Experimental Study On Developing Students' Practical Thinking In Grade Seven: Mathematical Open-ended Problem Solving

In mathematical teaching practice, a large number of teachers particularly emphasize on the logical operational and deductive ability of mathematics. Teachers pay great attention to logical preciseness and system formalization, but less attention to practical learning of solving everyday problem; They pay great attention to Individual Monologue Teaching, but less attention to the two-way dialogue > collaboration and interaction between teachers and students, based on real problem. They pay great attention to training students' skills, but less attention to deal with Mathematics directly from life. Therefore, the idea of national primary education on new mathematical curricular standard aims at training students' ability of mathematical application by open-ended problem solving, which is the realistic background where the research topic is raised. The theoretical and experimental studies of practical thinking, tacit knowledge, PIFS curricular and teaching for thinking are studied by the foreign researchers, whereas there is a little study on practical thinking in our country. Integrating the foreign studies with the characteristics of everyday problem, we present that the operational process of practical thinking includes four stages, ranging from raising problem from real life, integrating all materials relating to problem solving, solving problem by different ways to decision making coinciding with real life, which are just correspond to mathematical open-ended problem. On the basis of the corresponding relations between operational process of practical thinking and mathematical open-ended problem, the theory of Constructivism Learning and Situated Cognition and Learning, we present mathematical open-ended problem system and Subject Situated Teaching in order to adapt andconform realistic background of national primary education on new mathematical curricular reform and train students' practical thinking. The study gets the results as follows:i . To a certain extent, question open-ended problem and Subject Situated Teaching can develop students' problem consciousness in Grade seven.ii. Condition open-ended problem and Subject Situated Teaching can efficiently advance students' ability of information integration in Grade seven. The experiment effect of the students with high or medium level was more significant than of what with low level.iii. Method open-ended problem and Subject Situated Teaching can accelerate radiant thinking of students with high level.iv. Conclusion open-ended problem and Subject Situated Teaching can prevent the descent of situated thinking of students in Grade seven, and develop the situated thinking of students with high level.v . Mathematical open-ended problem solving can promote students' practical thinking.