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THE PROCESS OF DISCOVERING STUDENT’S CONJECTURE IN ALGEBRA PROBLEM SOLVING Yuniati, Suci; Nusantara, Toto; Subanji, Subanji; Sulandra, I Made
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 1 (2018)
Publisher : Universitas Negeri Malang

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Abstract

This exploratory descriptive research aims to describe the process of discovering student?s conjecture in mathematics problem solving. There were 2 students in grade VII of Junior High School who participated as the research subject. The instruments used in this research were problem solving test and interview. This research consisted of three stages which were: 1) data collection; data taken process where the researcher asked every student to solve the problem given; 2) analysis on students? work and interview; in this step the researcher analyzed the results of the students? work and carried out interview with the students for further examination of conjecture discovering process when solving the problem; and 3) examining and concluding students? work result and interview result. The result of this study shows that the stages in discovering conjecture were done sequentially although not all steps were done.
WHY DID THE STUDENTS MAKE MISTAKES IN SOLVING DIRECT AND INVERSE PROPORTION PROBLEM? Irfan, Muhammad; Nusantara, Toto; Subanji, Subanji; Sisworo, Sisworo
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 1 (2018)
Publisher : Universitas Negeri Malang

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Abstract

The purpose of this study is to describe the student's difficulties in solving direct and inverse proportion problem. This research uses explorative qualitative research type. The subject of this research is the second semester student of Mathematics Education Study Program in East Java. Subjects were selected based on purposive sampling. The findings of this study are 86% of students are wrong in solving the problem of inverse proportion, 28% of students are wrong in solving direct proportion problem, and 91% of students are wrong in solving both problems in a single question. Then, the students who made mistakes in solving the problem were chosen purposively for interview. The finding in this research is the student(1) do not understand the use of variables, (2) do not understand the use of formulas, (3) do not understand the key phrases on the problem, (4) Difference in ratio, fractional, and division, (5) do not understand the problem, (6) do not understand simplification of division, and (7) do not interpret proportion relation correctly.
REPRESENTATION TRANSLATION ANALYSIS OF JUNIOR HIGH SCHOOL STUDENTS IN SOLVING MATHEMATICS PROBLEMS Swastika, Galuh Tyasing; Nusantara, Toto; Subanji, Subanji; Irawati, Santi; As?ari, Abdur Rahman; Irawan, Edy Bambang
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 2 (2018)
Publisher : Universitas Negeri Malang

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Abstract

This research aims at analyzing the representation translation of Junior High School students in solving mathematical questions related to algebra. This research used descriptive qualitative approach. The focus of representation translation used in this research was the external representation which was a verbal translation into diagram, verbal into symbolic, symbolic into diagram, diagram into symbolic, and diagram into verbal. Based on the analysis of research findings, it shows that representation translation of students from verbal, symbolic, and diagram into verbal and diagram was not really mastered by the students. Meanwhile, the representation translation into symbolic was frequently used by the students although they were expected to do other translation rather than symbolic.
IMITATING FAILURES IN COMMUNICATING SOLUTION OF MATHEMATICAL PROBLEM SOLVING OF ELEMENTARY SCHOOL STUDENTS Lestari, Andika Setyo Budi; Nusantara, Toto; Irawan, Edy Bambang; Chandra, Tjang Daniel; As'ari, Abdur Rahman
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 2 (2018)
Publisher : Universitas Negeri Malang

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Abstract

Imitating performance is not a mediocre element, yet it is a unique ability possessed by humans. Researche concerning on imitating performance has been widely conducted in early childhood education and in adults educations. However, imitating performance studies related to elementary school context is rarely explored. This study was intended to figure out the imitating performance of 5th grade student. This study was analyzed qualitatively where the researcher involved in all stage of the research. The results of the research indicated that there were few imitating performance indicators that were not fullfiled. The students were not able to apply the examples in the new context, in other words the students had failed in applying the examples. Consequently, they faced difficulties in communicating the solutions of mathematical problems.  Instead of helping the students, the key words provide by a teachers make the students confuse in resolving different problems.
SERIES OF ARGUMENTS ON PROCESSES OF CRITIQUES TO MATHEMATICAL PROBLEMS Nugroho, Bayu; Nusantara, Toto; As'ari, Abdur Rahman; Sisworo, Sisworo
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 1 (2018)
Publisher : Universitas Negeri Malang

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This study was initially based on the researcher?s interest in a case found in students as they responded mathematical problems provided in the form of critiques to a problem. The study aimed to explore the students? arguments to describe the students? thinking processes while they are giving critiques to a mathematical problem. The study was qualitative research in a case study involving one student as a subject of research.  The finding showed that the students used 4 series of arguments as the main reason to give critiques to the given problem. The critiques were delivered due to several factors consisting of; (1) the students? inability to discover appropriate strategies to deal with the given problems; (2) the personal experiences kept in a Long Term Memory, and (3) the fallacy on reasoning.
STUDENT'S MATHEMATICAL CONNECTION TO PROBLEM-SOLVING BASED ON RATIONAL PERSONALITY TYPES Sutrisno, Alkans Sofyawati; Nusantara, Toto; Susiswo, Susiswo
Jurnal Pendidikan Sains Vol 7, No 1: March 2019
Publisher : Pascasarjana Universitas Negeri Malang (UM)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1523.311 KB) | DOI: 10.17977/jps.v7i1.12499

Abstract

Abstract: The purpose of this study is to describe students? mathematical connection of rational type students in solving mathematics problem. The research data was obtained by analyzing the answer sheets and interview of two subjects based on mathematical connection indicators. The results show the process of mathematical connection in everyday life that students do with rational personality type is complete. However, different results are found that in the connection between mathematical concepts and mathematical process connection processes as the equivalent representation of students with rational personality types is not yet complete.Key Words: mathematical connection, rational personality typesAbstrak: Tujuan penelitian ini untuk mendeskripsikan koneksi matematis siswa bertipe kepribadian rasional dalam memecahkan masalah Matematika. Penelitian ini merupakan penelitian deskriptif-kualitatif. Data diperoleh dari lembar jawaban dan wawancara terhadap dua subjek kemudian dianalisis berdasarkan indikator koneksi matematis. Hasil penelitian menyimpulkan bahwa subjek menunjukkan koneksi Matematika dalam kehidupan sehari-hari secara lengkap. Namun hasil berbeda ditemukan bahwa proses koneksi antar konsep Matematika dan proses koneksi prosedur Matematika sebagai representasi yang ekivalen dari siswa dengan tipe kepribadian rasional adalah belum lengkap.Kata kunci: koneksi matematis, tipe kepribadian rasional
Student’s thinking path in mathematics problem-solving referring to the construction of reflective abstraction Sopamena, Patma; Nusantara, Toto; Irawan, Eddy Bambang; Sisworo, Sisworo; Wahyu, Kamirsyah
Beta: Jurnal Tadris Matematika Vol 11 No 2 (2018): Beta November
Publisher : Universitas Islam Negeri (UIN) Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20414/betajtm.v11i2.230

Abstract

[English]: This article is a part of research which aimed to reveal the path of undergraduate students’ thinking in solving mathematical problems referring to the construction of reflective abstraction. Reflective abstraction is the process of thinking in constructing logical structures (logico-mathematical structures) by individuals through interiorization, coordination, encapsulation, and generalization. This article seeks to analyze a student with the simple closed path, as one of the two types of students’ thinking path found in the research, in solving limit problems. The thinking process of the student in solving mathematical problems occurred through the path of interiorization - coordination - encapsulation - generalization then to coordination - encapsulation - generalization. The path of the student’s thinking yields alternative to understand and marshal problem-solving activities in mathematics learning. Keywords: Thinking path, Limit problem, Reflective abstraction, Simple closed path [Bahasa]: Artikel ini merupakan bagian dari penelitian yang bertujuan mengungkap jalur berpikir mahasiswa dalam menyelesaikan masalah matematika berdasarkan konstruksi abstraksi reflektif. Abstraksi reflektif merupakan proses berpikir individu dalam membangun struktur logika (struktur matematis logis) melalui interiorisasi, koordinasi, enkapsulasi, dan generalisasi. Artikel ini akan menganalisis seorang mahasiswa yang memiliki jalur berpikir tertutup sederhan, salah satu dari dua jalur berpikir yang terungkap dalam penelitian, dalam menyelesaikan permasalahan limit. Proses berpikir mahasiswa dalam menyelesaikan masalah matematika berdasarkan konstruksi abstraksi reflektif dapat terjadi melalui jalur interiorisasi – koordinasi – enkapsulasi – generalisasi kemudian ke koordinasi – enkapsulasi – generalisasi. Hasil penelitian ini memberikan alternatif dalam memahami dan merancang aktivitas pemecahan masalah dalam pembelajaran matematika. Kata kunci: Jalur berpikir, Masalah limit, Abstraksi reflektif, Jalur tertutup sederhana
MATHEMATICAL MEANING IN MODELLING CONTEXT THROUGH THE ONTO-SEMIOTICS APPROACH Umam, Khoerul; Nusantara, Toto; Parta, I Nengah; Hidayanto, Erry
International Journal of Insights for Mathematics Teaching (IJOIMT) Vol 1, No 2 (2018)
Publisher : Universitas Negeri Malang

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Abstract

The main objective of this research will implement the onto-semiotics approach to analyse the conceptual of mathematical meaning in a modelling context corresponding to their use of the mathematical objects. Semiotics functions and mathematical object that emerged when solving mathematical modelling will be highlighted according to OSA. Students responses to modelling questions were used to classify the semiotics function that relates to the different mathematical objects.
SYARAT PERLU DAN CUKUP UNTUK KETERBATASAN POTENSIAL RIESZ DI RUANG MORREY KLASIK Utoyo, Mohammad Imam; Widodo, Basuki; Nusantara, Toto; Suhariningsih, Suhariningsih
Jurnal Natur Indonesia Vol 14, No 3 (2012)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (294.722 KB) | DOI: 10.31258/jnat.14.3.227-229

Abstract

This script was aimed to determine the necessary conditions for boundedness of Riesz potential in the classical Morrey space. If these results are combined with previous research results will be obtained the necessary and sufficient condition for boundedness of Riesz potential. This necessary condition is obtained through the use of characteristic function as one member of the classical Morrey space.
DEFRAGMENTING STRUKTUR BERPIKIR SISWA DALAM MENYELESAIKAN MASALAH PERTIDAKSAMAAN EKSPONEN Kumalasari, Fitri; Nusantara, Toto
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol.1, No.2, Februari 2016
Publisher : Graduate School of Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (586.846 KB) | DOI: 10.17977/jp.v1i2.6129

Abstract

The aim of this study is to describe the thinking structure students’ error related to solve inequality exponent problem and the effort of defragmenting. The subject of this study is student of X class SMAN 6 Malang which learned this material. The subject choose considered procedural error and their communication skill. The thinking structure students’ error found from think out loud result in a process to solve inequality exponent problem. The obtained data will code and be based to describe defragmenting process. The founding of this study is the thinking structure students’ error such as misgeneralization, misidentification, overspecialization, and repair theory. Defragmenting create disequilibration, conflict cognitive, and scaffolding.Penelitian ini bertujuan untuk mendapatkan deskripsi tentang kesalahan struktur berpikir siswa dalam menyelesaikan masalah pertidaksamaan eksponen serta upaya defragmentingnya. Penelitian ini dilakukan pada siswa Kelas X SMAN 6 Malang yang telah menempuh materi pertidaksamaan eksponen. Subjek penelitian dipilih dengan mempertimbangkan kesalahan prosedural yang dilakukan siswa ketika menyelesaikan masalah serta kemampuan komunikasi yang baik agar pengungkapan proses berpikir dapat dilakukan dengan baik. Kesalahan struktur berpikir siswa ditelusuri dari hasil think out loud siswa selama proses penyelesaian masalah pertidaksamaan eksponen. Data yang diperoleh kemudian dikodekan dan dijadikan dasar untuk menggambarkan proses defragmenting yang dilakukan. Dari hasil penelitian ditemukan bahwa kesalahan prosedural siswa dalam menyelesaikan masalah pertidaksamaan eksponen, antara lain berupa misgeneralization, misidentification, overspecialyzation, dan repair theory. Defragmenting yang dilakukan peneliti adalah menciptakan disequlibrasi, conflict kognitif, dan scaffolding.