The Research And Teaching Practice About The Relative Of Mathematical Meta-cognitive And The Quality Of Mathematical Thinking

This article based on the research related to the meta-cognitive and quality ofthinking in cognitive psychology, Combined with the qualities of the mathematicalmeta-cognitive and the quality of mathematical thinking, this paper makes a researchabout the relative of the mathematical meta-cognitive and the quality of mathematicalthinking, which opens a new way for the cultivation of the quality of mathematicalthinking. This article explores the problem about the development of the abilities ofmathematical meta-cognitive on the basis of the existing theories and relative research.It provides some concrete teaching principles and teaching method for teachers.Mathematics has been regarded as the gymnastics of thinking for many years,therefore to cultivate students' mathematical thinking abilities is the key in the wholemiddle school mathematical teaching .The new curriculum reform also stresses theimportance of developing students' thinking abilities in the mathematical teaching andof making students have high mathematical thinking abilities .Through the researchtowards the relative of the mathematical meta-cognitive and the quality of mathematicalthinking , this article finds a new break-through for the cultivation of the mathematicalthinking abilities, i ,e, to cultivate students' mathematical thinking abilities throughimproving students' mathematical meta-cognitive levels .Many research related to meta-cognitive and the qualities of mathematical thinkinghave been made both at home and abroad. Based on these researches, this article makesdefinitions towards meta-cognitive and the quality of mathematical thinking. Forinstance, meta-cognitive includes meta-cognitive knowledge, meta-cognitiveexperience and meta-cognitive control .The three parts interact, combine dynamicallyand compose meta-cognitive together. The quality of mathematical thinking mainlyconsists of compactness, flexibility, criticism, originality and broadness. These fiveaspects basically generalize students' quality of mathematical thinking and also reflectsthe levels of students' thinking abilities.The research related to the relative of mathematical meta-cognitive and the qualityof mathematical thinking requires some relative theories as the foundation, thereforethis article chooses some relative theories, intellectual research theories and constructivelearning theory in cognitive psychology as the theoretical basis. The research incognitive psychology studies the essential of the relation between meta-cognitive andthe quality of thinking , getting conclusion of the cause and effect relations and pointingout that the cognitive abilities is the key point for improving the thinking abilities . Themeta-cognitive part is reflected in modern intellectual research theories. As a key part ofintellect, it plays an important role. It coordinates, monitors, controls a person'sintellectual activities and reflects the difference of individual's intellect and thinkingabilities. The constructivism learning theory reveals the thinking constructive process inthe mathematical process. Self-examination is the basis form that mathematicalmeta-cognitive takes effect in the mathematical thinking constructive process. Thedeficiency of the habit of self-examination and lacking in self-examination abilities arealso the weakness of mathematical meta-cognitive. It will result in insufficiency in themathematical thinking.On the basis of existing research, this article makes some relative researchestowards middle school students' quality of mathematical thinking and mathematicalmeta-cognitive. Through the mathematical meta-cognitive investigation papers andmathematical thinking quality test papers, this paper makes tests and investigationstowards mathematical meta-cognitive and the quality of mathematical thinking. Havingadopted the software spss10.0 on computers to make some analysis of the data, someconclusions are made as follows. Firstly, generally speaking, middle school studentshave a relative low mathematical meta-cognitive levels and their developing levels arenot balanced. The levels of the students' quality mathematical thinking are different invarious aspects and the whole level is not satisfying, too. Secondly, the quality ofmathematical thinking has evident relevance with mathematical meta-cognitive. Thirdly,the quality of mathematical thinking and mathematical meta-cognitive have evidentrelationship with students' mathematical learning achievements and both of theminfluence students' mathematical learning achievements. The fourth, boy students andgirl students basically have no evident difference in mathematical meta-cognitive andmathematical thinking, and there are no instinct differences in individual aspects. Thelast, top students, middle students and poor students have evident differences in twoaspects. This article makes some investigations of the cause and provides the basis forthe teaching suggestions on the basis of analysis of the result.Combined the result of the investigation and researches with the existing theories,the article makes an analysis of the feasibility of the cultivation of the mathematicalmate-cognitive abilities and gives some concrete strategies and teaching methods. Last,this paper provides two teaching cases, hoping it can give mathematical teachers someinspiration and help them in some specific mathematics teaching works so that they canimprove students' mathematical meta-cognitive levels and cultivate their mathematicalthinking abilities.