models for teaching and learning mathematics -...
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Teaching and Learning model is a generalized instructional process which may be used for many different topics in a variety of subjects
Teaching and Learning Strategy is a particular procedure for teaching a specific topic or lesson
(Bell, 1978)
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Pola pembelajaran khusus yang direncanakanuntuk mencapai tujuan belajar tertentu.
Sesungguhnya disusun untuk mengarahkanbelajar, dimana guru membantu siswa untukmemperoleh informsi, ide, ketrampilan, nilaicara berfikir dan mengekspresikan dirinya.
Pola interaksi siswa dengan guru di dalamkelas yang mencakup strategi, pendekatan, metode, bahan ajar, media, teknikpembelajaran dan evaluasi yang diterapkandalam pelaksanaan kegiatan belajar mengajardi kelas.
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Models represent the broadest level of instructional practices and present a philosophical orientation to instruction.
Models are used to select and to structure teaching strategies, methods, skills, and student activities for a particular instructional emphasis.
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Within each model several strategies can be used. Strategies determine the approach a teacher may take to achieve learning objectives. Strategies can be classed as direct, indirect, interactive, experiential, or independent.
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Methods are used by teachers to create learning environments and to specify the nature of the activity in which the teacher and learner will be involved during the lesson. While particular methods are often associated with certain strategies, some methods may be found within a variety of strategies.
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Skills are the most specific instructional behaviour. These include such techniques as questioning, discussing, direction-giving, explaining, and demonstrating. They also include such actions as planning, structuring, focusing, and managing.
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Rasional teoritik yang logis yang disusun olehpara pengembangnya
Landasan tentang apa dan bagaimana siswabelajar (tujuan pembelajaran yang akandicapai)
Tingkah laku mengajar yang diperlukan agar model tersebut dapat diimplementasikandengan berhasil
Lingkungan pembelajaran yang diperlukanagar tujuan pembelajaran itu dapat tercapai
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Syntax
menyatakan aksi atau langkah-langkahimplementasi model
The Social System
Aturan yang berkaitan dengan peran guru dansiswa serta hal-hal yang mendukungnya
Priciples of Reaction
Bagimana guru memandang siswa danbagaimana merespon apa siswa kerjakan.
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Support system
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Behavioral models, yang menekankan pada aspekperubahan prilaku dalam belajar. Dalam kelompokini terdapat model-model pembelajaranContingency Management, Self Control ThoughOperant Methods, Training Model, Stress Reduction,Desensitization dan Assertiveness Training.
Social Interaction, yang menekankan padahubungan individu terhadap masyarakat atauorang lain. Model-model pembelajaran yangtermasuk dalam kelompok ini adalah GroupInvestigations, Role Playing, Jurisprudential Inquiry,Laboratory Training, Social Simulation dan SocialInquiry.
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Personal Source, yang penekanannya padaperkembangan individu yakni bagaimana individumembangun konsep dan mengorganisasikan realitasyang unik. Dalam kelompok ini terdapat beberapamodel pembelajaran Nondirective Teaching, Synectivs, Awareness Training dan Classroom Meeting Model.
Information Processing, yang penekanannya padaberfikir ptoduktif, menggunakan ketrampilanintelektual umum yang semuanya berasal dariakademik. Dalam kelompok ini terdapat model-model pembelajaran Concept Attaintment, Inductive Thinking, Inquiry Training, Memory Model, Cognitive Growth, Biological Science Inquiry Model dan Advance Organizer.
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• Sorting an ordering (rangking) students for job criteria and future
• Textbook oriented• Teacher-centre• Student passive
learning• Paper and pencil• Chalk and talk• One way
communication
• Real world• Applicable• Contextual• Student strategy
as starting point
• Student centre• Active participants• Reinvention• Problem Solving• Inquiry• Investigative• Explorative• Two way
communication
• Abstract• Realy-made• Strictly body of
knowledge• Immutable truth• Uncquistionable
Stu
den
t Th
emes
Student needs (interest, ability, etc.)
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Pr i nci pl es of Mat hemat i cs Teachi ng & Learni ng
• Actively involve students
• Learning is developmental.
• Build on previous learning
• Communications is integral
• Good questions facilitate learning
• Manipulative aid learning
• Metacognition affects learning
• Teacher attitudes are vital
• Experiences influence anxiety
• Gender aptitudes are equal
• Retention can improve
6/2/2010 Jarnawi Afgani
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6/2/2010 Jarnawi Afgani
Meaningful Learning/
problem solving
Knowledges and skills
Before
instruction
During Instruction After Instruction
Typical learning retention curve
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Direct Object in Learning Mathematics
Teaching /Learning Models
FactsSkillsConceptsPrinciples
Expository modelAdvanced Organizer modelDiscovery modelGame ModelIndividualized modelSpiral Model
Indirect Objects in Learning Math.
Theorem ProvingProblem SolvingTransfer of learningLearning how to learnIntellectual developmentWorking IndividuallyWorking GroupPositive Attitudes
Theorem proving modelProblem Solving ModelLaboratory ModelInquiry modelGroup Processes modelComputer-augmented model
Teaching /Learning Models
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Fakta berupa konversi-konversi yang diungkap dengan simbol tertentu. Misal simbol bilangan “3” secara umum dipahami sebagai bilangan “tiga”
Konsep adalah ide abstrak yang dapat digunakan untuk menggolongkan sekumpulan objek. Apakah objek tertentu merupakan contoh atau bukan contoh konsep.
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Definisi adalah ungkapan yang membatasi suatukonsep. Dengan definisi orang dapat membuatilustrasi, gambar atau lambang. Dari konsep yang didefinisikan, sehingga menjadi jelas apa yang dimaksud.
Definisi ada dua macam, definisi analitis dan definisigenetik.
Definisi analitis adalah definisi yang menyebutkangenus proksimum (genus terdekat) dan diferensiaspesifika (pembeda khusus)
Definisi genetik adalah definisi yang menyebutkanbagaimana konsep itu terbentuk atau terjadi
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Operasi adalah pengerjaan hitung, pengerjaanaljabar dan pengerjaan matematika yang lainnya.
Prinsip adalah objek matematika yang kompleks. Prinsip dapat terdiri dari beberapafakta, beberapa konsep yang dikaitkan olehsuatu relasi atau operasi. Contohnya aksioma, teorema, sifat, dll.