Although, the history of mathematics presented that mathematics came from ancient Babylonia,  but I disagree that ideas of mathematics have taken of  it until contemporary periode. Based on Hans Freudental’s comment (Sutarto Hadi, 2005)  mathematics as human activity, so i can assumpt that ideas of mathematics there was since first human being in world.
 we intuitively research the realm of mathematical truth. In history of mathematatics, Thales  found way of counting high of piramid not intentionally. We  can  can intuitively research in learning mathematics too. Experience of learning can make to research. For example,  communications between teacher and student earn  analysis, and made to research into.
Lesson Study represent an model construction of educator profession through study  by kolaboratif and continuation   have principal  kolegalitas and  mutual learning to develop build community learning. Lesson Study does not study, but in lesson studi activity teacher can choose and apply various method or   study strategy which according to  situation, condition and problem in learning. Teacher can do research in learning  into through lesson study. Marsigit (2007) said that Lesson studies for secondary mathematics were carried out by mainly Classroom Action Research approach. They carried out to improve the teaching learning practices and to find more appropriate methods for facilitating students learning. Teachers’ experiences have been shared with other teachers and the lectures.
I agree with katagiri,  attitude in learning mathematics not merely student sit better pay attention clarification of  teacher. I assume Mathematical attitude according to katagiri is visible student activity, like  Attempting to have questions, Attempting to maintain a problem consciousness, etc. But , how  do teacher develop mathematical attitude in learning mathematics?
Problem solving can and should be taught! The process has been analyzed and can be represented as a series of steps, referred to as a heuristic plan, or, simply, heuristics.  Teacher can develop problem solving process elicits mathematical thinking and method with develop reasoning and communication.
References.
Marsigit. (2007). Mathematics Teachers’ Professional Development through Lesson Study in Indonesia. Eurasia journal of mathematics, Science & Tehnology Education, 2007, 3(2), 141-144.
Sutarto Hadi. (2005). Pendidikan matematika Realistik. Banjarmasin: Tulip
 
 
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Bagus. Ibu telah menapak selangkah lebih maju. Sambil menyiapkan proposal sambil pula belajar, coba tolong ibu buat artikel tentang penelitian jenis R & D dan penerapannya untuk mengembangkan model-model pembelajaran. Selamat atas Blognya (Dosen: Dr. Marsigit)
Jika sudah mendapat referensi tentang R&D silahkan segera hubungi saya (Pembimbing: Dr. Marsigit)
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