Symbolic representation is a form of one's ideas interpretation to ease the problem-solving. The representation of symbols is an important thing in mathematical learning because it reflects the ...definition of a concept. Symbolic representation involves metonymy as the symbol scheme and metaphor as the denotation of the symbol. Metonymy and metaphor are related to each other and are involved in a symbolization system to discover new symbols in mathematics. The Civil Engineering students have to deal with a number of new symbols in Calculus II, such as the symbol of a function of two or more variables and its derivative. This symbol, needless to say, is nothing like the symbol of a function of one variable and its derivative which the students had learned in Calculus I offered in the previous semester. This study aimed to describe the ability of the Civil Engineering students to represent symbols as metonymy and metaphor through partial derivative problem-solving. This study was designed as a case study to detect the difficulties faced by the students in solving partial derivative problems. The students were provided with a worksheet containing partial derivative problems which focused on symbolic representation as metonymy and metaphor. The students' answers were analyzed based on how they denoted the partial derivative, both from the notation and the definition of the notation. Interview and observation were conducted to support worksheet findings. The results showed that the students had a poor ability in representing the partial derivative symbol of f with respect to x and y. The students' analogy was that the derivative symbol can be expressed with the d and prime notations such as in the derivative of functions of one variable. Therefore, this symbol was used in the partial derivative. The students were able to provide a correct solution to the partial derivative problems, but less careful in determining the partial derivative symbol. The error in using the partial derivative symbol was not noticed by the students because they focused more on the problem-solving procedure rather than the symbolization.
One of the purposes of learning mathematics in college is to improve the ability of critical thinking and problem-solving. Before solving the problems, the college students need to recognize the ...problems not excepted the mathematics symbols written in the problem. Thereover it is important for the problem solver to aware and recognizes the meaning of mathematics symbols, called recognition of mathematical symbols. This educational design research aims to describe the development of learning activities using a worksheet to recognize the mathematical symbol. The design research phase consists of four successive phases: knowledge, designing, experimenting and analyzing. Findings reveal that: College students can distinguish between the form of functions and the value of functions; College students transform ∂f(x,y)∂y to fy(x, y) when solving problems; College students can read ∂2z∂2x symbol but need more time to interpret that symbol rather than fxx(x, y) symbol. At the end of the learning practice, college students that doing error to recognize mathematics symbols are less than at the first teaching practice. The college students can recognize mathematical symbols well and then solve the problem correctly using correct mathematics symbols.
Mathematical representation is one of the mathematical recognition’s form. This study aimed to compare the ability of students' mathematical symbol recognition between learning using Student Activity ...Sheets characterized by mathematical representation and learning using group presentation assignment activities. The research method employed Posttest-Only Control Group Design, between the control class and the experimental class. The control class is a class with group presentation learning assignments while the experimental class is a class with learning that uses MFIs characterized by mathematical representations. The data were obtained by providing tests to measure students' mathematical recognition abilities. The data were analyzed by using the t-test. The results of calculations with the help of SPSS showed that data from both classes are normally distributed and homogeneous. The results of data analysis conducted by t-test showed sig. ≥0.05 so H1 is rejected and H0 is accepted which means that there was no difference in the ability to recognize mathematical symbols between the control class and the experimental class. There was no difference in recognition abilities between the control class and the experimental class because learning activities in both classes are student-centered learning.
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.
Almost all students understand the limit of a function only up to an intuitive definition and have difficulty understanding the concept of a limit function formally. This study aims to describe the ...growth of student understanding of functions limit concept in solving controversial problems based on Pirie Kieren's theory. There were twelve Calculus class students in the short semester as participants. The students selected were those who had taken calculus courses. Students are given the task of solving controversial problems to understand the concept of limit functions. There was only one student who showed a growing understanding of the concept of the limit of a function and was interviewed for further exploration. This research is a qualitative descriptive research. Therefore, the researchers analyzed the results of students' work through data reduction, data presentation, and conclusion drawing. The result shows that through controversial problems, students' understanding grows to an inventising level. However, students did ‘fold back’ at the observing level. At this level, students look at or re-read their notebooks to recall previously owned concepts. For further research it is suggested that researchers can design a learning process that can help grow student understanding through controversial problems.
Representasi simbol melibatkan metonymy dan metaphor. Metonymy sebagai rantai penanda, dalam hal ini simbol, sedangkan metaphor sebagai pemaknaan dari penanda (simbol). Metonymy dan metaphor saling ...terkait dan terlibat dalam sistem penyimbolan saat seseorang menemukan simbol baru dalam proses pembelajaran matematika. Mahasiswa Teknik Sipil banyak menemukan simbol baru dalam perkuliahan Kalkulus II, seperti simbol fungsi dua variabel atau lebih beserta turunannya. Simbol-simbol tersebut tentunya berbeda dengan simbol fungsi satu variabel dan turunannya yang telah dipelajari pada Kalkulus I semester sebelumnya. Penelitian ini bertujuan untuk mendeskripsikan kemampuan mahasiswa Teknik Sipil dalam merepresentasikan simbol sebagai metonymy dan metaphor melalui penyelesaian masalah Turunan Parsial. Penelitian ini merupakan penelitian studi kasus, sebagai salah satu upaya untuk mendeteksi kesulitan mahasiswa dalam belajar Turunan Parsial. Mahasiswa diberi worksheet berisi masalah Turunan Parsial yang difokuskan pada representasi simbol sebagai metonymy dan metaphor. Hasil penyelesaian masalah pada worksheet dianalisis berdasarkan representasi simbol turunan parsial baik dari notasinya maupun makna dari notasi. Hasil yang diperoleh adalah bahwa mahasiswa Teknik Sipil kurang mampu dalam merepresentasikan simbol turunan parsial fungsi f terhadap x maupun y. Mahasiswa mampu menentukan selesaian akhir turunan parsial dengan benar, namun kurang baik dalam penandaan simbol turunan parsial.
The purposes of this research are to analyze the digital literacy of students in using the GUI Matlab learning media and understanding the concept of set in junior high school students through ...digital literacy using the GUI Matlab. To answer these problems using a qualitative approach. The subjects of this study were five students of class VII tutoring. The research instruments used in this study were a test, an interview, and a questionnaire. Data are analyzed by reducing data, presenting narrative data, and concluding results. The results of this study show that the digital literacy of students in using GUI Matlab learning media is excellent. Besides, 80% of students can determine the members of the set correctly, 80% of students can determine the empty set correctly, 100% students can draw Venn diagrams correctly, determine the set of complements correctly, and determine the subset.
Representasi matematis diperlukan dalam menyelesaikan masalah realistik, yakni sebagai mediator penyelesaian permasalahan sehari-hari. Translasi representasi dari suatu permasalahan realistik menjadi ...model matematis diperlukan sebagai pemahaman terhadap permasalahan yang diberikan untuk ditentukan solusi permasalahannya. Penelitian ini bertujuan untuk mendeskripsikan proses translasi permasalahan realistik menjadi representasi matematis pada Mahasiswa Teknik Informatika. Penugasan penyelesaian masalah realistik dan tanya jawab pada perkuliahan Aljabar Linear dan Matriks digunakan untuk memperoleh deskripsi proses translasi. Data dianalisis berdasarkan tahapan translasi representasi matematis yaitu mengeksplorasi sumber, menyusun pengetahuan awal, membangun target representasi, dan menentukan kesesuaian hasil representasi dengan sumber. Hasilnya adalah mahasiswa mengeksplorasi sumber dengan membaca informasi sumber, selanjutnya menguraikan informasi sumber dengan bahasa alami, membuat kode berdasarkan informasi sumber dan mengaitkannya dengan konsep matematika, mengaitkan konsep matematika dari representasi sumber ke representasi target, serta mengevaluasi representasi target. Temuan-temuan ini dapat digunakan dosen sebagai dasar mendesain pembelajaran pada mahasiswa non-program studi matematika guna mengurangi peluang kesalahan dalam menyelesaikan masalah realistik. Kata kunci: Masalah realistik; representasi matematis; translasi. Mathematical representation is needed in solving realistic problems, namely as a mediator in solving realistic problems. Mathematical representation translation of a realistic problem into a mathematical model that is needed as an understanding of the given problem to determine the problem solution. This study aims to describe the process of translation of realistic problems into mathematical representations for Informatics Engineering Students. Realistic problem solving assignments and interviews in Linear Algebra and Matrix lecture is used to obtain a description of the translation process. Data were analyzed based on the stages of translation of mathematical representations, namely unpacking the source, preliminary coordination, constructing the target, and determining equivalence. The result is that students unpacking the source by reading source information, then describe source information in natural language, code based on source information and relate it to mathematical concepts, link mathematical concepts from source representation to target representation, and evaluate target representations. These findings can be used by lecturers as a basis for designing learning for students non-departement of Mathematics in order to reduce the chance of errors in solving realistic problems. Keywords: Mathematical representation; realistic problem; translation
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