Some Philosophical Consideration About The Mathematics Teaching By Using Mathematical Situations And Problem Posing In High Schools And Primary Schools

Consideration from the philosophy angle is significant to the practice and research of education. Teachers can build up correct education ideas and improve their teaching through philosophical thoughts. Education researchers can grasp the substance of education and consider dialectically through philosophical thoughts. It is a work of ages meaning to consider the philosophical base of the current mathematics course reform. Mathematics teaching by using mathematical situations and problem posing in high schools and primary schools (ie: the "situation—problem" teaching) is an education experiment to promote the mathematics course reform. Because the "situation—problem"teaching is guided by the principles of the mathematics course reform, consideration to the "situation—problem"teaching is also to the mathematics course reform. The views of mathematics philosophy are the base of the mathematics teaching theories. The change about the views of the knowledge is a background of the change about the views of mathematics philosophy. The static and absolute views of the knowledge is converting to dynamic and relative views. The absolute views of mathematics philosophy is also converting to the social views of mathematics philosophy. Mathematics is a compound system of many Factors. Mathematics is constitute of mathematical theories , mathematical methods and mathematical language inside. Mathematics is also human activities constitute of social , history ,culture factors outside. The inside core of mathematical is created through the outside human activities. There are two basic characters in the creating: the posing and solving of the mathematics problems and the constructing of the mathematics model. So mathematics problems are in core position in the "situation—problem"teaching. In the " situation — problem " teaching mathematical situations and problem posing, problem posing and problem solving are dialectical relations. The views of education philosophy are related to the purpose of the mathematics education. Education should service for the development of society as well as for the development of every individual. Scientism and Humanism should be integrated in education. Education promote the development of society in productivity andthe relations of production. Innovative education should be implemented in the mathematics education beside the traditional mathematics education purpose—knowledge education. Mathematics are the free creation of the human activities, which is the premise to implement innovative education in mathematics education. Developing the query spirit is an important way of the innovative education as well as the "situation—problem"teaching. Democracy characters are also developed through the development of "question consciousness". Education should also promote the healthily development of students ˊ personalities. The " situation — problem " teaching is practice of personalizition teaching in mathematics classroom. The views of mathematics teaching philosophy are related the question about "How to teach mathematics". In mathematics teaching students should be the subject role and teachers should be the leading role. In the "situation—problem"teaching the studentsˊ subject role is in three aspects: problem posing,problems solving and application. The teachersˊ leading role is also in three aspects: setting up the mathematics situation and promoting students to pose problems, guiding students to study and timely tuition. The constructism can be implemented in the mathematics teaching. The constructism teaching principles of the " situation —problem"teaching is composed of situation principle,problem principle , activity principle , indepence principle , cooperate principle. The scientific view of development should be applied to the mathematics education. The "situation—problem"teaching is the mathematics teaching in the scientific view of development.