Mathematical Understanding Of Teaching

Understanding is very important on the mathematical learning. Since the 20th century, the mathematical understanding's problem has drowned our mathematical educational circles'attention. Now, the mathematical understanding is a hotspot after the problem solving. Actually, no matter what from the angle of social development or being an educator, it all has important meaning to carry out research of mathematical understanding. According to these acquaintances, the author thinks that going in for teaching and learning's research of mathematical understanding is a very valuable subject of researching.First, this article summarizes the past researching and analyzes the orient of researching based on it. This article breaks through the past researching angle, and research it for students'angle.Second, In order to getting a better explanation and researching of the theme, this article chooses a good theory that belonging to cognition viewpoint, What is Pirie-Kieren model: "transcend and recurrence" mathematical understanding model. This theory describes the understandings process of student's understanding mathematical knowledge. So it provides theoretical foundation for this research. In addition, This article chooses some theories: constructivism and correlation theories.Third, the author analyzes student's understanding learning's conditions and the process factors of mathematical understanding. Subsequently, the article does some strategies of inquiry on understanding learning according to some educational theory, and gives some learning strategies: investigates strategy,errorredress strategy,organizational strategy and recursive strategy.Finally, the author come up with some teaching advices combine with educational theory and research results:In the process of teaching, the teacher should choose some teaching methods what can promote students'understanding learning; he (or she) should provide mathematical activity's opportunities to students; he (or she) should pay attention to classroom communication and reflection:he (or she) should care positive and negative cases teaching to highlight the key features of the concept; the teacher should clarify the process of knowledge generation. These proposals are concluded only on the basis of this study, the author hope it can bring help for understanding teaching.