mathematical understanding, especially in the new normal period.

ANALISIS PEMAHAMAN MATEMATIS SISWA DITINJAU DARI MOTIVASI BELAJAR PADA PEMBELAJARAN TATAP MUKA (PTM) TERBATAS

This study aims to analyze students' mathematical understanding in terms of learning motivation in limited face-to-face learning. This type of research is qualitative research. Subjects were taken using a learning motivation questionnaire and a mathematical ability test. Students who meet the indicators of learning motivation and the characteristics of the category of mathematical ability are determined as subjects and then given a mathematical understanding test and then interviewed. The data were then analyzed using the Miles and Huberman model. The results of data analysis show that students who have high learning motivation meet three indicators of mathematical understanding, namely the ability to classify objects according to certain properties (according to the concept), the ability to present concepts in various forms of mathematical representation and the ability to use, utilize and choose procedures or certain operations. However, students have problems in using and utilizing certain perating procedures. Subjects with moderate learning motivation only met two indicators of mathematical understanding, namely the ability to classify objects according to certain properties (according to the concept) and the ability to use, utilize and choose certain procedures or operations. However, students who are motivated to learn are having problems using and utilizing certain operating procedures. Subjects with low learning motivation fulfill one indicator of mathematical understanding, namely the ability to classify objects according to certain characteristics (according to the concept). Even though students do not work on the questions correctly, students still try to solve the questions given. It is recommended that teachers pay attention to students' mathematical understanding, especially in the new normal period.

Analisis Kemampuan Pemahaman Konsep Matematis Siswa SMP Pada Materi Relasi dan Fungsi Berdasarkan Teori Honey Mumford

The purpose of this study was to describe the understanding of mathematical concepts of junior high school students on Relation and Functions based on Honey Mumford Theory. The research uses a descriptive qualitative approach and the type of research used is a case study. In this study, there were 24 respondents, then 8 students were selected, representing 2 students from each learning style. The data collection method in this study was a learning style questionnaire LSQ (Learning Style Questionnaire) according to Honey Mumford, written tests and interviews. This study uses reduction, data presentation, and drawing conclusions into data analysis techniques. The results showed that: 1) Students with an activist learning style when studying tended to like new things so they were less careful with indicators that restated a concept, and did not like activities that took a long time which caused errors in calculating number operations. 2) Reflector learning style students at the time of learning are quite careful and calculating so that they are able to classify objects according to certain properties, but tend to focus on sources of information so that they are not able to present concepts in various forms of mathematical representation and apply concepts to problem solving. 3) Students with theoretical learning styles when learning many considerations and everything depends on theory so they are able to classify objects according to certain properties, but have not been able to present concepts in various forms of mathematical representation. 4) Students with pragmatic learning styles will study the material in detail so that they can restate a concept, but pragmatic students are too centered on sources of information which causes students not to be able to apply concepts or algorithms in problem solving. The conclusion of this study states that each student's learning style will lead to a different understanding of mathematical concepts.

Analysis of Students' Concept Understanding Ability Through E-Modules on Linear Program Materials

One of the mathematical abilities that students must master in order to learn mathematics is the ability to understand concepts, since it can affect the quality of learning and academic accomplishment of students. If the student's idea understanding is good, he or she will be able to solve the problem using the procedure. As a result, the goal of this study is to determine and describe students' grasp of mathematical ideas in linear programming material. This study's instrument is a set of learning outcomes test questions that refer to indications of concept comprehension. A qualitative research design is used in this study. Data reduction, data presentation, and generating conclusions were used to examine the data in this study. According to the findings, 33 students were able to meet the indicators of the ability to understand mathematical concepts by providing examples and non-examples, which received the highest percentage value, followed by indicators presenting concepts in various forms of mathematical representation, which received the second highest percentage value.

Analisis Kemampuan Pemahaman Konsep Pertidaksamaan Linear Satu Variabel Ditinjau Dari Gaya Kognitif Siswa

The main objective is to determine the students' conceptual understanding ability in terms of cognitive style. The type of research used is a qualitative research conducted at UPT SPF SMPN 49 Makassar. Research subjects as many as 4 people who were selected each 2 FD and 2 FI. The data collection technique used GEFT test, concept understanding ability test and interview. The instruments used were first validated by two experts. The data collected were analyzed by descriptive and qualitative analysis through the stages that include data collection, data reduction, data presentation, and drawing conclusions. Test the validity of the data using triangulation techniques. The results of this study conclude that there are differences in the ability to understand concepts of students with FI and FD cognitive styles with the description: (1) the ability to understand concepts of students with field dependent cognitive style (FD) fulfills the three indicators of giving examples and not examples of a concept, presenting concepts in various ways. form of mathematical representation, and apply concepts into problem solving, (2) The ability to understand concepts of students with field independent cognitive style (FI) fulfills the four indicators restating a concept, giving examples and not examples of a concept, presenting concepts in various forms of mathematical representation, and apply concepts to problem solving.

ANALISIS PROFIL KEMAMPUAN PEMAHAMAN KONSEP MATEMATIS SISWA PADA MATERI OPERASI BILANGAN BULAT KELAS VII

The purpose of this study was to analyze the profile of students' mathematical concept understanding abilities. This research is descriptive research. The strategy used is descriptive qualitative. This research was conducted at SMP Negeri 17 Sinkawang for the 2020/2021 academic year in class VII. The source of this research data is in the form of test results. The results of this study indicate that students' understanding of mathematical concepts with indicators restating a concept, the percentage obtained is 40% and falls into the low category. In the indicator of classifying objects according to the properties according to the concept, the percentage obtained is 33% and falls into the low category. The indicator presents the concept in various forms of mathematical representation, the percentage obtained is 57% and falls into the medium category. The results of this study indicate that the ability to understand the concept of Shiva is still low, it can be seen from the indicators used 2 of them are in the low category.

Proses Transformasi Visual ke Simbolik Mahasiswa dalam Menyelesaikan Masalah Luas Daerah di Bawah Kurva

Mathematical representation is an idea interpretation form of solving mathematical problems. The process of mathematical representation is essential to pay attention to, especially in carrying out transformations between forms of representation, because it impacts the final solution obtained. This study describes the flow of students' thinking in carrying out the transformation process from visual to symbolic representation. This descriptive research was carried out with a qualitative approach. This research phase includes preparing representation tests and interview guidelines, giving tests to 48 students, conducting interviews with selected students based on the accuracy of the mathematical representations produced, and evaluation. The evaluation is carried out by reducing the results of the incorrect representation test, presenting visual and symbolic representation data and the transformation process, and concluding the transformation process. The result of the transformation process from visual to symbolic representation in solving the problem of the area under the curve is carried out with a flow of thought, namely translating the shape of the polygon area into a collection of rectangles, determining the width and length of the partition of the polygon area, and determining the area of the polygon area as a collection of rectangles. In determining the area as a collection of rectangles, there are two different processes, making a mathematical model in the form of sigma notation and addition. This study provides insight into the flow of thinking in changing between forms of mathematical representation in the hope that it can anticipate errors in solving the broad problem under the curve.

Analisis Pemahaman Konsep Matematika pada Materi Operasi Bilangan Bulat di SMP Negeri 4 Gorontalo

This research is a qualitative approach to analyze the understanding of concepts in the material of integer operations. The research was conducted at SMP Negeri 4 Gorontalo involving 25 students as the object of research. This is a descriptive study with indicators used to describe students’ understanding of mathematical concepts, among others (1) Presenting a concept in various forms of mathematical representation, (2) Restating a Concept, (3) classifying objects according to certain properties (according to the concept), (4) Applying the problem-solving concept or algorithm. Furthermore, interviews were conducted to deepen information about students’ understanding of mathematical concepts. The analysis of the results showed that students’ understanding of mathematical concepts on integer operations material was classified as moderate, which was indicated by the ability of students who only met some indicators of understanding the measured mathematical concepts.