Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

Procedural fluency and conceptual understanding are two aspects of mathematical proficiency discussed worldwide, including in Indonesia. In the algebra domain, algebraic proficiency concerns an ability to deal with symbolic representations that can be viewed from a symbol sense perspective. This algebraic proficiency is considered indispensable for prospective mathematics teachers for their future careers. This research aims to analyze prospective mathematics teachers’ algebraic proficiency from the perspective of symbol sense. To achieve this aim, we set up a qualitative case study, involving 19 Indonesian mathematics education students (21-23 years old) as prospective mathematics teachers, in the form of a two-week online teaching and learning process (4 x 50 minutes) and its corresponding formative assessment for solving quadratic, cubic, and rational inequalities. The results revealed that the majority of the participants lack algebraic proficiency as they use procedural strategies more than symbol sense strategies to solve inequalities

Realistic Mathematics Education Principles for Designing a Learning Sequence on Number Patterns

The number pattern is one of mathematics topics taught for junior high school students that relate between arithmetic and algebra domain. This topic bridges arithmetical and algebraic thinking. Therefore, the learning for this topic should be designed meaningfully. This research aims to design a learning sequence on the number patterns using principles of Realistic Mathematics Education (RME). To do this, we used design research method, particularly the preliminary design phase, with the following three steps. First, literature study was conducted to collect student difficulties in the learning of number patterns, relevant studies, and the theory of RME. Second, we observed Indonesian mathematics textbooks addressing the number patterns to see a learning sequence for this topic. Finally, we designed a learning sequence for the number patterns using the RME principles, particularly the reality principle, level principle, and intertwinement principle. The result of this research includes the learning sequence for the number patterns according to the RME principles, which consists of three activities: relationship between patterns and numbers; exploration of numbers; and generalization of number patterns. We conclude that the three principles of RME are fruitful for designing a meaningful learning sequence for the topic of number patterns

An investigation of students algebraic proficiency from a structure sense perspective

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for advanced study or professional work. This study, therefore, aims to investigate students algebraic proficiency in terms of structure sense. To reach this aim, we set up a qualitative case study with the following three steps. First, after conducting a literature study, we designed structure sense tasks according to structure sense characteristics for the topic of equations. Second, we administered an individual written test involving 28 grade XI students (16-17 year-old). Third, we analyzed students written work using a structure sense perspective. The results showed that about two-Thirds of the participated students lack of structure sense in which they tend to use more procedural strategies than structure sense strategies in solving equations. We conclude that the perspective of structure sense provides a fruitful lens for assessing students algebraic proficiency

AN INVESTIGATION OF STUDENTS’ ALGEBRAIC PROFICIENCY FROM A STRUCTURE SENSE PERSPECTIVE

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for advanced study or professional work. This study, therefore, aims to investigate students’ algebraic proficiency in terms of structure sense. To reach this aim, we set up a qualitative case study with the following three steps. First, after conducting a literature study, we designed structure sense tasks according to structure sense characteristics for the topic of equations. Second, we administered an individual written test involving 28 grade XI students (16-17 year-old). Third, we analyzed students’ written work using a structure sense perspective. The results showed that about two-thirds of the participated students lack of structure sense in which they tend to use more procedural strategies than structure sense strategies in solving equations. We conclude that the perspective of structure sense provides a fruitful lens for assessing students’ algebraic proficiency

The development of mathematics teacher professional competencies through social media

One of the competencies for mathematics teachers that needs to be developed continuously is professional competence. However, even if efforts for developing teachers’ competencies have been made formally by the government, it seems still lacking. This study, therefore, aims to develop mathematics teacher professional competencies through an informal development model using social media. This research used a qualitative method, a case study design, involving 19 mathematics teachers from various regions in Indonesia in the informal development process in the range of 2019-2021. The informal approach was carried out using question-and-answer techniques and guided discussions on mathematical problems. From the teacher development processes, 30 mathematics problems and their solutions were collected. As an illustration of this development process, this article presents five problems and their solutions, including solutions for two mathematics problems on conceptual understanding and three mathematics problems on problem-solving. We conclude that this informal approach is fruitful in helping mathematics teachers solve mathematics problems. This study implies that the teacher development process carried out in this study can be used as a model for informal teacher development by other higher education academics in their respective places

PENGARUH MODEL EXPERIENTIAL LEARNING TERHADAP PENINGKATAN KEMAMPUAN PEMAHAMAN MATEMATIS SISWA SMA (Penelitian Kuasi Eksperimen terhadap Kelas X di Salah Satu SMA Negeri di Cimahi)

Penelitian ini bertujuan untuk mengetahui peningkatan kemampuan pemahaman matematis antara siswa SMA yang memperoleh pembelajaran experiential learning dengan yang memperoleh pembelajaran konvensional. Penelitian ini termasuk kedalam jenis penelitian kuasi eksperimen dengan menggunakan Desain Kelompok Kontrol Non-Ekivalen (The Non-Equivalent Control Group Design). Populasi penelitian adalah seluruh siswa kelas X di salah satu SMA negeri di Cimahi dengan sampel penelitian adalah dua kelas yang dipilih oleh pihak sekolah dimana satu kelas sebagai kelas eksperimen dan satunya lagi sebagai kelas kontrol. Instrumen penelitian terdiri dari tes pemahaman matematis, jurnal harian, dan lembar observasi. Kesimpulan dari penelitian ini adalah kemampuan pemahaman matematis siswa SMA yang memperoleh pembelajaran experiential learning tidak lebih tinggi daripada yang memperoleh pembelajaran konvensional yang diduga karena kurangnya pengalaman dalam menampilkan perilaku kognitif guru yang luwes sebagai karakteristik kepribadian guru yang dapat memotivasi siswa dalam belajar, kurang menghayati setiap tahapan dalam model experiential learning sehingga belum dapat mengimplementasikan model pembelajaran tersebut dengan baik, dan terdapat variabel luar yang tidak terkontrol selama penelitian.Kata Kunci: model experiential learning, kemampuan pemahaman matematis

E-Cordial Labeling for Cupola Graph Cu(3, b, n)

Graph labeling is a map that maps graph elements such as vertices, edges, vertices, and edges to a set of numbers. A graph labeling is named e-cordial if there is a binary mapping f:E(G)→{0,1} which induces the vertex labeling defined by g(v)=Ʃ_{uvϵE(G)}f(uv)(mod 2), so that it satisfies the absolute value of the difference between the number of vertices labeled 1 and the number of vertices labeled 0 is less than equal to 1, and also for the number of edges labeled 0 and labeled 1. A graph that admits the e-cordial labeling is called an e-cordial graph. In this paper, we proved that some of the cupola graph Cu(3,b,n) is e-cordial. Keywords: E-Cordial Labeling; E-Cordial Graph; Cupola Graph Cu(a, b, n).   Abstrak Pelabelan graf merupakan pemetaan yang memetakan unsur-unsur graf seperti simpul, sisi, simpul dan sisi ke himpunan bilangan. Sebuah pelabelan dinamakan pelabelan e-cordial jika terdapat pemetaan biner f:E(G)→{0,1} yang menginduksi pelabelan simpul yang didefinisikan g(v)=Ʃ_{uvϵE(G)}f(uv)(mod 2) sehingga nilai mutlak dari selisih banyaknya simpul yang dilabeli 1 dan banyaknya simpul yang dilabeli 0 kurang dari sama dengan 1, dan nilai mutlak dari selisih banyaknya sisi yang dilabeli 1 dan banyaknya sisi yang dilabeli 0 kurang dari sama dengan 1. Sebuah graf yang dapat dilabeli secara e-cordial dinamakan graf e-cordial. Pada makalah ini dibuktikan bahwa beberapa graf kubah Cu(3,b,n) adalah e-cordial. Kata Kunci : Pelabelan E-Cordial; Graf E-Cordial; Graf Kubah Cu(a, b, n)

Peran Representasi Matematis dalam Pembelajaran Perkalian Bentuk Aljabar melalui Pendekatan Matematika Realistik

Algebra is an abstract topic in mathematics that should initially be learned by students in junior high school level. In order that this topic is easier to understand by students meaningfully, relevant mathematical representations should be used in the learning process. This research aims to analyze the role of mathematical representations in the learning of multiplication of algebraic expressions through the use of realistic mathematics education approach. To do so, we used a qualitative research method, in the form of the learning and teaching process involving 23 grade VII students (12-13-year-old) from one of the schools in Bandung. We analyzed video data of the learning process and the student written work from a formative test. The results showed that visual representations are frequently used by students at the beginning of the learning process and symbolic representations are used after the students get used to using visual representations. The result of the formative test indicated that the use of mathematical representations meaningfully could help students in solving multiplication of algebraic expressions problems. We conclude that the use of mathematical representations—in particular of visual representations using geometry context in algebra learning—helps students to understand the topic of multiplication of algebraic expressions

Convergence Numerically of Trinomial Model in European Option Pricing

A European option is a financial contract which gives its holder a right (but not an obligation) to buy or sell an underlying asset from writer at the time of expiry for a pre-determined price. The continuous European options pricing model is given by the Black-Scholes. The discrete model can be priced using the lattice models ih here we use trinomial model. We define the error simply as the difference between the trinomial approximation and the value computed by the Black-Scholes formula. An interesting characteristic about error is how to realize convergence of trinomial model option pricing to Black-Scholes option pricing. In this case we observe the convergence of Boyle trinomial model and trinomial model that built with Cox Ross Rubenstein theory

Peran Representasi Matematis dalam Pembelajaran Perkalian Bentuk Aljabar melalui Pendekatan Matematika Realistik

Algebra is an abstract topic in mathematics that should initially be learned by students in junior high school level. In order that this topic is easier to understand by students meaningfully, relevant mathematical representations should be used in the learning process. This research aims to analyze the role of mathematical representations in the learning of multiplication of algebraic expressions through the use of realistic mathematics education approach. To do so, we used a qualitative research method, in the form of the learning and teaching process involving 23 grade VII students (12-13-year-old) from one of the schools in Bandung. We analyzed video data of the learning process and the student written work from a formative test. The results showed that visual representations are frequently used by students at the beginning of the learning process and symbolic representations are used after the students get used to using visual representations. The result of the formative test indicated that the use of mathematical representations meaningfully could help students in solving multiplication of algebraic expressions problems. We conclude that the use of mathematical representations—in particular of visual representations using geometry context in algebra learning—helps students to understand the topic of multiplication of algebraic expressions