Anwar Mutaqin
Universitas Sultan Ageng Tirtayasa, Serang

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EQUIVALENCE OF n-NORMS ON THE SPACE OF p-SUMMABLE SEQUENCES Mutaqin, Anwar; Gunawan, Hendra
Journal of the Indonesian Mathematical Society Volume 16 Number 1 (April 2010)
Publisher : IndoMS

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Abstract

We study the relation between two known n-norms on lp, the space ofp-summable sequences. One n-norm is derived from GÄahlers formula (1969), whilethe other is due to Gunawan (2001). We show in particular that the convergence inone n-norm implies that in the other. The key is to show that the convergence ineach of these n-norms is equivalent to that in the usual norm on lp.DOI : http://dx.doi.org/10.22342/jims.16.1.27.1-7
Understanding on Strategies of Teaching Mathematical Proof for Undergraduate Students Syamsuri, Syamsuri; Marethi, Indiana; Mutaqin, Anwar
Jurnal Cakrawala Pendidikan CAKRAWALA PENDIDIKAN EDISI JUNI 2018, TH.XXXVII, NO.2
Publisher : LPPMP Universitas Negeri Yogyakarta

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Abstract: Many researches revealed that many students have difficulties in constructing proofs. Based on our empirical data, we develop a quadrant model to describe students’ classification of proof result. The quadrant model classifies a students’ proof construction based on the result of mathematical thinking. The aim of this article is to describe a students’ comprehension of proof based on the quadrant model in order to give appropriate suggested learning. The research is an explorative research and was conducted on 26 students majored in mathematics education in public university in Banten province, Indonesia. The main instrument in explorative research was researcher itself. The support instruments are proving-task and interview guides. These instruments were validated from two lecturers in order to guarantee the quality of instruments.Based on the results, some appropriate learning activities should be designed to support the students’ characteristics from each quadrant, i.e: a hermeneutics approach, using the two-column form method, learning using worked-example, or using structural method.Keywords:proof, proving learning, undergraduate, quadrant model Memahami Strategi Pengajaran Pembuktian Matematis di Perguruan TinggiAbstrak: Banyakpeneliti pendidikan matematika menyatakan bahwa siswa mengalami kesulitan dalam mengonstruksi bukti. Berdasarkan kajian empiris, penulis membangun suatu model kuadran untuk mendeskripsikan kategori konstruksi bukti yang dibangun siswa. Model kuadran tersebut mengklasifikasikan konstruksi bukti berdasarkan cara berpikir matematis saiwa. Adapun tujuan dari artikel ini ialah mendeskripsikan pemahaman siswa dalam mengonstruksi bukti berdasarkan model kuadran serta memberikan saran strategi pembelajarannya. Penelitian ini merupakan penelitian eksploratif yang melibatkan 26 mahasiswa Jurusan Pendidikan Matematika pada universitas negeri di Provinsi Banten. Instrumen utama dalam penelitian eksploratif adalah peneliti sendiri. Instrumen pendukungnya ialah tugas pembuktian matematis dan panduan wawancara. Kedua instrumen pendukung tersebut telah divalidasi untuk menjamin kualitas instrumen yang digunakan. Hasil penelitian ini memberikan saran terkait aktivitas pembelajaran yang seharusnya dilakukan oleh pengajar agar sesuai dengan karakteristik berpikir siswa dalam mengonstruksi bukti pada masing-masing kuadran, misalnya : pendekatan heurmenistik, menggunakan metode dua-kolom, pembelajaran worked-example ataupun menggunakan metode terstruktur.Kata Kunci: bukti, pengajaran bukti, mahasiswa, model kuadran
MODEL BLENDED LEARNING DI PROGRAM STUDI PENDIDIKAN MATEMATIKA UNTIRTA Mutaqin, Anwar; Marethi, Indiana; Syamsuri, Syamsuri
Jurnal Cakrawala Pendidikan CAKRAWALA PENDIDIKAN EDISI FEBRUARI 2016, TH. XXXV, NO. 1
Publisher : LPPMP Universitas Negeri Yogyakarta

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Abstrak: Penelitian ini bertujuan meningkatkan pengetahuan bidang studi (content knowledge) sebagai unsur pembentuk kompetensi mahasiswa calon guru matematika dengan pembelajaran blended learning. Pengetahuan bidang studi dalam hal ini disebut hasil belajar. Desain penelitian menggunakan kuasi eksperimen karena akan membandingkan pengaruh suatu perlakuan. Teknik pengumpulan data dilakukan dengan tes. Untuk uji persyaratan normalitas, digunakan uji Kolmogorov-Smirnov, sedangkan uji homogenitas digunakan uji Levene. Untuk mengetahui perbedaan rerata, digunakan uji-t jika data berdistribusi normal. Sementara, jika data tidak berdistribusi normal digunakan uji Mann-Whitney. Hasil tes akhir pembelajaran dibandingkan untuk mengetahui pengaruh blended learning terhadap hasil belajar. Hasil pengolahan data menunjukkan bahwa hasil belajar kelas blended learning lebih baik daripada kelas biasa. Selain itu, mahasiswa blended learning lebih aktif mengerjakan tugas daripada kelas biasa. Kata Kunci: blended learning, calon guru matematika, content knowledge A BLENDED LEARNING MODEL IN THE MATHEMATICS EDUCATION STUDY PROGRAM IN UNTIRTA Abstract:This study was aimed to improve the content knowledge as an element for developing students? competence through blended learning. In this study, this content knowledge is called learning achievement. The study used the experimental design. The data were collected using a test. To test the normality of data distribution, the Kolmogorov-Smirnov test was utilized, while to test the homogeneity of the variances, the Levene?s test was used. To test the hypothesis, the t-test was used. The findings showed that the learning achievement of the students taught using blended learning was better than that of those taught using the conventional method. In addition, the students taught using the blended learning were more active in doing the assignment than those in the conventional class. Kata Kunci: blended learning, mathematics students, content knowledge
MENINGKATKAN KEMAMPUAN BERPIKIR REFLEKTIF MATEMATIS MELALUI MODEL PEMBELAJARAN PROBLEM BASED LEARNING BERBASIS LINGKUNGAN Nismawati, Nismawati; Nindiasari, Hepsi; Mutaqin, Anwar
Jurnal Penelitian dan Pembelajaran Matematika Vol 12, No 1 (2019): Jurnal Penelitian dan Pembelajaran Matematika Volume 12 Nomor 1 Februari 2019
Publisher : Universitas Sultan Ageng Tirtayasa

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Abstract

The ability of mathematical reflective thinking is the ability to interpret a case based on the mathematical concepts involved, can evaluate the truth of an argument, can draw analogies from two similar cases, can analyze and clarify questions and answers, can generalize, and can distinguish between relevant data and not relevant. This ability is one of the high-level thinking skills that can be optimized through integrated learning in everyday life, namely learning with Environmental Based Problem Based Learning. To find out, a quasi-experimental study was conducted which aimed to find out the improvement of mathematical reflective thinking skills in terms of the high, medium and low mathematical abilities of the group. The subject of the research was class XI in SMA Negeri 1 Cilegon which was selected by cluster random sampling in the sequence and series material. The results of the data analysis showed that the Environmental Based Problem Based Learning model was better than the expository learning in improving the achievement and improvement of students' mathematical reflective thinking skills both viewed as a whole and viewed from the initial high, medium and low mathematical abilities. Keywords: Ability Of Mathematical Reflective Thinking, Environment-Based Problem Based Learning