Contextual Analysis Of Mathematical Concepts And Empirical Research On Their Energy Efficiency

In both deductive emphatically era during Euclidean and strict axiomatic period of modern mathematics,mathematical concept is the first.Mathematical concept has universality of entity concept and particularity of mathematical meaning.The theory of interaction among logic-language environment-situation has profound influence in the field of mathematics education.Language environment,math particularity and mental operation is a medium during knowledge shaping of students which has far meaning during math education.So it is important to know the way to make use of language environment in mathematical education which may help students to understand concepts well,construct knowledge structure,recognize relevance and clear thinking.In this paper the influence of language environment to education and learning is redefined with Multiple representation theory of mathematical concepts.which combined with response of mathematical concept.By analyzing the case named "The concept of circle and definite integra" language environment of mathematical concepts is clearly shown on details of math.The beingness and effectiveness of language environment is proved here.In order to explore what language environment plays in the process of actual learning and how it works to influence cognitive of learners,the author made an empirical research as an example which associated with concept of functional meaning sequence.First of all,the author compared the mathematical concepts of sequence on different edition of textbooks,visited teachers with variant language environment levels,and researched subjective attitudes of students on concepts of sequence.In addition students were tested to explore the degree of understanding concepts on sequence,and language transition were compared among students with different cognitive levels.Finally,the author analyzed the data and result,and found the meaning of language environment on recognition,transference,application,construction of network structures,and cultivation of mathematical intuition.Successfully the author answered how the language environment effects the cognitive transition and meaning construction,and gave suggests on education at the same time.Conclusion:language environment is the foundation of mathematical concepts learning,and especially has positive effects on concepts recognizing and knowledge transference;Different levels of language environment may influence application of mathematical concepts;Students with different cognitive level has distinctions on mathematical concepts learning.The characteristics of this essay is based on the general theory of language environment,supplemented by practical cases for specific instructions,explore research significance through demonstration.