ISLAMIC VALUES IN MATHEMATICS LEARNING THROUGH THE REALISTIC MATHEMATICS EDUCATION (RME) MODEL

Mathematics is one of the subjects that are less attractive to students who attend Islamic boarding schools. They assume that mathematics has nothing to do with Islamic values. Whereas mathematics material has a relationship with Islamic values such as the material for arithmetic sequences and series. In this case, a teacher needs to use the right learning model to deliver the subject matter, for example with the Realistic Mathematics Education (RME) model. RME is a model of mathematics learning that can connect mathematics learning objects with real life so that students can easily understand mathematics. This study aims to describe the effect of internalizing Islamic values in mathematics learning through the Realistic Mathematics Education (RME) model in arithmetic sequences and series subjects which were carried out for two meetings. The research method used is descriptive qualitative method with the research subjects are 29 students of class XI IPA MA Matsaratul Huda. Data collection techniques used teacher and student activity observation sheets, student response questionnaire sheets, documentation, and test sheets. The results of the observation data analysis of teacher and student activities can be categorized as "very good" and students also respond "positively" to learning. From the results of student learning tests can be said to be "complete" classically with the results of 89.65% 85%. Based on the results of this study, it can be said that the internalization of Islamic values in mathematics learning through Realistic Mathematics Education (RME) affects student learning activities and outcomes and helps students understand the material and can provide new knowledge about the relationship between mathematics and Islamic values. This research can be used as an alternative in providing better learning.

Antisipasi Didaktis dengan Strategi Scaffolding pada Pembelajaran Barisan dan Deret Aritmetika

This study aims to explain didactic anticipation in learning arithmetic sequences and series. The study was conducted using a didactic design study with three stages: prospective analysis, metapedadidactic, and retrospective analysis. Data were collected through tests, interviews, and documentation. Researchers compile HLT based on the analysis of learning constraints for students in learning arithmetic sequences and series. From the HLT, a didactic design was designed. The didactic design is implemented with results showing that there are three didactic events that researchers anticipate didactic with a scaffolding strategy, namely: 1) when determining the value that satisfies the number pattern, the researcher anticipates the didactic by providing directions in the form of directions to solve the given problem; 2) when determining the definition and example of arithmetic sequences, the didactic anticipation by the researcher by providing another example of the form of a number sequence makes students better understand the learning given; 3) when determining the value of the nth term and the sum of the first n terms of an arithmetic sequence and series, the didactic anticipation is given namely with their respective shirts to check their work and make direct interactions. The didactic anticipation that the researchers gave in this study was adjusted to the conditions of the environment around the classroom.

Students’ Obstacles in Learning Sequence and Series Using Onto-Semiotic Approach

Sequences and series is one of the mathematical topics that are related to everyday life. The topic is also taught at several levels of education in Indonesia. However, many students still experrienced difficulties in learning this topic. This study uses an interpretive paradigm that is part of the Didactical Design Research (DDR). This research aims to analyze students’ learning obstacles on the topic of sequence and series using the onto-semiotic approach. To do so, written test consists of five questions related to the conceptual understanding of an arithmetic sequences and series was administered to 23 students from one of the senior high schools in Kota Tangerang Selatan followed by interviews with 4 students. The results show that learning obstacles are classified into epistemological, ontogenic, and didactical obstacles. Based on the onto-semiotics approach, the students had difficulties in defining a mathematical idea on sequences and series topics. They could convert a problem into mathematical model but were confused to use a proper procedure. It can be concluded that students still experience obstacles in learning sequences and series topic. The results of this study can be used by teachers as considerations in designing learning situation on the topic of sequence and series.

How to Learning Arithmetic Sequences with Project-Based Learning in Terrace Culture?

Integrating mathematics into local culture is a way to enhance students' interest in local wisdom. The concept of mathematics is explored to find out the existence of mathematics in society's culture which has not been seen so far. The Mathematical concept is used to explore the existence of mathematics in terrace culture on the Panyaweuyan terrace of Majalengka city. This study to describe the result of exploratory project-based learning of the Panyaweuyan terrace with this kind of exploratory research. The exploring of the relationship between the terrace culture of panyaweuyan and concept mathematics, especially in the concept of arithmetic sequences is analyzed and described through literature studies, observation, and interviews with 4 informants who are local farmers. The results that there is a relationship between the arithmetic sequence concept with the local culture of Panyaweuyan Majalengka city. The results of the study stated that each mound on each step on the Panyeweuyan terraces was formed through an arithmetic sequence formula. Farmers in Panyaweuyan terraces are naturally able to make terraces according to the arithmetic sequence formula without knowing the basics of mathematics. Therefore, the concept of mathematics is part of local culture which has an important role in preserving the nation's culture.

On a Tauberian theorem of Ingham and Euler–Maclaurin summation

We discuss two theorems in analytic number theory and combinatory analysis that have seen increased use in recent years. A corollary to a Tauberian theorem of Ingham allows one to quickly prove asymptotic formulas for arithmetic sequences, so long as the corresponding generating function exhibits exponential growth of a certain form near its radius of convergence. Two common methods for proving the required analytic behavior are modular transformations and Euler–Maclaurin summation. However, these results are sometimes stated without certain technical conditions that are necessary for the complex analytic techniques that appear in Ingham’s proof. We carefully examine the precise statements and proofs of these results, and find that in practice, the technical conditions are satisfied for those cases appearing in recent applications. We also generalize the classical approach of Euler–Maclaurin summation in order to prove asymptotic expansions for series with complex values, simple poles, or multi-dimensional summation indices.

Pengaruh Model Pembelajaran Discovery Learning Menggunakan Alat Peraga Jam Baretika terhadap Pemahaman Konsep Siswa pada Materi Barisan dan Deret Aritmetika

The purpose of this study was to determine the effects of the discovery learning model using Baretic Clock teaching aids on students' understanding of the concept of arithmetic sequences and arithmetic series in class XI SMA Negeri 4 Kota Pagar Alam for the 2019/2020 academic year. The research method used in this research is the experimental method in the category of Pre-Test Post-Test Only Control Design. The population in this study were students of class XI MIPA at SMA Negeri 4 Kota Pagar Alam. Meanwhile, the samples in this study were students of class XI MIPA 4 and XI MIPA 6, respectively 34 and 33 students. Data collection using documentation and test methods. After the data is collected, the normality and homogeneity test is carried out to find out the data to be analyzed comes from data that is normally distributed and homogeneous. From the results of this analysis, the data were processed based on the conceptual understanding indicator to determine the effect of the Discovery Learning model using baretic clock teaching aids on students' conceptual understanding. So the results of the study show that there is an effect of the Discovery Learning model using baretic clock teaching aids on students' conceptual understanding of the arithmetic sequence and series material for class XI SMA Negeri 4 Kota Pagar Alam for the 2019/2020 academic year

Pengaruh Penerapan Model Pembelajaran Logan Avenue Problem Solving (LAPS-Heuristik) terhadap Kemampuan Pemecahan Masalah pada Soal Cerita Barisan dan Deret Aritmetika

The poor problem solving abilities of students is still a scourge in mathematics learning, mainly in terms of solving mathematical story problems. This is because in the case of story problems, students are required to understand the information and the questions in mathematical problems at the beginning in order to create a mathematical model which reflects the problem being solved. This study aimed to examine the achievement and improvement of students’ abilities in solving mathematical story problems about arithmetic sequences and series using LAPS-Heuristic learning model. The study method was the Intact-Group Comparison. The subjects were 43 students who were divided into two groups. The first group received conventional learning, while the other group received LAPS-Heuristic learning. The results showed that both achievement and improvement of students’ abilities in solving mathematical story problems who received LAPS-Heuristic learning model were better than in students’ abilities who received conventional learning.