Advanced Mathematical Thinking

MENINGKATKAN ADVANCED MATHEMATICAL THINKING DAN SELF-RENEWAL CAPACITY MAHASISWA MELALUI PEMBELAJARAN MODEL PACE Oleh Andri Suryana 1103040 Sebuah Disertasi yang diajukan untuk meme[r]

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.

Mathematical concepts in college are generally more complex than mathematical concepts in school because that concepts which is given in college is more abstract. Therefore, students of mathematics education program must have ability in constructing and finding mathematical concepts themselves, proving logically, and developing their mathematical abilities. This is very important for them in completing mathematical tasks in college, especially advanced mathematical courses [1], such as Mathematical Statistics course. To realize that expectation, students' mathematical thinking abilities should be developed and connected to mathematicians' thinking in order to create Advanced Mathematical Thinking abilities that focus more on formal definitions, logical deductions, and creative thinking [2]. Advanced Mathematical Thinking ability include several components. There are representation, abstraction, connecting between representation and abstraction, creative thinking, and mathematical proof [1]. However, the student’ Advanced Mathematical Thinking, especially in Mathematics Statistics course, is still relatively low.

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.

1. Pembelajaran Model PACE sebagai alternatif pembelajaran pada Mata Kuliah Statistika Matematika untuk meningkatkan Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa, baik secara keseluruhan maupun berdasarkan level kemampuan awal matematis. Hal ini dikarenakan implementasi pembelajaran Model PACE diakui oleh mahasiswa memiliki kontribusi positif dalam meningkatkan Advanced Mathematical Thinking dan Self-Renewal Capacity-nya.

Perception of And Interactions with external world Objects --- --- Actions Advanced Mathematical Thinking Inspired by concept images, formalised by Concept definitions and log[r]

Tujuan utama penelitian ini adalah untuk menganalisis secara komprehensif pencapaian dan peningkatan Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa sebagai akibat dari implementasi pembelajaran Model PACE (Proyek, Aktivitas, Pembelajaran kooperatif, Latihan) dan konvensional. Penelitian ini merupakan penelitian kuasi eksperimen menggunakan pretest- posttest control group design. Populasi dalam penelitian ini adalah seluruh mahasiswa regular Program Studi Pendidikan Matematika di salah satu PTS di Jakarta Timur, sedangkan sampelnya adalah mahasiswa yang sedang menempuh mata kuliah Statistika Matematika. Penelitian ini menggunakan beberapa instrumen, yaitu tes kemampuan awal matematis, tes Advanced Mathematical Thinking, skala Self-Renewal Capacity, lembar observasi, dan pedoman wawancara. Analisis data dalam penelitian ini menggunakan statistik parametrik dan non-parametrik. Adapun hasil dari penelitian ini adalah: (1) pencapaian dan peningkatan Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa yang memperoleh pembelajaran Model PACE lebih baik daripada mahasiswa yang memperoleh pembelajaran konvensional; (2) tidak terdapat interaksi antara pembelajaran (Model PACE dan konvensional) dan kemampuan awal matematis (tinggi, sedang, rendah) terhadap pencapaian dan peningkatan Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa; serta (3) terdapat asosiasi antara Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa.

Andri Suryana, 2016 Meningkatkan Advanced Mathematical Thinking dan Self-Renewal Capacity Mahasiswa melalui Pembelajaran Model PACE.. Struktur Organisasi Disertasi ...[r]

ELDA HERLINA, 2015 PENINGKATAN KEMAMPUAN ADVANCED MATHEMATICAL THINKING DAN DISPOSISI BERPIKIR KREATIF MATEMATIS MAHASISWA MELALUI PENDEKATAN M-APOS Universitas Pendidikan Indone[r]

Dalam menerapkan pembelajaran Model PACE, harus diperhatikan faktor kemampuan awal matematis (KAM) mahasiswa karena sifat dari bidang studi matematika yang sistematis. Hal ini penting untuk diperhatikan dalam proses pembelajaran matematika (Dasari, 2009 dan Suryadi, 2012) dan diprediksi memiliki kontribusi terhadap peningkatan Advanced Mathematical Thinking dan Self-renewal Capacity mahasiswa. Untuk dapat mengetahui lebih jauh terkait penerapan pembelajaran Model PACE dalam meningkatkan Advanced Mathematical Thinking dan Self-renewal Capacity mahasiswa, maka dilakukan suatu penelitian dengan judul ” Meningkatkan Advanced Mathematical Thinking dan Self-Renewal Capacity Mahasiswa melalui Pembelajaran Model PACE ”. Dalam penelitian ini, Advanced Mathematical Thinking dan Self-Renewal Capacity mahasiswa ditinjau secara keseluruhan dan berdasarkan KAM.

The population of this research were students of grade VII (seven) Junior High School in Ngawi which were implementing Curriculum 2013. We used stratified cluster random sampling as sampling technique. By this sampling technique, there was obtained 261 students as sample, which were consisted of 87 students in Experimental Class I, 88 students in Experimental Class II, and 87 students in Control Class. The research instruments consisted of pretest and posttest of mathematical conceptual understanding and mathematical strategic competence in plane‟s per imeter and area material. Data analysis was using two ways MANOVA, two ways ANAVA, and Scheffe ’ .

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.

The Lesson Study project was proven to be very effective in lifting students’ enthusiasm in learning science, helping students to develop their experimental and discussion skill, and in giving opportunities to students in developing their own scientific concept by themselves. It was also reported that by using constructivism approach, the students may find out their best style of learning. Competition rises among groups of students in presenting the results of their work and in defending their presentations. This forces students to learn more theory more for their own sake. As a result of Lesson Study activities there were many teaching material developed either by lecturers or by teachers. Those materials were either developed by lecturers or teachers in their own classroom or by lecturers and teachers altogether during Lesson Study activities. In general, lecturers and/or teachers developed the teaching materials after thinking extensively what and how to develop teaching materials for a certain topic, and then develop the materials. Further, they tried out the teaching materials in their classroom and revised those based on the result of the try out.

Learning material designed with problem based learning gives students reflective thinking skills better. Problem-based learning by Boud & Felleti (1997), and Fogarty (1997), stated that the problem-based learning is an approach of learning by making the confrontation to the students with the practical problems, ill-structured, or open-ended stimulus in learning. A more complete explanation expressed by Cunningham et.al. (2000), that is problem-based learning is a teaching strategy that simultaneously develops problem solving strategies, disciplinary knowledge, and skills to put the students in problem solving activities by making the confrontation of the problem structure in the form of real problems in their daily lives. A similar view was also expressed by Barrett (2005), that problem based learning is a process of determining the solution of problem through activities that focus on understanding the problem solution.

Berdasarkan uraian di atas, maka kemampuan mathematical thinking merupakan kemampuan siswa dalam mengambil contoh (exemplifying), mengelompokkan (specializing), melengkapi (completing), menghapus (deleting), memperbaiki(correcting), membandingkan (comparing), meringkas (sorting), mengolah (organizing), merubah (changing), membuat variasi (varying), membuat balikan (reversing), membuat alternatif (altering), menggeneralisasi (generalizing), membuat konjektur (conjecturing), menjelaskan (explaining), menjustifikasi (justifying), memverifikasi (verifying), meyakinkan (convincing), memberikan bantahan (refuting) ketika mereka diberikan tugas/ soal matematik. Adapun indikator dari kemampuan ini adalah Specializing, yakni mencoba beberapa soal, dengan melihat contoh; Generalizing, yakni mencari pola dan hubungan; Conjecturing, yakni memprediksi hubungan dan hasil; dan Convincing, yakni menemukan dan mengkomunikasikan alasan mengapa ‘sesuatu itu’ benar.

Visual Thinking atau Berpikir Visual adalah proses intelektual intuitif dan ide imajinasi visual, baik dalam pencitraan mental atau melalui gambar (Brasseur, 1997 : 130). Goldschmidt (1994), Laseau (1986) menyatakan mengandalkan proses berpikir bahasa gambar visual, bentuk, pola, tekstur, symbol. Namun Visual Thinking memerlukan lebih banyak dari pada visualisasi atau representasi. John Steiner (1997) menyatakan “ Ini adalah mewakili sensasi pengetahuan dalam bentuk struktur ide, aliran ide itu bisa sebagai gambar, diagram, penjelasan model, lukisan yang diatur ide- ide besar dan penyelesaian sederhana.

Dengan ini saya menyatakan bahwa tesis dengan judul “ Meningkatkan Kemampuan Mathematical Visual Thinking Dan Self-Efficacy Siswa SMP Melalui Metode Discovery Learning ” ini beserta seluruh isinya adalah benar- benar karya saya sendiri, dan saya tidak melakukan penjiplakan atau pengutipan dengan cara yang tidak sesuai dengan etika keilmuan yang berlaku dalam masyarakat keilmuan. Atas pernyataan ini, saya siap menanggung resiko/sanksi yang dijatuhkan kepada saya apabila kemudian ditemukan adanya pelanggaran terhadap etika keilmuan dalam karya saya ini, atau ada klaim dari pihak lain terhadap keaslian karya saya ini.

In this research, creative thinking is viewed as a single unit or a combination of logical thinking and divergent thinking to produce something different (novelty), which is one indication of the emergence of mathematical creative thinking abilities of students. Another indication is associated with the ability of logical thinking and divergent thinking. In addition to novelty, someone who thinks creatively also bring flexibility in solving a problem. According to Haylock (1997), creative thinking is considered almost always involves flexibility and smoothness as well as in the context of mathematics, smoothness criteria seem less useful than flexibility. Flexibility also emphasizes the many different ideas were used. So in mathematics to assess the divergence can use the product flexibility and novelty criterion. Another is the eligibility criteria (appropriateness). Mathematical response may indicate that high novelty, but it is useless if it does not fit in the general mathematical criteria. So, based on some opinions that creative thinking skills can be shown of flexibility, fluency, originality, feasibility or usability. This indicator can be simplified or combined with common sense look into suppleness, smoothness, and novelty. While the feasibility or utility is included in these three aspects.

Scristia, 2014 MENINGKATKAN KEMAMPUAN MATHEMATICAL VISUAL THINKING DAN SELF-EFFICACY SISWA SMP MELALUI METODE DISCOVERY LEARNING Universitas Pendidikan Indonesia | repository.upi.ed[r]

David Tall indicated that various studies carried out by doctoral students at Warwick University in countries around the world reveal a widespread goal of ‘raising standards’ in mathematics learning, which are tested by tests that could promote conceptual long-term learning, but in practice, often produce short-term procedural learning that is may be less successful in developing long-term flexibility in understanding and solving non-routine problems. Looking at the total picture of long-term learning, what emerges is the absolute necessity of the teacher helping the student to construct thinkable concepts that not only enable students to solve current problems, but also to move on to greater sophistication. In a given situation, the learning of efficient procedures to do mathematics is an important part of learning, but in the long-term, it is essential to compress knowledge into thinkable concepts that will work in more sophisticated ways. This can be done by building on embodied experiences that can give insightful meanings suitable for initial learning but may include met-befores that can hinder future sophistication. Here it is essential to focus on the development of flexible thinking with the symbolism that compresses processes that can be used to solve mathematical problems into procepts that can be used to think about mathematics.