On The Mathematical Symbol Meaning And Obtaining Ability Cultivation

Why do students feel more difficult and boring to learn mathematics in the higher grade, not understand what teachers teach repeatedly, not do what they have understood, and do wrong with what they can do? A statistics of symbols of the mathematics teaching materials show that the quantity of new symbols the junior students need to learn is3times the elementary students. A questionnaires survey to the students’ mathematical Symbol-meaning-obtain-ability found that38%have symbol recognition difficulty,45%only get one meaning,17%can get two or more meaning, and all stages students have no obvious difference. It shows that the numbers of mathematical symbols with concise form and complex meaning increase sharply but the students’ mathematical symbol meaning obtaining ability is still in low level is the root cause of mathematical learning difficulty. For this, the research puts forward a hypothesis:to cultivate students’ mathematical symbol meaning obtain ability is the effective method to solve the above problem.First of all, this paper expounds the basic methods and basic principle of semiotics. The existence state and change law of things is influenced by both internal elements and external environment factors. Each symbol is a union of symbolic form (sign) and exists in symbol structure. To get the symbol meaning need study the element structure, coupling structure and meaning structure three levels of symbol structure.Secondly, this paper discusses the semiotics’ teaching implication and the new interpretation of traditional "symbol","knowledge","learning" and "teaching". Symbols is a kind of objective existence form to stimulate people’s senses in essence which include both language symbols and other known object to cause meaning association. All things that can stimulate students producing meaning association, help students understand the content of the teaching in teaching activities such as model, gestures, video, teaching material and so on should be regarded as symbols, as teaching resources. Knowledge is the union of knowledge external (sign) and knowledge internal representation (experience) and it should not only as experience, and should be regarded as symbol structure. Any human thoughts can transfer to others through the symbol directly or through the symbol structure indirectly. The external representation of Individual knowledge constitutes the individual "mark world"(mark structure) with the real world correspondingly, and the internal representation of the individual constitutes "cognitive world"(cognitive structure) with "mark world" correspondingly. Symbol structure with mark structure and cognitive structure represent the individual all knowledge and the comprehensive ability to adapt to and remake the real world. The human sensory can only sense the part attributes of the whole things. The stimulus (sign) sensing attribute and meaning (feel representation) are united together to become a natural symbol. When feeling representation constitute perceptual representation (perceptual experience) by perceptual thinking process, the sign with sensory representation correspondingly coupling into natural symbol structure and Establish corresponding relation with objective things. When feeling representation constitute a perceptual image (concept) not existing in the world by rational thinking process, human beings need create artificial symbols to represent the image and establish corresponding relation between the rational experience based on the concept and artificial symbol structure. Therefore, the process of learning knowledge is essentially the process to construct symbol structure which includes three mutual conversion processes:objective things become experience; symbol become experience; experience become symbol. Knowledge teaching is the process that teacher help students construct symbol structure.thirdly, based on the semiotics the study define connotation of the mathematical symbol, mathematical symbol meaning, mathematical symbol meaning obtain ability, analyzes the factors and difficulties in cultivating the ability to obtain mathematical symbol meaning, and make case studies in the mathematics concept teaching, mathematical proposition teaching and mathematical problem-solving teaching. In the semiotics perspective, mathematical symbol is symbol bearing mathematical information, mainly including mathematics natural symbol, mathematics model symbol, mathematics phonetic symbol, mathematics text symbols, mathematics professional symbol, mathematics chart symbol, mathematics behavior symbol. Mathematical symbol meaning is the whole mathematical symbol structure activated by the mathematical symbols, mainly including the mathematical symbol’s form significance, basic meaning, conversion significance, implicit meaning and aesthetic significance, personalized significance, operational meaning seven kind of significance, and it can be measure with the number of marks in the mathematical symbol structure. Mathematical symbol meaning obtaining ability refers to the capacity constructing mathematical symbol structure with the mathematical symbol stimulus, mainly including the mathematical symbol form perceptual ability, meaning association ability, meaning transformation ability, meaning integrated ability and mark operation ability. The factors to Influence the cultivation of mathematical symbol significance are mainly mathematics teachers’ mathematical symbol view, teaching resource view, mathematics teaching view and teaching method view. In the mathematics teaching, teachers should change teaching view, select, arrange and present mathematical symbol resources scientifically, apply symbol structure analysis method flexibly, teach students the basic method and thinking mode to construct mathematical symbol meaning structure, discusses the multiple representation of mathematical symbol, construct the mathematical symbol meaning structure comprehensively, and make it become students’cognitive structure in order to promote students’ mathematical quality, to promote the all-round development of students on the basis of the request of mathematics curriculum.Finally, the paper summarize the basic logic of this study:(1) not getting mathematical symbol rich mathematical meaning is the main cause making students be afraid of, and hate mathematics, feeling difficult to learn mathematics;(2) the teachers’ignoring mathematical symbol teaching is the main reason to lead to students’ mathematical symbol meaning obtain ability lower;(3) the teacher’one-sided mathematical symbol view and knowledge view is the main reason causing teachers ignore mathematical symbol teaching;(4) mathematical symbol structure contains all information of the mathematical knowledge which need the learner’ perception, discovery, digestion and construction;(5) getting the information of mathematical symbol structure need students with higher mathematical symbol meaning obtain ability;(6) the core to training mathematical symbol meaning obtain ability is to think "what it means" more than "what it is";(7) training students’mathematical symbol meaning obtain ability need teachers to change their one-sided symbolic view, knowledge view, learning view and teaching view. The final conclusion is that cultivating and improving the students’ mathematical symbol meaning obtain ability is the effective, feasible, operational ways and methods to solve some problems in teaching.