scholarly journals PEMAHAMAN KONSEP MATEMATIS DAN REPRESENTASI DALAM PENGAJARAN MATEMATIKA

JURNAL CURERE ◽  
2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Novi Tari Simbolon
Keyword(s):  
Mathematical Problem ◽  
Internal Representation ◽  
External Representation ◽  
Mathematical Representation ◽  
Algebraic Form ◽  
Mathematical Ideas ◽  
Concrete Objects ◽  
Standard Component ◽  
Principles And Standards ◽  
Two Stages

The inclusion of representation as a standard component of the process in Principles and Standards for School Mathematics in addition to problem solving, reasoning, communication, and connection skills is reasonable because to think mathematics and communicate mathematical ideas one needs to represent it in various forms of mathematical representation. Besides, it can not be denied that objects in mathematics are all abstract so that to learn and understand abstract ideas that would require a representation. Representation occurs through two stages, namely internal representation and external representation. Examples of external representations include: verbal, drawing and concrete objects. Thinking of a mathematical idea that allows a person's mind to work on the basis of the idea is an internal representation. A mathematical problem posed to the student and the student can solve it, so at least the student understands the problem, so that students can plan the settlement, perform the calculations appropriately, and be able to check or review what has been processed correctly. The smoothness and flexibility of students in constructing representations is largely lacking. This is evident from at least the structured algebraic form, as well as the way in which most representations are found very little. In addition, the quantitative scores of respondents in the representation are still in the low category with a moderate tendency.

scholarly journals Analisis kemampuan represenasi matematis siswa MAN II Kota Batu pada materi deret geometri

AKSIOMA ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 195-208
Author(s):  
Mohammad Archi Maulyda ◽  
Ratna Yulis Tyaningsih ◽  
Baidowi Baidowi
Keyword(s):  
Qualitative Research ◽  
Internal Representation ◽  
External Representation ◽  
Mathematical Representation ◽  
Key Factors ◽  
Learning Mathematics ◽  
Descriptive Approach ◽  
Geometrical Series

The representation ability possessed by students is one of the key factors in learning mathematics in schools. Because it needs a study to understand how the ability of representation of students when given a problem. The purpose of this study is to describe the mathematical representation ability of students in class XI IPA MAN II Batu on geometrical series material. For this reason, the research conducted is a qualitative research with a descriptive approach so that researchers can describe how the students' representational abilities. Students are grouped in the ability category of high (KT), moderate (KS), and low (KR). The results of this study are KT, KS, and KR have not met the indicators of the ability of representation that has been determined. The non-fulfillment of these indicators is due to a mismatch between external representation and internal representation.

scholarly journals Representasi Matematis Siswa Tuna Rungu dalam Menyelesaikan Soal Cerita Matematika

2019 ◽  
Vol 4 (7) ◽  
pp. 971
Author(s):  
Elis Dwi Wulandari ◽  
Erry Hidayanto ◽  
Rustanto Rahardi
Keyword(s):  
External Representation ◽  
Mathematical Representation ◽  
Story Problems ◽  
Deaf Students ◽  
Student Work ◽  
Mathematical Ideas ◽  
Verbal Representation ◽  
Mathematical Expressions ◽  
Mathematical Symbols ◽  
Real Objects

<p><strong>Abstract:</strong> Mathematical representation is the way of communicating mathematical ideas and problems solutions. Communicating mathematical ideas requires external representation in the form of actions, verbal, symbolic, visual and real objects. This study aims to describe the form of representation of Deaf Students in solving mathematical story problems. The research was conducted by giving types of text questions as well as text and image questions to three DS at Banyuwangi State of Special Need High School. The results of student work analysis found that there are two types of mathematical representations that appear in solving story problems, namely verbal representation indicated by writing words, numbers, letters, sentences and oral and representation of mathematical expressions in the form of symbols and numbers. DS are able to representing, make mathematical symbols, explain in writing or sign language what they think are.</p><strong>Abstrak:</strong><em> </em>Representasi matematis adalah cara mengomunikasikan ide-ide matematis maupun solusi permasalahan. Mengomunikasikan ide-ide matematis diperlukan representasi eksternal berbentuk tindakan, verbal, simbolik, visual dan objek nyata. Studi ini bertujuan untuk mendeskripsikan bentuk representasi siswa Tuna Rungu dalam menyelesaikan soal cerita matematika. Penelitian dilakukan dengan memberikan jenis soal teks serta soal teks dan gambar kepada tiga siswa TR di SMALBN Banyuwangi. Hasil analisis pekerjaan siswa ditemukan terdapat dua tipe bentuk representasi matematis yang muncul dalam menyelesaikan soal cerita, yaitu representasi verbal yang ditunjukkan dengan tulisan kata, angka, huruf, kalimat serta lisan dan representasi ekspresi matematis berupa simbol dan angka. Siswa TR mampu merepresentasikan, membuat simbol matematis, menjelaskan dengan tulisan maupun bahasa isyarat apa yang mereka pikirkan.

scholarly journals ANALISIS KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL PEMECAHAN MASALAH MATEMATIKA

Ta dib ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 19
Author(s):  
Ummul Huda ◽  
Edwin Musdi ◽  
Nola Nari
Keyword(s):  
Problem Solving ◽  
Quantitative Data ◽  
Qualitative Data ◽  
Mathematical Problem ◽  
Field Research ◽  
Mathematical Representation ◽  
Mathematical Problem Solving ◽  
Test Results ◽  
Interview Guide ◽  
Descriptive Method

This research is motivated by the low mathematical representation ability of students in solving mathematical problem solving questions based on TIMSS data and facts in the field. The study aims to analyze the mathematical representation ability of MTsN Batusangkar students visually, verbally and symbolically in solving mathematical problem solving problems. This field research uses descriptive method. The instrument used is a description question and interview guide. Quantitative data based on test results were analyzed to determine the predicate of mathematical representation ability, while Miles and Huberman model wwas used to analyze qualitative data from interviews. The results show that students' mathematical visual and symbolic abilities are satisfactory, while verbal mathematical representations are less satisfactory.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

Activites for Students: Dynamic Diagrams

2001 ◽  
Vol 94 (7) ◽  
pp. 566-574
Author(s):  
Elizabeth George Bremigan
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Visual Representations ◽  
Mathematical Concept ◽  
Mathematics Textbooks ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematical Problems

Reasoning with visual representations is an important component in solving many mathematical problems and in understanding many mathematical concepts and procedures. Students at all levels of mathematics frequently encounter visual representations—for example, diagrams, figures, and graphs—in discussions of mathematical ideas, in mathematics textbooks, and on tests. Teachers often use visual representations in the classroom when they present a mathematical problem, explain a problem's solution, or illustrate a mathematical concept. Although they frequently encounter and use visual representations in the mathematics classroom, neither teachers nor students may explicitly recognize the power of reasoning with visual representations or the potential for misconceptions that can arise from their use.

Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections

2002 ◽  
Vol 7 (9) ◽  
pp. 484-488
Author(s):  
Christine Thomas ◽  
Carmelita Santiago
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Natural Inclination ◽  
Points Of View ◽  
Principles And Standards

Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

scholarly journals Fragmentation of the Thinking Structure of Translation in Solving Mathematical Modelling Problems

2019 ◽  
Vol 9 (1) ◽  
pp. 25-36
Author(s):  
Kadek Adi Wibawa
Keyword(s):  
Mathematical Modeling ◽  
Graphical Representation ◽  
Mathematical Problem ◽  
Structured Interview ◽  
Mathematical Problem Solving ◽  
Algebraic Form ◽  
Verbal Representation ◽  
Initial Representation ◽  
The Brain ◽  
Modelling Problems

Fragmentation of the thinking structure is the process of construction of information in the brain that is inefficient, incomplete, and not interconnected, and hinders the process of mathematical problem solving. In solving mathematical modeling problems, students need to do translation thinking which is useful for changing the initial representation (source representation) into a new representation (target representation). This study aims to discover how the occurrence of the fragmentation of the thinking structure of translation within students in their solving of mathematical modeling problems. The method used is descriptive qualitative with the instrument in the form of one question for the mathematical modeling of necklace pendants and semi-structured interview sheets. The results showed that there were three errors that occurred in solving mathematical modeling problems. First, the error in changing a verbal representation to a graph. Secondly, errors in changing a graphical representation to symbols (algebraic form). Thirdly, errors in changing graphical representation and symbols into mathematical models. The three errors that occur are described based on the four categories of Bosse frameworks (Bosse, et al., 2014), namely: (1) unpacking the source (UtS), (2) preliminary coordination (PC), (3) constructing the target (CtT), and (4) determining equivalence (DE). In this study, there were 3 subjects who experienced fragmentation of the thinking structure in solving mathematical modeling problems. One of the highlights is the fragmentation of the structure of translation thinking often starts from the process of unpacking of the source due to the incompleteness of considering all the available source details.

scholarly journals Analysis of Mathematical Representation Ability Based on Level of Reading Interest in Geometry Course

2021 ◽  
Vol 5 (2) ◽  
pp. 271
Author(s):  
Destia Wahyu Hidayati ◽  
Arie Wahyuni
Keyword(s):  
Data Analysis ◽  
Reading Level ◽  
Mathematical Representation ◽  
Research Subjects ◽  
Reading Levels ◽  
Ability Test ◽  
Mathematical Representations ◽  
Mathematical Ideas ◽  
Literacy Activities ◽  
Reading Interest

Reading literacy activities are currently being held by all levels of education. Literacy activities have a positive effect on students in understanding information. The ability to understand information can be realized through mathematical representation, which is one of the main elements in mathematical understanding. This research can help educators in mapping the mathematical representation ability based on the reading interest of students. The purpose of this research is to identify which indicators can be mastered by students who have reading interests at high, medium, and low levels. This research is qualitative. The research subjects were students of the Mathematics Education Department of Ivet University. The data collection procedures used were scale, test, and interview. The instruments of this study were the reading interest scale, mathematical representation ability test, and interview sheets. The data analysis technique of this study adopted data analysis techniques from Miles and Huberman. The conclusions of this study are (1) students with high and medium reading levels have the ability to represent mathematical representations to model and interpret physical, social, and mathematical phenomena; have the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts; have the ability of mathematical representations in selecting, applying, and translating mathematical representations to solve problems, (2) students with a low reading level have lacked on the ability of mathematical representations to use representations to model and interpret physical, social, and mathematical phenomena, thus it caused them couldn’t mastering the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts and the ability of mathematical representations to select, apply, and translate mathematical representations to solve problems. Keywords: mathematical representation ability, reading interest, geometry.

scholarly journals Kemampuan Representasi Matematis Siswa Kelas VIII SMP Ditinjau dari Gaya Kognitif Visualizer dan Verbalizer

2019 ◽  
Vol 6 (2) ◽  
pp. 98-111
Author(s):  
Fergi Faranijza Fatri ◽  
Maison Maison ◽  
Syaiful Syaiful
Keyword(s):  
High School ◽  
Junior High School ◽  
Qualitative Method ◽  
Mathematical Representation ◽  
Problem Analysis ◽  
Mathematics Students ◽  
Ability Test ◽  
Image Information ◽  
Mathematical Ideas ◽  
Mathematical Problems

Mathematical representation skill is students' ability to express mathematical ideas (such as problems, statements, and definitions) in various ways to solve problems through multiple representations, such as images, words, tables, and symbols mathematics. Students are struggling in representing mathematical ideas. It hampers them in determining the solution of mathematical problems. They are careless in reading the word problems, lacking problem analysis, less thorough, and struggling to connect concepts. The subjects of this study were in two students from one of the junior high school in Jambi. The instruments used for this research were VVQ, Mathematical Representation Ability Test and interviews. This study used a descriptive qualitative method. The results showed that the representation abilities of students with visualizer and verbalizer style were quite good. However, each subject had a different way of solving problems. Visualizers were more interested in questions with image information in solving the problem. Verbalizer tended to prefer information with detailed wording.

Fundamental Ideas

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Variational Principles ◽  
Radioactive Decay ◽  
Geometrical Optics ◽  
Mathematical Representation ◽  
Mathematical Ideas ◽  
Partial Differentiation ◽  
Reflection And Refraction ◽  
Mathematical Techniques ◽  
Fundamental Equations

Chapter 1 offers a simple introduction to the use of variational principles in physics. This approach to physics plays a key role in the book. The chapter starts with a look at how we might minimize a journey by car, even if this means taking a longer route. Soap films are also discussed. It then turns to geometrical optics and uses Fermat’s principle to explain the reflection and refraction of light. There follows a discussion of the significance of variational principles throughout physics. The chapter also covers some introductory mathematical ideas and techniques that will be used in later chapters. These include the mathematical representation of space and time and the use of vectors; partial differentiation, which is necessary to express all the fundamental equations of physics; and Gaussian integrals, which arise in many physical contexts. These mathematical techniques are illustrated by their application to waves and radioactive decay.

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