Reflective Theory Of Mathematics Learning And Teaching Strategies

On the basis of the previous achievement of reflective mathematicslearning and from the idea of quality-oriental education and thebackground of new curriculum reform, this article has researched onreflective mathematics learning on the aspects of theories and teachingstrategies. This article has marked a boundary among the three termsreflection, reflection, mathematics reflection and reflectivemathematics learning. It has preliminarily researched on the connotationof reflective mathematics learning on the basis of previous theoreticalresearch, analyzed the theoretical foundation, model, content, and thefactors that impact the effect of reflective mathematics learning. Thearticle has also discriminated several interrelated ideas, such asreflective mathematics learning, operational mathematics study andexploratory mathematics study. At last, it puts forward some teachingstrategies related to reflective mathematic study. Specificallyspeaking, this article emphatically expounds some content as follows.1.The chief idea of new curriculum standard is to promotestudents'progress. At the same time, students'progress is realized bymeans of mathematics study. Therefore ,the mathematics study process ofstudents'should be earnestly focused on. That is to say, the reform onstudents'mathematics study pattern should be discussed and reflectivemathematics study should be initiated. This article classifies reflectivemathematics study and differentiate some interrelated ideas.2. The characteristics of reflective mathematics study are as follows.Exploration: The spirit of reflective mathematics study is "puttingforward questions---exploring questions---solving questions".Exploration is the most fundamental characteristic of reflectivemathematics study. Initiative: Reflective mathematics study is anindependent action process of students. They make researches in theprocess of independently, conscientiously and actively. Development:Reflective mathematics study is a complicated, exploratory, reasonablestudy action. It aims at "learning how to study" and pays attention tothe future development of students. Creation: Reflection shows theessence of questions, explores general law, connects the interrelationbetween all kinds of knowledge, promotes assimilation and shift ofknowledge and then makes students get discovery and invention. Criticism:The reflective of mathematics study shows the color of self –negation.The whole process reflects the courage of self –dissection and self–criticism. Situation: Reflective mathematics study is in view theconcrete process of study. There is no immutable reflection.3. The article expounds the theoretical foundation of reflective studyfrom the aspects of meta cognitive theory, subjective education theory,constructivism study theory and D .P .Ausubel's cognitive study theory.The formation of meta cognitive theory and the expansion of reflectiveidea not only clarify the connotation and step and make them understoodeasily, but also turn reflection to be concrete practice from a purepsychological phenomenon. Subjective education theory put the idea ofgiving scope to subjectivity into a predominant position. Reflectivemathematics study does work by means of students' subjective reflection.Therefore, in this kind of study process, students' subjective positionshould be fulfilled so that students' initiative can be stimulated.Constructivism study theory holds study to be reflective, because"reflection" is students' self-estimate, which can promote theformation and development of new ideas so that constructive actions canbe promoted .D .P .Ausubel's cognitive study theory holds thatstudents' previous knowledge level and cognitive level should be paidattention to when new knowledge is input. Students' ability of insight,self-check and self-estimate should be focused on. In other words,students' reflection should be thought highly of.4. The process of reflection is the meta cognitive process as wellas question –solving process. The article shows cognitive reflectionmodel and fundamental steps of reflective mathematics study, which includeself-examination stage, estimate-stage, perceiving question stage,practice test stage and conclusion and enhancement stage. In addition,reflective content of reflective mathematics study is one of the importantContents in this article, which is expounded from three aspects. First,students should be asked to self-reflect on the aspects of mathematicsstudy cognition. Second, students should be asked to self-reflect on theaspect of mathematics study action. Third, students should be asked toself-reflect on the aspect of emotion experience.5. There exist two factors that impact the effect of reflectivemathematics study. Firstly, students themselves' factors. Students'thought development level, non-cognitive factor and their mathematicsstudy style impact the effect of reflective mathematics study. Secondly,external factors, such as teachers have an effect on reflectivemathematics study. Teachers' teaching model, teachers' reflectionlevel and quality, education, circumstances are all include in theexternal factors.6. In order to guide students' reflective mathematics study, makethem obtain knowledge effectively and at the same time, raise myinnovation ability and practice ability , the following teachingstrategies related to reflective mathematics study are put forwardspecially: create question situation and enlighten students' reflectionmotive;pay attention to the teaching of reflective mathematics studyprocess and help students form new mathematics cognitive framework;design reflective mathematics questions and improve the effect of theirreflective mathematics study;instruct students reflect conscientiouslyand cultivate their mathematics reflective ability.