The Research Of Mathematical Understanding Teaching Based On Metacognition In High School

In the new high school curriculum reform, it prominently reflects the value of " process and method", whose essence is to emphasize the understanding of learning and teaching. In mathematics education, it is well known that the primary prerequisite whether students can learn well mathematics is whether students can understand mathematics. How to effectively promote students to understand mathematics is becoming a popular topic in the study of mathematical understanding.The domestic and foreign scholars have done lots of research on it with abundant results. Generally speaking, the research focuses on researching the mathematical understanding of the concept, function, mode and level, evaluation of mathematical understanding, and internal mechanisms of mathematical understanding for students, etc. On the contrary, it is less to focus on the teaching strategies and empirical analysis of mathematical understanding at the stage of secondary school. Numerous studies have shown that metacognition controls the human thinking activity, and is the core of thinking activity as well as the cognitive ability of individual cognition. Mathematical understanding is the means and target in the students’ mathematical cognizance. Metacognition plays an important role in the process of students’mathematical understanding. In view of this, the author puts forward the hypothesis:Metacognitive understandinig teaching positively promotes mathematical teaching in the high school with following research and trial done for the hypothesis.Firstly, the author searched and deeply analysised the literature:analysing related research achievements about the mathematical metacognitive theories, making a critical analysis on the differences of teaching theories about mathematical understanding, including the level of understanding of mathematics, definition of understanding teaching, and the relationship between metacognitive and mathematical understanding.Secondly, the author summarized the expert teachers and his own teaching practice and put forward the understanding teaching principles of high school based on metacognition:promoting the students’matacongition in the principle of growth, principle of returning, principle of multiple representations and principle of circular. It is a conclusion that in the high school mathematical understanding teaching is based on the patterns of metacognitive questions teaching strategies, the process of teaching strategies, reflective teaching strategy.Thirdly, one term of teaching experiments which is based on metacognition of senior mathematical understanding teaching have been executed in high school where the author working for. The results indicated that the obvious progresses could be observed on student math scores by carrying out understanding teaching based on metacognition, meanwhile, according to the questionnaire survey to students,the non-cognitive factors of math study have been improving after beginning of one month experiment, which indicated it really worked on student ability of non-perceiving. In conclusion, the positive impact of teaching for understanding with metacognition on teaching effect could be results from combination both of student scores and non-perceiving factors.At the end, the author reflected on the whole study of teaching experiment to go a step further on advantages and disadvantages of executing understanding teaching with metacognition in math teaching of high school, and the author is trying to put forward some advice based on metacognition in this essay.