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.

Neither ancient nor modern: Wallis and Barrow on the composition of continua. Part one: Mathematical styles and the composition of continua

1996 ◽  
Vol 50 (2) ◽  
pp. 165-178 ◽  
Keyword(s):  
Early Modern ◽  
Trinity College ◽  
Early Modern England ◽  
Transitional Period ◽  
Mathematical Ideas ◽  
New Methods ◽  
Mathematical Techniques ◽  
John Wallis ◽  
Geometric Mode ◽  
Regius Professor

John Wallis and Isaac Barrow were key figures in a transitional period in the development of mathematics in early modern England: their work reveals a tension between the emerging algebraic techniques and the more traditional geometric mode of thought. Both men were among the first professional mathematicians in England. Wallis studied at Cambridge, deciphered Royalist codes for Parliament during the Civil War, and was one of the secretaries to the Assembly of Divines at Westminster. He was rewarded for his support of Parliament with the Savilian Professorship of Geometry at Oxford. Barrow was also a student at Cambridge and, in 1660, was appointed Regius Professor of Greek at Trinity College. He subsequently became Professor of Geometry at Gresham College, before finally becoming the Lucasian Professor of Mathematics at Cambridge. The work of both Wallis and Barrow was at the forefront of English mathematics in the second half of the seventeenth century. But even though both enjoyed very similar educations and careers, their mathematical techniques were quite different. Wallis’s style is usually considered algebraic, while Barrow’s is considered geometric. At the same time each man’s work exhibited a similar tension between tradition and innovation - between the mathematical ideas inherited from the Greeks and the demands of the new methods and problems.

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.

scholarly journals KEMAMPUAN REPRESENTASI MATEMATIS SISWA PADA MATERI SEGITIGA

2021 ◽  
Vol 2 (1) ◽  
pp. 122
Author(s):  
Monika Sari ◽  
Edy Yusmin ◽  
Ahmad Yani T
Keyword(s):  
Qualitative Approach ◽  
Mathematical Representation ◽  
Average Score ◽  
Ability Test ◽  
Verbal Form ◽  
Mathematical Representations ◽  
Mathematical Ideas ◽  
Verbal Representation ◽  
Data Collection Technique ◽  
Essay Test

AbstractThe mathematical representation ability referred to in this study is the ability to express mathematical ideas or ideas to solve a problem with various mathematical representations of visual forms (pictures) and verbal forms (writing).This type of research is descriptive with a qualitative approach which aims to describe systematically the ability of visual mathematical representations and the ability of verbal mathematical representations.The data collection technique in this study was carried out using essay. Test questions were given to student an grade VIII A at SMP Negeri 1 Mandor, where there were three groups, namely the upper, middle, and lower group. Students who will be interviewed are selected based on the representation ability test scores where only two students will represent for each group.The results showed that the ability of visual mathematical representation when given verbal form questions to answer indicators using pictures was in the percentage of students' average score 66.67% and the ability of verbal mathematical representation if given visual questions, for the answer indicator using words is in the percentage of the student's average score of 33.33%. Students still have difficulty with verbal representation if given a visual form. Keywords: visual representation, verbal representation and trangle material

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 ANALYSIS OF STUDENTS MATHEMATICAL REPRESENTATION AND CONNECTION ON ANALYTICAL GEOMETRY SUBJECT

2016 ◽  
Vol 5 (2) ◽  
pp. 99 ◽  
Author(s):  
Muchamad Subali Noto ◽  
Wahyu Hartono ◽  
Dadan Sundawan
Keyword(s):  
Research Method ◽  
Mathematical Representation ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Analytical Geometry ◽  
Average Ability ◽  
Mathematical Ideas ◽  
The Subject ◽  
Written Word ◽  
Mathematical Connection

The importance ability of mathematical representation and connection to owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. The use of mathematical representation and the correct connection by students will help students make mathematical ideas more concrete and can connect a concept to another concept, so that students can develop a view of mathematics as a whole integration. This research aims to describe and analyze the ability of representation and mathematical connection on the topics of analytical geometry. The research method was descriptive with the subject as much as 22 mathematics students. Data collected through tests and interviews. The results show that the average ability of representation is 46.00; the average mathematical connection ability is 36.77. This means both the abilities still belongs to low, particularly for the ability of mathematical connection.

scholarly journals ANALYSIS OF STUDENTS MATHEMATICAL REPRESENTATION AND CONNECTION ON ANALYTICAL GEOMETRY SUBJECT

2016 ◽  
Vol 5 (2) ◽  
pp. 99 ◽  
Author(s):  
Muchamad Subali Noto ◽  
Wahyu Hartono ◽  
Dadan Sundawan
Keyword(s):  
Research Method ◽  
Mathematical Representation ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Analytical Geometry ◽  
Average Ability ◽  
Mathematical Ideas ◽  
The Subject ◽  
Written Word ◽  
Mathematical Connection

The importance ability of mathematical representation and connection to owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. The use of mathematical representation and the correct connection by students will help students make mathematical ideas more concrete and can connect a concept to another concept, so that students can develop a view of mathematics as a whole integration. This research aims to describe and analyze the ability of representation and mathematical connection on the topics of analytical geometry. The research method was descriptive with the subject as much as 22 mathematics students. Data collected through tests and interviews. The results show that the average ability of representation is 46.00; the average mathematical connection ability is 36.77. This means both the abilities still belongs to low, particularly for the ability of mathematical connection.

scholarly journals PENINGKATAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA KELAS IX-G SMP NEGERI 2 BANDUNG PADA MATERI PERSAMAAN KUADRAT DENGAN DISCOVERY LEARNING MODEL

2019 ◽  
Vol 19 (1) ◽  
pp. 38-46
Author(s):  
Siti Tuti Alawiyah ◽  
Jarnawi Afgani Dahlan
Keyword(s):  
Action Research ◽  
Mathematics Learning ◽  
Discovery Learning ◽  
Student Response ◽  
Mathematical Representation ◽  
Learning Models ◽  
Student Activities ◽  
Mathematical Ideas ◽  
Classroom Action Research ◽  
Learning By Using

Representative ability is the ability to express mathematical ideas that are used to show the results of his work in certain ways as a result of the interpretation of his mind. Based on the results of observations obtained data that the class on IX-G SMP 2 Bandung experienced a difficulty in presenting mathematical ideas. Difficulties experienced by students of class IX-G are a problem that must be addressed immediately because of how students can express mathematical ideas if students cannot develop representations properly. After the initial test, it turns out that the representation ability of students in class IX-G is in the low category. Based on the background of the problem found, the researcher carried out classroom action research to overcome the problems experienced by class IX-G. The objectives of this study are: (1) Knowing the increase in students' mathematical representation abilities with discovery learning models in class IX-G of SMP Negeri 2 Bandung. (2) Describing the response of students of class IX-G SMP Negeri 2 Bandung to the implementation of learning using discovery learning models. (3) Analyzing the effectiveness of the implementation of mathematics learning by using discovery learning models in improving the ability of mathematical representation. This classroom action research was conducted in 2 cycles. The subjects in this study were class IX-G, which amounted to 32 students consisting of 18 men and 14 women. Data collection was done using formative tests of mathematical representation abilities, student response questionnaires, and observation sheets of teacher and student activities. The results of this study as a whole have been successful because they have been able to improve students' representation abilities significantly and student learning outcomes are completed in a classical manner. This can be seen by the increase in the value of classical absorption ability of students' mathematical representation abilities from cycle I to cycle II. The absorption ability of students' mathematical representation in the first cycle was 31.25%, in the second cycle it increased to 87.50%. In addition, students' responses to learning are in good criteria. The effectiveness of implementing mathematics learning by using discovery learning models in improving the ability of mathematical representation is good.

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