The .7-9 Grade Students' Mathematical Understanding Of Symbolic Language, Said

Since "symbol sense" is looked on as a core concept of mathematics learning as "space idea" and " reason capability " in the standard of mathematics curriculum for compulsory education, studying the students' the use of mathematical symbols gradually becomes a more active field. These studies are focused on the characteristics and functions of mathematical symbols, focused on the meaning and training's approaches of "symbol sense". These studies are based on theory or experience and lack the systematic analysis to the real situation of the students using mathematical symbols. In this paper, the use of mathematical symbols being placed on the scope of language, the studies is to the real situation of the students using the language of mathematical symbols.The article will study the understanding and representation of mathematical symbols. The studies envelop several problems: Which differences the students have in the understanding and representation of mathematical symbols? What these differences' essence is? Based on these differences and essence, how to teach the language of mathematical symbols?To solve these problems, 496 students are surveyed though the questionnaires. In order to understand the students' ideas in the process of understanding and representation of mathematical symbols interview, some students are interviewed. 12 students are concerned with the task-based interviews to further explore the process of understanding and representation. To these data from the questionnaires and the interviews, the article uses the methods of statistic to analyze.The basic of theories that the article is according as are from the cognition to the language of mathematical symbols, also are from the philosophy, pedagogy, psychology and linguistics. The article exerts basically the theory of representing and connecting about understand and the model of the epistemological triangle.In the article, the studies' main conclusions are:i) To the same language of mathematical symbols, the understanding results and process of students are some differences. These differences are reflected in four aspects: the understanding extent, the understanding to the relationship between the symbols, the understanding to the letters' meaning, and the understanding strategy.ii) To the same mathematical meaning, the symbolic representation's results and process are some differences. These differences are reflected in four aspects: multiformity, system, veracity and strategy.iii) With the grade increasing, the students don't obtain the substantial improvement in the understanding and representation of mathematical symbols. In other words, the growth of the other mathematical knowledge does not indicate the growth of understanding and representation of mathematical symbols.iv) The students' level of mathematical achievement is accord with their situation in the understanding and representation of mathematical symbols. In general, the higher students are obviously better than the poorer students in understanding and representation of mathematical symbols. In other words, the problems existing the students' understanding and representation of mathematical symbols is also constrained the development of students in the mathematics.v) In the process of the understanding and representation, the mathematical symbols not only are concise, accurate and universal, but also complicated, faint and self-sufficiency.vi) The reasons to induce the differences in the understanding and representation of mathematical symbols are from multi-aspects. But, they can be concluded two aspects in substance: the knowledge of language and symbol sense. In the embody, the differences in the knowledge of language are between the more and the little knowledge of language which the students hold, are between the systematic knowledge of language and the fragmentary knowledge of language, are between the tightness and the loosen which the knowledge of language is contact with the other knowledge, are between the flexible ways and the inflexible ways to handle knowledge of language. The differences in the symbol sense are the exact sense and the wrong sense, are the strong sense and the weak sense. The affection to the understanding and representation of mathematical symbols is both produced because of uniting the knowledge of language with the symbol sense and produced because of the singleness.vii) The teachers are usually able to think over the symbolic teaching in the mathematical teaching. But, as a whole, the symbolic teaching is on the way in the other mathematical teachings. The symbolic teaching is still a kind of aimless and unconscious action. There are also some problems in the process of symbolic teaching as to learn by rote. For this reason, some suggestions are put forward: the symbolic teaching should be self-conscious and intentional; the symbolic teaching should pay attention to the characteristics of mathematical symbols in the education; the symbolic teaching not only should take into account the symbolic form, but also should consider the symbolic content; the symbolic teaching also should adequately consider the students' behaviors.This article has three innovative aspects. First, the article obtains systemically the students' situation in the understanding and representation of mathematical symbols. Second, the article considers the mathematical symbols as a language and analyzes the problems and the reasons from the language of view. Third, the article pays attention to the teaching of mathematical symbols. According to the problems and shortages of students' understanding and representation to mathematical symbols, the article puts forward some suggestion to the teaching of mathematical symbols.The study is a broad field about the language of mathematical symbols in the middle school. This article only involves some parts in the field. The article is not more sufficient in the psychological level's analysis. The article also doesn't study the actual effect of the teaching suggestions. Hence, the article can continue the study according to the above-mentioned shortage.