The Teaching Modle Research For The Development Of Primary School Students Mathematical Language Ability

Mathematical language is a specific professional language which conveys mathematical knowledge,expresses mathematical ideas and methods and embody the characteristic of mathematics.The key point of education used to emphasis on common language(English)and it has been turned to stress the subject language in the process of globalization which leads us to a high-tech era.And mathematical language has been widely used in many fields such as science and arts and gradually become the core of subject language because of its favored characteristics like conciseness and preciseness.At the same time,mathematical language has also become a core competence for students to gain success in the future.Therefore,more and more scholars start to pay attention to the development of students' mathematical language ability.However,lots of researches focus on the aspects of mathematics teaching and conduct discussion about the connotation,structure,and development strategies of mathematical language ability based only on experience and speculation,which lacks of practical study and systematic research.So,an integral teaching model having practical significance and theoretical support can be formed after systematically studying on the development of elementary school students' mathematical language ability from multiple aspects including linguistics,psychology as well as mathematics teaching.In this way,elementary school students' mathematical language ability and thinking capability can be facilitated and a kind of new perspective and possibility can be provided to realize efficient elementary mathematics teaching.The objective of this paper is to develop elementary school students' mathematical language ability and to form a reliable teaching model.Based on the development of the elementary school students' mathematical language ability,this paper conduct the study from four questions:What should be developed;Why should it be developed;How to develop it;What is the effect of the development,in order to get the cognizable foundation,practical foundation,process of the construction and the practical efficiency.This paper usesmany methods such as literature review,classroom observation,questionnaires,experience summarizing and teaching experiment to get the following conclusions :1.Mathematical language has generality and individuality.The generality sets the goal for the development of elementary school students' mathematical language ability,while the individuality provides teachers' initiative with the space and possibility to shine.Generality expand the implication of mathematical language.Studies show that mathematical language,which is a specific professional language conveying mathematical knowledge,expressing mathematical ideas and methods and embodying the characteristic of mathematics,has three ways to characterization:The usage of words;The usage of symbols;The usage of graphs.It also has four features:accuracy,preciseness,abstraction,conciseness and three practical forms:The knowledge form of mathematical subject language;The learning form of mathematical teaching language;The living form of mathematical speaking language.Based on language generating and language learning,this paper has established the structure of mathematical language.That is the mathematical language ability to understand,translate and express.This paper has also specified the structure by combining the features of elementary mathematics.Individuality helps to point out the two limitation to the development of elementary school students' mathematical ability—age limitation and textbook limitation.The age limitation are reflected in three aspect.Firstly,age confines the features of elementary school students' mathematical language.and there are three obvious characters of mathematical language:Concreteness overweigh abstraction;Words overweigh symbol;Science depends on non-science.Secondly,age brings disadvantages to elementary school students' mathematical language ability.The ability of understanding is restricted by “einstellung”;The ability of translating depends on “imitation”;The ability of expressing declines to “ego”.Thirdly,age has a strong influence on the speed of the development of elementary school students language ability and it should be combine with the basic law of their cognition.The textbook limitation are also reflected in three facets.First of all,the textbook confines the content of language.Elementary mathematic textbook related to four categories:Number and Algebra;Geometry and Graphics;Statistics and Probability;Integrity and Practice.Although some students excel a little,they are still in the content of the textbook.Furthermore,textbook confines the key point of language ability.The key point of calculation lies in “principle”;The key point of graph lies in “the forming process of formula”;The key point of statistics lies in “the ability to recognize the graph”;The key point of integrity and practice lies in “the idea to solve the problem”.In addition,Textbook restricts the development of language.The development of elementary school students language abilities is in line with the development of the textbook which presents a spiral posture.2.The language feature is in correspondence with the language ability.Elementary school students mathematical language ability embody in the features of the language itself including,accuracy,preciseness,abstraction and conciseness.In order to get a clear picture of the present situation of the development of elementary school students mathematical,this paper carried out inquires in 32 classes of various districts including Chongqing and Yunnan according to the features of mathematical language and practical experience.It turn out that the students mathematical language ability is not every ideal and there are three reasons of this phenomenon:Because of the lack of knowledge,they do not know how to speak;Because of the lack of nurturing translating skill,they can not speak;Because of the lack of attention to the inner world,they are unwilling to speak.In addition,little attention paid by the teachers to mathematical language ability also contributes the problem.3.The right way is needed to solve the problem that common elementary students mathematical language ability is not very ideal.According to the connotation of “development”,there is two ways to develop elementary students mathematical language ability—the interior way which should be felt in meditation and the exterior way which should be reinforced in training.Through the questionnaires towards teachers,it turns out that most teachers take the former way to reflect themselves which result in many problems such as the break between practice and cognition,the lack of strategy and the departure of consequence and goal.By professional analyzing of the feature and the mathematical thinking pattern of elementary school students as well as the teachers' proficiency,the possibility of exterior training is proved to be existence.So it is a must to switch form the interior way to the exterior way to develop elementary school students mathematical language ability.4.For the exterior training method to develop elementary school students mathematical language ability,a realistic teaching model is needed which should be originated from the minor extent of each class.This paper propose an assumption to establish a inductive model based on the basic methods of constructing model.After summarizing the practical experiments to improve elementary school students mathematical language ability,it turns out that “speaking” is the only concrete way to present students mathematical language ability and there are four stages to illustrate “speaking”—Speaking is an idea,which points to teaching philosophy;Speaking is the teachers' accomplishment,which points to teaching objectives;Speaking is a strategy,which points to the process of teaching design;Speaking is a method to teaching evaluation,which points to teaching reflect.So,the “Three Speakings” teaching model are proposed and elaborated from the aspects of theoretical foundation,functional goals,implementing principle,operational program,realization condition in this paper.The “Three Speakings” teaching model is based on system theory;The basis of its psychology is based on the relationship between language and idea in social and cultural theory;The the basis of its teaching theory is based on pyramid theory.And all of these theories and methods aim at facilitating the development and the enrichment of elementary school students' emotion and the implement emphasis the involvement of the students.Before the class,much attention should be paid to “Say something to refine”;In the class,much attention should be paid to “Repeat the training”;After the class,much attention should be paid to “The said topic exercise”.5.The “Three Speakings” model is an effective way to improve elementary students mathematical language ability.The quality of the expression of mathematical language directly reflect the mathematical language ability,while the mathematical thinking and mathematical emotion indirectly reflect it.Therefore the actual efficiency of the teaching model depends on the corroboration of the expression,emotion and thinking.According to single factor experiment,three conclusion can be drawn:The “Three Speakings” model can improve the total level of elementary students mathematical language.Its effect for first-class students is not so significant as for the secondary students.Meanwhile the “Three Speakings” model has a prominent effect on students with poor grades;The “Three Speakings” model can improve the mathematical thinking ability.Its effect for first-class students is not so significant as for the secondary students.Meanwhile the “Three Speakings” model has a prominent effect on students with poor grades;The “Three Speakings” model can improve the the ability to express their emotion.Its effect for first-class students is not so significant as for the secondary students.Meanwhile the “Three Speakings” model has a prominent effect on students with poor grades.In summary,this paper adopt several scientific methods to study the teaching model of the development of the elementary school students' mathematical language ability.To a theoretical extent,this paper expand mathematical language and its connotation,Meanwhile,it analyzes the theories and methods to improve the mathematical language ability;To a practical extent,this paper explore the current situation,problems,reasons of the development of elementary school students mathematical language ability scientifically to construct a teaching model and conduct teaching experiment.So,this paper provide a new perspective and a new teaching model to elementary school mathematical teaching research as well as the front-line elementary school teachers,which has both theoretical and practical significance to the development of elementary school students mathematical language ability and the teachers' research.