Advanced Mathematical Thinking

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Association between the students’ Self-Renewal Capacity and Advanced Mathematical Thinking

Association between the students’ Self-Renewal Capacity and Advanced Mathematical Thinking

The results show that there is an association between students’ Self-Renewal Capacity (SRC) and Advanced Mathematical Thinking (AMT). These findings are based on statistical test results. These results indicate that if students have high SRC, then they also have high AMT and if students have low SRC, then they also have low AMT. The association between students’ SRC and AMT can be seen from sub-indicator ‘exploration’ on SRC and components of AMT. If person has creative ideas, has an interest in the process of generalization, proof, and representation, and has a high curiosity about new something relatively, then they can develop representation, abstractions, creative thinking, and mathematical proofs ability. Otherwise, if person hasn’t creative ideas, hasn’t an interest in the process of generalization, proof, and representation, and has n’t a high curiosity about new something relatively, then they can not develop representation, abstractions, creative thinking, and mathematical proofs ability well.
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PENINGKATAN KEMAMPUAN ADVANCED MATHEMATICAL THINKING DAN DISPOSISI BERPIKIR KREATIF MATEMATIS MAHASISWA MELALUI PENDEKATAN M-APOS - repository UPI D MAT 1101193 title

PENINGKATAN KEMAMPUAN ADVANCED MATHEMATICAL THINKING DAN DISPOSISI BERPIKIR KREATIF MATEMATIS MAHASISWA MELALUI PENDEKATAN M-APOS - repository UPI D MAT 1101193 title

Dengan ini saya menyatakan bahwa disertasi dengan judul “ Peningkatan Kemampuan Advanced Mathematical Thinking dan Disposisi Berpikir Kreatif Matematis Mahasiswa melalui Pendekatan M-APOS ” ini adalah benar-benar karya saya sendiri, dan saya tidak melakukan plagiarisme atau pengutipan dengan cara-cara yang tidak sesuai dengan etika yang berlaku dalam tradisi keilmuan. Atas pernyataan ini, saya siap menerima tindakan/sanksi yang dijatuhkan kepada saya apabila kemudian ditemukan adanya pelanggaran atas etika akademik dalam karya saya ini, atau ada klaim terhadap keaslian karya saya ini.
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PENINGKATAN KEMAMPUAN ADVANCED MATHEMATICAL THINKING DAN DISPOSISI BERPIKIR KREATIF MATEMATIS MAHASISWA MELALUI PENDEKATAN M-APOS.

PENINGKATAN KEMAMPUAN ADVANCED MATHEMATICAL THINKING DAN DISPOSISI BERPIKIR KREATIF MATEMATIS MAHASISWA MELALUI PENDEKATAN M-APOS.

This study examines the enhancement of college students’ advanced mathematical thinking ability and disposition of mathematical creative thinking through M- APOS approach. The aim of this study is to examine comprehensively the contribution of M-APOS approach application toward achievement and enhancement of AMT ability and Disposition of Mathematical Creative Thinking (DMCT) of college students. This study applied quasi-experiment design. The samples of this study were all students in Mathematics Education of Faculty of Teacher Training and Educational Sciences who took Algebra subject. The research instrument used pretest and posttest for AMT ability, attitude scale for DMCT, observation sheet, and interview guidance. The results of this study are: (1) there is no achievement and enhancement difference between AMT ability of the students who got M-APOS approach and the students who got conventional learning; (2) there is no achievement and enhancement difference between AMT ability of the students who got M-APOS approach and the students who got conventional learning in upper and middle of PMA, while in the lower level of PMA, the enhancement of the students ’ AMT ability of M-APOS class is the higher than that of conventional class; (3) there is no interaction between teaching and the level of PMA toward the achievement and enhancement of students’ A MT ability; (4) there is no the achievement and enhancement difference between DMCT of the students who got M-APOS approach and the students who got conventional learning, but the achievement of students’ DMCT who got M -APOS approach is significantly higher than the students who got conventional learning; and (5) there is interaction between teaching and the level of PMA toward the achievement and enhancement of the students’ DMCT.
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T MTK 1103040 Chapter 5

T MTK 1103040 Chapter 5

1. a. Pencapaian dan peningkatan Advanced Mathematical Thinking mahasiswa yang memperoleh pembelajaran Model PACE, baik secara keseluruhan maupun untuk semua level kemampuan awal matematis (tinggi, sedang, dan rendah), lebih baik daripada mahasiswa yang memperoleh pembelajaran konvensional. Pencapaian dan peningkatan Advanced Mathematical Thinking mahasiswa secara keseluruhan dan berkemampuan awal matematis tinggi yang memperoleh pembelajaran Model PACE berada pada kategori sedang, sementara untuk mahasiswa berkemampuan awal matematis sedang dan rendah, pencapaiannya berada pada kategori rendah, tetapi peningkatannya berada pada kategori sedang. Lain halnya dengan mahasiswa yang memperoleh pembelajaran konvensional, pencapaiannya secara keseluruhan dan tiap level kemampuan awal matematis (tinggi, sedang, dan rendah) berada pada kategori rendah, tetapi peningkatannya berada pada kategori sedang.
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T MTK 1103040 Abstract

T MTK 1103040 Abstract

The main purpose of this research is to analize of achievement and enhancement of the students` Advanced Mathematical Thinking and Self-Renewal Capacity comprehensively as a result of the implementation of PACE (Project, Activity, Cooperative learning, Exercise) model learning and conventional learning. This research used a quasi-experimental with pretest-posttest control group design. The population of this research included all students of regular class in the mathematics education department of one of the private universities in East Jakarta and the sample was group of students joining Mathematical Statistic Subject. This research used various instruments. They were test of mathematical prior knowledge, test of advanced mathematical thinking, self-renewal capacity scale, observation sheet, and interview sheet. For data analysis, this research used parametric and non-parametric statistic. The result of this research are: (1) the achievement and enhancement of the students` Advanced Mathematical Thinking and Self-Renewal Capacity taught by using PACE model learning are better than the achievement and enhancement of those who were taught by using conventional learning; (2) there is no interaction between learning (PACE model learning and conventional learning) and mathematical prior knowledge (high, intermediate, low) towards the achievement and enhancement of the students` Advanced Mathematical Thinking and Self-Renewal Capacity; and (3) there is association between the students’ Advanced Mathematical Thinking and Self- Renewal Capacity.
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A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

Penelitian ini bertujuan untuk mengetahui apakah terdapat hubungan yang signifikan antara kemampuan mathematical thinking dengan problem solving mahasiswa program studi sistem informasi dan untuk mengetahui seberapa besar kemampuan problem solving mempengaruhi kemampuan mathematical thinking mahasiswa. Populasi dalam penelitian ini adalah seluruh mahasiswa yang mengontrak mata kuliah matematika diskrit pada program studi Sistem Informasi dan program studi pendidikan matematika. Berdasarkan hasil analisis data diperoleh bahwa terdapat pengaruh yang signifikan antara kemampuan problem solving dan mathematical thinking baik pada mahasiswa prodi sistem informasi maupun pendidikan matematika. Pada penelitian ini, ditemukan fakta bahwa pengaruh kemampuan problem solving terhadap mathematical thinking lebih besar terjadi pada mahasiswa prodi pendidikan matematika. Ini disebabkan, karena kegiatan memecahkan masalah dalam perkuliahan mahasiswa prodi pendidikan matematika lebih sering dilakukan dibandingkan dengan mahasiswa prodi sistem informasi. Hampir 75% mata kuliah yang ada dalam program studi pendidikan matematika melibatkan problem solving dalam tujuan mata kuliahnya, sementara itu, pada program studi sistem informasi, hanya terdapat 10% saja mata kuliah tersebut. Akibatnya mahasiswa pendidikan matematika lebih terlatih kemampuan problem solvingnya dibandingkan dengan mahasiswa prodi sistem informasi.
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KONTRIBUSI FAKTOR-FAKTOR SELF-EFFICACY TERHADAP MATHEMATICAL HIGH ORDER THINKING SKILL

KONTRIBUSI FAKTOR-FAKTOR SELF-EFFICACY TERHADAP MATHEMATICAL HIGH ORDER THINKING SKILL

Penelitian ini dilaksanakan di Program Studi Pendidikan Matematika FKIP Universitas Lampung. Populasi penelitian ini adalah seluruh mahasiswa Program Studi Pendidikan Matematika FKIP Universitas Lampung yang menempuh mata kuliah Analisis Real 1 pada semester ganjil tahun akademik 2017/2018. Dengan menggunakan teknik random sampling, terpilih 25 orang mahasiswa sebagai sampel penelitian. Penelitian ini adalah penelitian korelasional. Variabel bebas dalam penelitian ini adalah faktor-faktor dari self-efficacy, yaitu (1) pencapaian kinerja, (2) pengalaman orang lain, (3) persuasi verbal, dan (4) keadaan dan reaksi fisiologis. Variabel terikat dalam penelitian ini adalah mathematical high order thinking skill.
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Welcome to ePrints Sriwijaya University - UNSRI Online Institutional Repository

Welcome to ePrints Sriwijaya University - UNSRI Online Institutional Repository

Pendidikan Matematika Realistik Indonesia is the Indonesian adaptation of the Dutch Realistic Mathematics Education (RME). Freudenthal revealed that "mathematic is a human activity". Mathematics as activity or process, Freudhenthal does not put mathematics as finished product. Freudenthal suggested that mathematics should not be taught as finished product but as students’ activity that supports the construction of mathematical concepts. In Education Realistic, realistic problems are used as a foundation for building a mathematical concept or referred to as a source for learning . Gravemeijer in Sembiring (2008) said: "There are three basic tenets of RME items, namely guided reinvention, didactical phenomenology models and the mediating principle". At first principles which are guided rediscovery use works mathematician who had invented the concept of formal mathematics instruction so that students as early as rediscovered mathematical concepts. The next principle is that didactic phenomenology found the problem or situation that allows to generalize mathematical concepts that can be the basis for mathematical problem solving. The last principle is mediation model which describes the role of mathematics as a bridge between the informal to the formal mathematics mathematics.
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VISUAL THINKING AND MATHEMATICAL PROBLEM SOLVING OF THE NATION CHARACTER DEVELOPMENT.

VISUAL THINKING AND MATHEMATICAL PROBLEM SOLVING OF THE NATION CHARACTER DEVELOPMENT.

Mathematical problem solving is the heart of mathematics and visualization is the core of solving mathematics. Visual thinking is the most effective and powerful in mathematics instruction. The way we learn, and then remember, sustaining a strong relationship with the way our senses operate solve math problems. Schools have the freedom to manage and choose approach to learning mathematics. How can character education is taught to students and therefore will have the opportunity to emphasize the special character of the school. While each school has the freedom to choose the kind of values that, for nation building must have some values taught in every school. Those values must be the most important value to support the Indonesian nation-building project. First, multicultural values. Indonesia consists of various ethnic, religious, and cultural. If the nation wants to be stronger in the future, we must accept differences between us. Without accepting the differences, we will easily slip into fights and conflicts. The spirit of multiculturalism and religious diversity would encourage all people to accept others as members of the Indonesian nation. This is the spirit of Bhineka Tunggal Ika: although different, but still one. We sometimes lack of respect that spirit. Some of us want to impose our ideas on others Second, honesty. One important reason why corruption is very difficult to be eradicated in Indonesia is the lack of honesty. Most of us are not honest anymore. The spirit of honesty in the learning of mathematics must be inculcated in school. Students should learn about the value of honesty and implementation. Students must learn to be honest in school, to be honest with yourself, honest with others, be honest with their life and honest about what they do. Students should be honest when completing math problems, tests and national
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PROFIL ABSTRAKSI SISWA KELAS IX DITINJAU DARI KEMAMPUAN RIGOROUS MATHEMATICAL THINKING.

PROFIL ABSTRAKSI SISWA KELAS IX DITINJAU DARI KEMAMPUAN RIGOROUS MATHEMATICAL THINKING.

Rigorous Mathematical Thinking atau RMT didefinisikan sebagai perpaduan dan pemanfaatan operasi mental untuk: memperoleh pengetahuan tentang pola dan hubungan; menerapkan peralatan dan skema yang diperoleh secara kultural untuk menguraikan pengetahuan tersebut bagi organisasinya, korelasinya, teknik mengarangnya dan representasi abstraknya untuk membentuk pemahaman dan pengertian; merencanakan penggunaan ide-ide tersebut untuk memfasilitasi penyelesaian masalah dan penurunan pengetahuan baru dalam berbagai konteks dan bidang aktivitas manusia; serta melakukan pemeriksaan kritis, analisis, instropeksi dan pemantauan struktur, operasi dan proses RMT untuk pemahaman dirinya dan integritas intrinsiknya.
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PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI) DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI) DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

Gambaran psikologis siswa terhadap pemahaman matematik akan terlihat lemah pada masa awal pembelajaran, soal – soal/ tugas – tugas matematika yang dimunculkan pada masa ini didesain untuk menstimulasi ide – ide, strategi dan representasi (Develop Understanding). Setiap ide, strategi dan representasi ini, kemudian akan dikoreksi untuk melihat ketepatan dan kelengkapannya, serta diperluas dan dikoneksikan dengan beberapa materi terkait, melalui pemberian stimulant atau pengalaman pada siswa sehingga ide – ide, strategi dan representasi yang telah mereka dapatkan sebelumnya menjadi lebih nyata, kuat dan bermakna (Solidify Understanding). Dalam kerangka CMI, ide-ide yang telah menjadi lebih kuat dan tegas disebut konsep; strategi yang kuat menjadi algoritma; dan representasi yang bermakna menjadi alat. Meskipun kemampuan pemahaman telah dikembangkan dan dikuatkan, akan tetapi, tetap masih perlu perbaikan lebih lanjut untuk menjadi mencapai kemahiran (Practice Understanding). Dalam kerangka CMI, ide yang telah disempurnakan akan berkembang menjadi definisi atau properti; algoritma yang tepat berkembang menjadi prosedur; dan alat-alat yang telah disempurnakan berkembang menjadi sebuah model matematik. Definisi dan sifat, prosedur, dan model yang telah diperoleh, kemudian harus disesuaikan dengan hasil – hasil pemikiran yang dilakukan oleh teman – temannya, melalui kegiatan diskusi, sehingga setaip siswa memperoleh keyakinan bahwa proses pemikiran mereka telah tepat. Pada komponen Continuum of Mathematical Understanding ini, proses – proses konseptualisasi matematik, doing mathematics dan representasi matematik berlangsung pada sepanjang garis kontinum, seperti tergambar pada gambar 4 di bawah, dengan demikian, diharapkan tujuan pembelajaran matematika yakni pencapaian pemahaman matematik yang mendalam akan tercapai.
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PROBLEM BASED AND METACOGNITIVE LEARNING TO IMPROVE MATHEMATICAL REFLECTIVE THINKING SKILLS.

PROBLEM BASED AND METACOGNITIVE LEARNING TO IMPROVE MATHEMATICAL REFLECTIVE THINKING SKILLS.

Recognizing the importance of a strategy and learning approach to develop the students thinking skills, it is absolutely necessary to mathematics learning that more actively involve students in the learning process itself. This can be realized through an alternative learning that is designed such that it reflects the involvement of students actively and constructively. Students as learners need to get used to being able to construct their own knowledge and being able to transform into other that more complex situations so that such knowledge will become the property of the learner itself, which is attached forever. The process of constructing knowledge can be done by the learners themselves based on the experience that has been previously owned, or may also be a result of the discovery that involve environmental factors. Based on the views of constructivism, a learning strategy must have characteristics as follows: use more time to develop an understanding that can enhance the ability of learners to use the knowledge, involve students in the learning process so that the abstract concepts presented more concrete, implementation of small group discussions, presentation of the problems that are not routine.
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SENIOR HIGH SCHOOL TEACHERS’ MATHEMATICAL QUESTIONING ABILITY AND METAPHORICAL THINKING LEARNING

SENIOR HIGH SCHOOL TEACHERS’ MATHEMATICAL QUESTIONING ABILITY AND METAPHORICAL THINKING LEARNING

Studi ini dirancang dalam bentuk eksperimen dengan disain kelompok kontrol dan postes saja yang bertujuan menelaah peranan pembelajaran yang mengajarkan berpikir metaforik terhadap kemampuan bertanya matematis guru SMA. Populasi dalam penelitian ini adalah guru SMA mata pelajaran matematika di Provinsi Jawa Barat, sedangkan sampel penelitian ini adalah 124 orang guru SMA mata pelajaran matematika yang ditetapkan secara purposif kemudian ditetapkan secara acak yang termasuk ke dalam kelas eksperimen dan kelas kontrol. Berdasarkan hasil dan pembahasan diperoleh kesimpulan: (1) Kemampuan bertanya matematis guru yang memperoleh pembelajaran Metaphorical Thinking lebih baik daripada yang memperoleh pembelajaran biasa; (2) Faktor pembelajaran dan KAM masing-masing mempengaruhi ketercapaian kemampuan bertanya matematis guru. Selain itu, terdapat efek interaksi antara pembelajaran dan KAM secara bersama-sama dalam mengembangkan kemampuan bertanya matematis guru; (3) Ketercapaian penguasaan kemampuan bertanya matematis guru masih belum tercapai dengan baik pada indikator pengajuan permasalahan berupa pertanyaan non-rutin dan pertanyaan terbuka.
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Eksperimentasi Model Pembelajaran Rigorous Mathematical Thinking dan Problem Based Learning terhadap Pemahaman Konseptual dan Kompetensi Strategis pada Materi Geometri ditinjau dari Perbedaan Jenis Kelamin Siswa SMPN di Kabupaten Ngawi Tahun Pelajaran 201

Eksperimentasi Model Pembelajaran Rigorous Mathematical Thinking dan Problem Based Learning terhadap Pemahaman Konseptual dan Kompetensi Strategis pada Materi Geometri ditinjau dari Perbedaan Jenis Kelamin Siswa SMPN di Kabupaten Ngawi Tahun Pelajaran 201

This research was a quasi-experimental research, which aimed to determine: the effect comparison of Rigorous Mathematical Thinking (RMT), Problem Based Learning (PBL), and Direct Learning (DL) to mathematical conceptual understanding and mathematical strategic competence of Junior High School„s students in Ngawi on Academic year 2016/2017. In addition to the factor of learning model, in this research we also examined the factors of sex difference, and the interaction between learning model and sex difference.

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Copper Oxide Nanoparticles for Advanced Refrigerant Thermophysical Properties: Mathematical Modeling.

Copper Oxide Nanoparticles for Advanced Refrigerant Thermophysical Properties: Mathematical Modeling.

he nanoparticle is suspended into the conventional refrigerant with 1% volume fraction which causes an increase in the thermal conductivity about 3121% enhancement from 0.0139 W/m ⋅ K to 0.4477 W/m ⋅ K. he signiicant enhance- ment occurred due to interfacial layer consideration in the mathematical modeling. It created equivalent particles with no overlapping between particles. he use of nanoparticle volume fraction up to 5% increased the thermal conductivity of nanorefrigerant more than 100% as the conventional refrigerant, R-134a, itself has higher thermal conductivity compared to other types of base luid such as water and ethylene glycol.
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Students’ Critical Mathematical Thinking Skills and Character: Experiments for Junior High School Students through Realistic MathematicsEducation Culture-Based

Students’ Critical Mathematical Thinking Skills and Character: Experiments for Junior High School Students through Realistic MathematicsEducation Culture-Based

As with many other disciplines, mathematics is also heavily influenced by the cultural values in the development and teaching. Although the results are the same calculations, mathematical methods and techniques are different in every culture of the world community. Leung (2009) pointed out, the math on the Chinese calendar and the Islamic calendar. Although both are calculated based on the circulation of the month, but the beginning of the calculation is different. It shows there are cultural influences in the methods and techniques, but in the end, the result and the formula is the same. He also added to the cultural diversity of Indonesia, should also apply etnopedagogik in learning and teaching culture. "Should a country with distinctive culture is superior, because we can learn mathematics in two different cultural perspectives and values.
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D MAT 1101193 bibliography

D MAT 1101193 bibliography

Klopper, M. and Grosser, M. (2014). The Critical Thinking Disposition of Prospective Mathematics Teacher at a South African University: New Direction for Teacher Training . International Journal Education Science. Vol.7 No. 3 pp. 413-427

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Mathematical thinking in school1

Mathematical thinking in school1

discussion of the following problem: "James had 13 marbles. He lost 8 of them. How many marbles does he have left?" Carpenter notes that "such problems frequently are not included in discussions of problem solving because they can be solved by the routine application of a single arithmetic operation. A central premise of this paper is that the solutions of these problems, particularly the solutions of young children, do in fact involve real problem solving behavior" (page 17). Heller and Hungate (1985) implicitly take their definition of "problem solving" to mean "being able to solve the exercises at the end of a standard textbook chapter," as does Mayer. At the other end of the spectrum, "the fundamental importance of epistemological issues (e.g. beliefs, conceptions, misconceptions) is reflected in the papers by Jim Kaput, Richard Lesh, Alan Schoenfeld, and Mike Shaughnessy. (p. ix.)" Those chapters took a rather broad view of problem solving and mathematical thinking. Similarly, the chapters reveal a great diversity of methods and their productive application to issues related to problem solving. Carpenter's chapter presents detailed cross-sectional data on children's use of various strategies for solving word problems of the type discussed above. Heller and Hungate worked within the "expert-novice" paradigm for identifying the productive behavior of competent problem solvers and using such behavior as a guide for
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Teaching Mathematical Thinking

Teaching Mathematical Thinking

Example 2: If, while teaching addition, with the example of “3 and 5 make 8,” students only write the answer 8, he or she will not know what the original amounts were, or what operation was used to result in 8. In order to clearly express this, it is necessary to use 5, 3, and 8, as well as a symbol to express the operation used. The attitude and necessity of attempting to express things more clearly reveal the benefits of thinking that symbolize. In other words, by writing the equation “3+5=8,” one can communicate the understanding that bringing 3 items and 5 items together results in 8 items. This equation succinctly and clearly expresses the idea that this 8 did not come into being through the addition of 6 and 2, for instance.
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T MTK 1103040 Chapter 1

T MTK 1103040 Chapter 1

Selain itu, rendahnya Advanced Mathematical Thinking mahasiswa juga diungkapkan oleh Herlina (2015) dalam studi pendahuluannya, yaitu mahasiswa mengalami kesulitan dalam memahami konsep dalam bentuk notasi matematika, membuktikan, mengaitkan antar konsep, serta menghasilkan ide-ide kreatif dalam menyelesaikan permasalahan matematika. Berkaitan dengan rendahnya Advanced Mathematical Thinking, Tall (2002) mengatakan bahwa salah satu penyebabnya adalah dosen masih terbiasa mengajar secara prosedural dan akan membenarkan jawaban mahasiswa jika mengikuti prosedur tersebut.
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