“The problem is the heart of mathematics” means that the core of mathematics teaching is focusing on problems. Through problems’ analyses and solving process, the key part is the problem-solving thinking, which directly affects the students’ problem-solving efficiency and results. As a consequence, it is of great importance to work on students’ thinking ability. Researching on this topic, teachers should know about the thinking barriers occurring in the process of developing students’ thinking ability and the breakthrough strategies to these barriers.Constructivism holds the view that it is reconstructing the knowledge that is the essence of students’ learning and that solving problems is a crucial process of the students’ learning. The knowledge system for students in Senior High is larger and more complex and the knowledge reconstruction is fully embodied in the process of problem solving. Hence, what teachers should pay most attention to is the thinking barriers in students’ problem solving as well as how students reflect on and solve a problem.This study firstly discusses on the main thinking barriers that students have in solving a problem, then focuses on how to break through these barriers effectively based on the author’s accumulated experience and gains from teaching practice, so as to improve students’ mathematical thinking ability and form a good mathematical quality. In order to guarantee the innovation and authenticity of the research,this essay mainly adopts the methods of literature research and questionnaire survey. By analyzing the questionnaire survey, the author works on the particular examples of students’ thinking barriers. As for the questionnaire, it consists of two parts. The first part is to classify some items in accordance with the lately three-year mathematic after-school assignments’ quality statistics. Then it combines these items into a test paper, which is used to survey the students’ main thinking barriers. The second part is to further design a questionnaire to survey the thinking situations occurring in the first part’s items. Lastly, this study, according to the author’s own teaching understanding and experience, summarizes some strategies and methods to break through the barriers occurring in the development of thinking ability. |