Reflection On Mathematics Problem Solving And Ability

Mathematics study is a kind of activity far from being concrete relatively, and from the reality. It highlights self-consciousness. It needs even more study ability, self-questioning, coordination and unity in between. However, teachers in maths teaching, at present, haven't realized its' importance. Instead, they dispise the basic conception, madly cling to doing masses of exercises. And they are satisfied with obtaining the correct answers. Teachers seldom introspect the solving course, or summerize the experience and lessons. What's worse, the fact that they scarecely do amplificaiton , and generalize the thinking methods, results in "High Investment, Low output", as a result, both teachers and students suffer a lot and bear much burder. Therefore, students should be given chances to repeat what they've leaned so that they could have time and oppotunities to introspect their thoughts to develop the ability of the reflection on Mathematics problem solving.The reflection of solving problems is one to the activity of doing exercises. It's the re-thinking in a deep level, it not only simply review or repeat the solving-problems study, but it's for the research in the aspects of knowledge, methods, thinking process and strategies in the process of doing mathematics exercises, which remains critical and initiative with possibility for research.The reflection of mathematics solving problems includes: to reflect the process of understanding, to reflect the knowledge, the strategies and the results. In a way, teachers and students both have to make efforts to develop and improve the ability of reflection.