The Study Of Cultivating Mathematical Problem Consciousness Of Junior Middle School Students

"The mathematics curriculum standards of full-time compulsory education"(2011)clearly states: "The cultivation of innovation consciousness is the basic task of mathematics education in modern,should be reflected in the process of mathematics teaching and learning." The cultivation of innovative consciousness should start from the compulsory education stage,throughout the mathematics education.This study aims to cultivate students' consciousness of mathematics,and realize the goal of cultivating innovation consciousness in mathematics teaching.We try to establish a relationship between the cultivation of mathematical problem consciousness and the improvement of mathematical problem solving ability to lay the foundation for students' sense of innovation.By optimizing the teaching process of mathematical problems solving,and penetrate the "problem consciousness" is needed for the teaching of mathematical problem solving,but also to to provide operational strategies for teaching of mathematical innovation awareness.The formation of mathematical problem consciousness is a raising level process,which is based on cultivating in purpose.So,it is related naturally to the level of development of mathematical problems awareness.The level of development of mathematical problem consciousness proposed in this study is through three latitudes that were problem solving process,thinking development and problem type.As a first step in the process of mathematical problem solving,the mathematical problem consciousness is also an important starting point for the interrelations of the rest of the rings(ie,finding problems,asking questions,analyzing questions,answering questions,reflecting questions,etc.).At the same time,the links of mathematical problem consciousness continue to improve in each link,and then enter the formation of "reflection consciousness" link it will enter a higher level of problem awareness.At the thinking level,we will analyze the mathematical problem consciousness from seven levels,concluding the real level,the relationship level,the method level,the knowledge level,the ability level,the thinking level and the theoretical level.For relating to innovation consciousness,we divide the problem into two categories: inevitable and contingent.The teacher's design training program is focus on inevitable problem.The development level of the problem consciousness on contingent problem is the important link of students' independent thinking and inquiry based on study of inevitable problem.It is also a important place of cultivation and improvement of the students' innovation consciousness.It is a new way to study the mathematical problem consciousness from different development level.Finally,based on the systematic and hierarchical research of mathematical problem consciousness,it is also an important point to study design program both in macro and micro.At the macro level,from the perspective of teaching and learning on the three aspects like pre-class,classroom,after class,we designed training program of mathematical problems awareness.And in the micro,as carrier of algebra content of the "practical problems and one yuan equation" in junior middle school,we gives a detailed mathematical problem awareness training program.The main idea is to execute the "six step" problem solving steps on the two issues of inevitable and contingent,at different levels of thinking,which are headed by problem consciousness.It is hoped that this study will play an active role in the teaching process of cultivating the mathematical problem consciousness,and the optimization of teaching process of mathmatical capacity,and the research of mathematics teaching problems,also in cultivating student's innovation consciousness.