Pada penelitian ini yang berhubungan dengan belajar menurut konstruktivisme adalah bahwa dalam pembelajaran matematika terdapat proses
pemecahan masalah. Dalam pembelajaran menggunakan model Problem Based Learning dengan strategi Problem Posing dalam pembelajaran siswa diajarkan
bagaimana proses dalam pemecahan masalah.
2.1.2 Model Pembelajaran
Model pembelajaran matematika adalah kerangka kerja konseptual tentang pembelajaran matematika. Pembelajaran matematika dimaksud adalah peserta
didik belajar matematika dan pengajar mentransformasi pengetahuan matematika serta memfasilitasi kegiatan pembelajaran Hamzah Muhlisrarini, 2014.
Ciri-ciri model pembelajaran menurut Rusman 2014 adalah: 1 berdasarkan teori pendidikan dan teori belajar dari para ahli teorema; 2
mempunyai misi atau tujuan pendidikan tertentu; 3 dapat dijadikan pedoman untuk perbaikan kegiatan belajar mengajar di kelas; 4 memiliki bagian
– bagian model yang dinamakan urutan langkah-langkah syntax, adanya prinsip-prinsip
reaksi, sistem sosial, dan sistem pendukung; 5 memiliki dampak sebagai akibat terapan model pembelajaran; dan 6 membuat persiapan pengajaran desain
instruksional dengan pedoman model pembelajaran yang dipilihnya. Sedangkan ciri-ciri khusus yang harus dimiliki model pembelajaran
matematika secara umum adalah: 1 rasional teoritik yang logis yang disusun oleh para pencipta atau pengembangnya; 2 tujuan pembelajaran yang harus
dicapai; 3 tingkah laku mengajar yang diperlukan agar model tersebut dapat dilaksanakan dengan baik dan berhasil; dan 4 lingkungan belajar yang
diperlukan agar tujuan pembelajaran dapat tercapai Hamzah Muhlisrarini, 2014.
2.1.3 Model Pembelajaran PBL
Model Problem Based Learning merupakan model pembelajaran yang melibatkan siswa dalam memecahkan masalah nyata. Model ini menyebabkan
motivasi dan rasa ingin tahu menjadi meningkat. Model PBL juga menjadi wadah bagi siswa untuk dapat mengembangkan cara berpikir kritis dan keterampilan
berpikir yang lebih tinggi Gunantara, 2014. Menurut CTL 2001 “overall, PBL
is an effective method for improving student‟s problem solving skills”. Model pembelajaran PBL sesuai dengan filosofi konstruktivis, yaitu
pebelajar peserta didik diberi kesempatan lebih banyak untuk aktif mencari dan memproses informasi sendiri, membangun pengetahuan sendiri, dan membangun
makna berdasarkan pengalaman yang diperolehnya Sudewi, 2014. Hilman 2003 menyatakan bahwa:
PBL constitutes a problem to be solved. There are many differences between an ill structured and a well-structured problem. Instruction
about problem solving in the classroom is a process whereby students are presented with a problem and it is solved by the end of
the lesson. This is different from professional problem solving where the problem is the first point of contact and leads to investigation and
knowledge. PBL gives students the chance to experience professional style ill structured and pragmatic problems. The curriculum and
design of PBL allows.
Dengan membiasakan pembelajaran berbasis masalah diharapkan siswa percaya diri, gigih, berfikir fleksibel dalam mengeksplorasi ide-ide matematis, dan
senang belajar matematika sehingga meningkatkan disposisi matematiknya Choridah, 2013. Hal ini didukung pendapat CTL 2001 bahwa:
PBL promotes students‟ confidence in their problemsolving skills
and strives to make them self-directed learners. These skills can put PBL students at an advantage in future courses and in their careers.
Dalam Problem Based Learning peran guru adalah menyodorkan berbagai masalah autentik sehingga jelas bahwa dituntut keaktifan siswa untuk dapat
menyelesaikan masalah tersebut. Setelah masalah diperoleh maka selanjutnya melakukan perumusan masalah, dari masalah masalah tersebut kemudian
dipecahkan secara bersama sama dengan didiskusikan Wulandari, 2013. Terdapat lima kunci utama dalam PBL menurut Newman 2005 adalah sebagai
berikut: 1.
Teacher as Facilitator In the classroom, the PBL teacher employs his or her knowledge
of the „„subject‟‟ area to support the processes of cognitive or metacognitive development andor enculturation. The PBL
literature suggests a number of techniques that PBL teachers may adopt in their interactions with students.
2. The Use of an Explicit Process to Facilitate Learning
The tutorial process is used as a framework to assist in the development and practice of affective, cognitive, and
metacognitive skills. There are different models of the PBL tutorial process.
3. Use of „„Problems‟‟ to Stimulate, Contextualize and Integrate
Learning. In the literature on PBL the terms „„problem,‟‟ „„trigger,‟‟ and
„„scenario‟‟ are used to refer to the material presented to students in initiating a specific learning cycle. Often these terms
are used interchangeably, even when, in practice, there appear to be significant differences in the material presented. To avoid
confusion, the term „„scenario‟‟ will be used here. 4.
Learning in Small Groups The „„structures‟‟ in small group PBL, along with the tutorial
process and the use of scenarios, help the students learn how to learn in groups and learn how to anticipate, prevent, cope with,
and deal with the difficulties that they will experience working in this way. This is not to say that these structures are present in
the organization of all PBL small group learning environments.
5. Assessment and Problem Based Learning
There is a shared view among PBL advocates that assess-ment drives learning and that there should be alignment between the
goals of a PBL program and what is assessed. However, the consequences of this view are interpreted differently.
Arends dalan Burris, 2005 menggambarkan lima fase utama dalan Problem Based Learning PBL. Arends mengidentifikasi fase-fase tersebut
disertai dengan tindakan guru dalam setiap fase pembelajaran. Fase-fase Problem Based Learning PBL dapat dilihat pada Tabel 2.1.
Tabel 2.1 Fase Problem Based Learning Phase
Behavior Phase 1 Orient student to
the problem Teacher goes over the objectives the lesson,
discribes important logistical requirements, and motivates student to engange in self-selected
problem-solving activity.
Phase 2 Organize students for study
Teacher help student define and organize study tasks related to the problem.
Phase 3 Assist independent and
group investigation
Teacher encourages
students to
gather appropriate information, conduct experiment,
and search for explanations and solution.
Phase 4 Develop and
present artifacts and exhibits
Teacher assists student in planning and preparing appopriate artifacs such as reports,
videos, and models and helps them share their work with others.
Phase 5 Analyze and
evaluate the
problem-solving process
Teacher help students to reflect on their investigations and the processes they used.
2.1.4 Strategi Problem Posing
