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Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof? Syamsuri, Syamsuri; Purwanto, Purwanto; Subanji, Subanji; Irawati, Santi
International Journal on Emerging Mathematics Education IJEME, Vol. 1 No. 2, September 2017
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (327.094 KB) | DOI: 10.12928/ijeme.v1i2.5659

Abstract

Mathematical thinking is necessary in mathematics learning especially in college level. One of activities in undergraduate mathematics learning is proving. This article describes students’ thinking process who unable to construct mathematical formal proof. The description uses APOS Theory to explore students’ mental mechanism and students’ mental structure while they do proving. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using think-aloud and then following by interview based task. Results show that the students could not construct a formal proof because they unable to appear encapsulation process. They merely enable to think interiorization and coordination. Based on the results, some suitable learning activities should designed to support the construction of these mental mechanism.
PEMAHAMAN KONSEP FUNGSI INVERS SISWA MELALUI PEMBELAJARAN KOOPERATIF TIPE JIGSAW Aulia, Al Aini; Parta, I Nengah; Irawati, Santi
Jurnal Kajian Pembelajaran Matematika Vol 1, No 2 (2017): Jurnal Kajian Pembelajaran Matematika
Publisher : FMIPA UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (545.714 KB)

Abstract

Abstract : Mathematics is a branch of science that play a pivotal role in human life . In the process of learning mathematics, many aspects must be considered so that the goal of learning can be achieved.  Learning paradigm that just makes students memorize many do not understand mathematical concepts. While understanding the concept is a very important factor in the learning of mathematics and basic things that should be owned by the students. Students who have a good understanding of the concepts that will have an impact on its ability to resolve problems and tasks given in the study of mathematics, this is indicated by the learning outcomes in the form of test scores. The success of achieving standards that have been defined. To achieve this, there are various strategies that can be used, one strategy is through cooperative learning of Jigsaw. Jigsaw type of cooperative learning characterized by spesialias assignment (team of experts). The study describes the students' understanding on the concept of inverse function through cooperative learning jigsaw. This research is a classroom action research using a qualitative approach, the instrument used (1) a test sheet, (2) observation sheets teacher activity and student activities, and (3) sheet autorefleksi. Based on the research, test data that 90, 63% of students to retrieve a value of more than or equal to 75 in accordance with the chief engineer, the data of teacher activity observation 98% category very well and observation data of student activity 90% very good category, as well as data auto reflection students feel happy with the model of learning is done. So meet the success criteria of the study.
PENERAPAN REALISTIC MATHEMATICS EDUCATION MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA Rasyid, Anwar Nur; Irawati, Santi
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol 2, No 12: Desember 2017
Publisher : Graduate School of Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (335.237 KB) | DOI: 10.17977/jptpp.v2i12.10287

Abstract

This article discusses the results of classroom action research conducted over two cycles. This study describes the implementation of learning activities by applying realistic mathematics education to improve students mathematical representation in class VII SMP comparative material. The action steps of math learning with the application of RME are done using problems based on student experience, soliciting student ideas in solving problems, discussing student ideas in groups, comparing group work with other groups, and looking for relevance with other materials in solving more complex problems. The results showed that students mathematical representation ability increased after the second cycle action process.Artikel ini membahas hasil penelitian tindakan kelas yang dilakukan selama dua siklus. Penelitian ini mendeskripsikan pelaksanaan kegiatan pembelajaran dengan melakukan penerapan realistic mathematics education untuk meningkatkan kemampuan representasi matematis siswa pada materi perbandingan kelas VII SMP. Langkah-langkah tindakan pembelajaran matematika dengan penerapan RME dilakukan dengan menggunakan masalah berdasarkan pengalaman siswa, meminta gagasan siswa dalam menyelesaikan masalah, mendiskusikan gagasan siswa secara berkelompok, membandingkan hasil kerja kelompok dengan kelompok lain, dan mencari keterkaitan dengan materi lainnya dalam menyelesaikan masalah yang lebih kompleks. Hasil penelitian menunjukkan kemampuan representasi matematis siswa meningkat setelah proses tindakan siklus II.
BERPIKIR MATEMATIS KOMEDIAN DALAM MENGONSTRUKSI BAHAN KOMEDI: STUDI KASUS PADA STAND UP COMEDY INDONESIA Arsyad, Abdurrahim; Subanji, Subanji; Irawati, Santi
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol.1, No.1, Januari 2016
Publisher : Graduate School of Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (747.889 KB) | DOI: 10.17977/jp.v1i1.6745

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Mathematical thinking has been studied by many researchers in different contexts. Lesh & English (2005) conduct a study about the connection between the someone’s success and his/her mathematical thinking ability. Shmakov & Hannula (2010) study about the creative thinking of students based on the fun mathematics teaching process, Young (2013) uses improv comedy to help the learning activities in class, and the finding of Nicewonder (2001) shows that introducing comedy during mathematics class in any given level could help students understanding the material and also could make mathematics become more fun. Basically, comedy uses the pattern of setup – punchline formula which offers expectation and gives unexpected surprise. In this matter, the thinking process known as assimilation – accomodation creates the condition equilibrium and disequilibrium. Furthermore, to analyze the mathematical thinking happens, the researcher conducts a research on Stand Up Comedy Indonesia. In short, mathematical thinking used by the comedians is an implicational logical pattern. A condition of “if” is as the setup while a condition of “then” is as the punchline. Different techniques of punchline used by different comedians are based on their stage persona which covers language, background, and the sensitivity of comedy.Berpikir matematis telah dikaji oleh banyak peneliti dengan konteks yang berbeda-beda. Lesh & English (2005) melakukan penelitian tentang hubungan kesuksesan seseorang terhadap kemampuan berpikir matematis, Shmakov & Hannula (2010) meneliti tentang kreativitas berpikir siswa dari pembelajaran matematika yang menyenangkan, Young (2013) menggunakan komedi improv untuk membantu kegiatan belajar mengajar, dan penelitian dari Nicewonder (2001) mengungkapkan bahwa mengenalkan komedi di kelas matematika pada jenjang mana pun dapat membantu siswa untuk mengerti dan membuat matematika menjadi menyenangkan. Pada dasarnya komedi menggunakan pola setup – punchline, menawarkan harapan dan memberikan kejutan. Hal ini di dalam proses berpikir dikenal dengan proses asimilasi – akomodasi, yang menciptakan kondisi equilibrium dan disequilibrium. Selanjutnya, untuk mengkaji proses berpikir matematis yang terjadi, dilakukan penelitian terhadap Stand Up Comedy Indonesia. Secara singkat, berpikir matematis yang digunakan oleh komedian adalah pola logika implikasi. Kondisi “jika” sebagai setup, dan kondisi “maka” sebagai punchline. Teknik punchline yang berbeda digunakan oleh setiap komedian sesuai dengan persona panggung yang meliputi gaya bahasa, latar belakang, dan sensitivitas komedi.
Kemampuan Pemecahan Masalah Kontekstual Siswa SMA pada Materi Barisan dan Deret Jayanti, Meylia Dwi; Irawan, Edy Bambang; Irawati, Santi
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol 3, No 5: MEI 2018
Publisher : Graduate School of Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (455.979 KB) | DOI: 10.17977/jptpp.v3i5.11092

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Abstract: This article was a study that aims to describe the contextual problem solving skills of senior high school students. We used problem solving indicator based on Polya. The results of this study indicated that on stage of understanding the problem, 8% of all students could understand every word of the problem but some students were wrong in writing what was known and asked from the problem. At the stage of planning the strategies of solving problems, 43% of all students could construct the solving plan for the question given. At the stage of implementing a plan, 33% of all students could finish all steps chosen to solve the problems systematically. In the last stage, i.e: checking the answers obtained, 16% of all students were able to check the answers back but some students were not able enough to check back the answers obtained.Abstrak: Artikel ini merupakan suatu kajian yang bertujuan untuk mendeskripsikan kemampuan pemecahan masalah kontekstual siswa SMA. Analisis data dalam kajian ini menggunakan indikator kemampuan pemecahan masalah Polya. Hasil kajian menunjukkan pada tahap memahami masalah sebesar 8% siswa dapat memahami setiap kata pada soal tetapi beberapa siswa salah dalam menuliskan apa yang diketahui dan ditanyakan dari soal. Pada tahap menyusun rencana penyelesaian sebesar 43% siswa dapat menyusun rencana penyelesaian dari soal tersebut. Pada tahap melaksanakan rencana sebesar 33% siswa mampu menyelesaikan semua langkah yang telah disusun untuk menyelesaikan soal tersebut dengan runtut dan sitematis. Pada tahap terakhir memeriksa kembali hasil jawaban sebesar 16% siswa mampu melakukan pengecekan jawaban, tetapi beberapa siswa kurang mampu dalam mengecek kembali jawaban yang didapatkannya.
Characterization of students formal-proof construction in mathematics learning Syamsuri, Syamsuri; Purwanto, Purwanto; Subanji, Subanji; Irawati, Santi
Communications in Science and Technology Vol 1 No 2 (2016)
Publisher : Komunitas Ilmuwan dan Profesional Muslim Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21924/cst.1.2.2016.2

Abstract

Formal proof is a deductive process beginning from some explicitly quantified definitions and other mathematical properties to get a conclusion. Characteristics of student formal-proof construction are required to identify the appropriate treatment can be determined. The purpose of this study was to describe the characteristics of the construction of formal-proof based overview of the proof structure and conceptual understanding that the student possessed. The data used in this article were obtained from the 3-step processes: students are asked to write down the proof of proving-question, they are asked about the knowledge required in constructing proof using questionnaire, and then they are interviewed. The results showed that formal-proof construction could be modeled by the Quadrant-Model. First Quadrant describes correct construction of formal-proof, Second Quadrant describes insufficiencies concept in construction formal-proof, Third Quadrant indicates insufficiencies concept and proof-structure in construction formal-proof and Fourth Quadrant describes incorrect proof-structure in construction of formal-proof. This model could give consideration on how to help students who are in Quadrant II, III, and IV to be able to construct a formal proof like Quadrant I.
Komunikasi Matematis Siswa Bergaya Belajar Teoritis dalam Menyelesaikan Soal Kesebangunan Rachmawati, Indah; Irawati, Santi; Parta, I Nengah
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol 3, No 7: JULI 2018
Publisher : Graduate School of Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (787.826 KB) | DOI: 10.17977/jptpp.v3i7.11354

Abstract

Abstract: The purpose of this research is to describe the mathematical communication of theoritist student in SMP Negeri 5 Malang in solving similarity problem. Subject of this research is one theoritist students. The indicators of mathematical communication that used in this research are adapted from the NCTM indicator then combined to the four Polyas steps. The results of this research show that the subject’s mathematical communication structure tends to be complete. Furthermore,  the diagram created by the subject is proportional and completed by the length, unit, and label. Then, the words used by the subject in writing the reason of similarity tend to be ambiguous. In addition, the subject has used mathematical symbols formally but there are still some errors. Abstrak: Tujuan penelitian ini adalah mendeskripsikan komunikasi matematis siswa teoritis SMP Negeri 5 Malang dalam menyelesaikan soal kesebangunan. Subjek penelitian ini adalah satu siswa bergaya belajar teoritis. Indikator komunikasi matematis yang digunakan pada penelitian ini diadaptasi dari indikator NCTM kemudian dikombinasikan dengan empat tahapan penyelesaian masalah Polya. Hasil penelitian menunjukkan bahwa struktur komunikasi matematis subjek cenderung lengkap. Gambar yang dibuat oleh subjek proporsional yang dilengkapi dengan panjang, satuan, dan label. Namun, kata-kata yang digunakan oleh subjek dalam menuliskan alasan kesebangunan cenderung ambigu. Selain itu, subjek telah menggunakan simbol matematika secara formal, namun masih terdapat beberapa kesalahan.
Students’ Semantic-Proof Production in Proving a Mathematical Proposition Syamsuri, Syamsuri; Purwanto, Purwanto; Subanji, Subanji; Irawati, Santi
Journal of Education and Learning (EduLearn) Vol 12, No 3: August 2018
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (546.955 KB) | DOI: 10.11591/edulearn.v12i3.5578

Abstract

Proving a proposition is emphasized in undergraduate mathematics learning. There are three strategies in proving or proof-production, i.e.: procedural-proof, syntactic-proof, and semantic-proof production. Students’ difficulties in proving can occur in constructing a proof. In this article, we focused on students’ thinking when proving using semantic-proof production. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using think-aloud and then following by interview based task. Results show that characterization of students’ thinking using semantic-proof production can be classified into three categories, i.e.: (1) false-semantic, (2) proof-semantic for clarification of proposition, (3) proof-semantic for remembering concept. Both category (1) and (2) occurred before students proven formally in Representation System Proof (RSP). Nevertheless, category (3) occurred when students have proven the task in RSP then step out from RSP while proving. Based on the results, some suitable learning activities should be designed to support the construction of these mental categories.
Reciprocal Teaching assisted by GeoGebra to Improve Students Mathematical Communication Muqtada, Moh. Rikza; Irawati, Santi; Qohar, Abdul
Jurnal Pendidikan Sains Vol 6, No 4: December 2018
Publisher : Pascasarjana Universitas Negeri Malang (UM)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/jps.v6i4.11803

Abstract

Abstract: This Classroom Action Research (CAR) aims to describe the implementation of the reciprocal teaching learning model assisted by Geogebra to improve the mathematical communication skills of the 11th graders of Vocational students. The researcher conducted this research in two cycles. The results of this study indicate that there is an increase in students’ mathematical communication skills from cycle I to cycle II. Reciprocal teaching consists of four stages: summarizing, questioning, predicting and clarifying.Key Words: reciprocal teaching, GeoGebra, mathematical communicationAbstrak: Penelitian Tindakan Kelas (PTK) ini bertujuan untuk mendeskripsikan implementasi model pembelajaran reciprocal teaching berbantuan Geogebra yang dapat meningkatkan kemampuan komunikasi matematis peserta didik kelas XI SMK. Peneliti melakukan penelitan ini dalam dua siklus. Hasil penelitian ini menunjukkan bahwa kemampuan komunikasi matematis peserta didik meningkat dari siklus I ke siklus II. Reciprocal teaching terdiri dari empat tahap yaitu merangkum (summarizing), menanya (questioning), memprediksi (predicting), dan mengklarifikasi (clarifying).Kata kunci: reciprocal teaching, GeoGebra, komunikasi matematis
Students’ Spatial Reasoning in Solving Geometrical Transformation Problems Evidiasari, Serli; Subanji, Subanji; Irawati, Santi
Indonesian Journal on Learning and Advanced Education (IJOLAE) Vol 1, No. 2, July 2019
Publisher : Faculty of Teacher Training and Education, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/ijolae.v1i2.8703

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This study describes spatial reasoning of senior high school students in solving geometrical transformation problems. Spatial reasoning consists of three aspects: spatial visualization, mental rotation, and spatial orientation. The approach that is used in this study is descriptive qualitative. Data resource is the test result of reflection, translation, and rotation problems then continued by interview. Collecting data process involves 35 students. They are grouped to three spatial reasoning aspects then selected one respondent to be the most dominant of each aspect. The results of this study are: (1) the students with spatial visualization aspect used drawing strategy and non-spatial strategy in solving geometrical transformation problems. She transformed every vertex of the object and drew assistance lines which connect every vertex of the object to center point; (2) the students with mental rotation aspect used holistic and analytic strategies in solving geometrical transformation problems. Using holistic strategy means imagining the whole of transformational objects to solve easy problems. While using analytic strategy means transforming some components of objects to solve hard problems; (3) the students with spatial orientation didn’t involve mental imagery and she only could determine the position and orientation of the object in solving geometrical transformation problems