Research On The Cultivation Of Mathematics Ideas In Middle School

From the original knot rope record to the number and shape of the attention.From the expression of cuneiform,pictographic to the emergence of elementary mathematical symbols.From scattered mathematical rules of life practice to systematic mathematical system.The ancient subject of mathematics,after a long history of development,continues to take root in the process of education.As a basic subject of education in school,mathematics is not only committed to the transmission of mathematical knowledge and laws,but more importantly,in the process of integration with other subjects so that students could understand mathematical ideas,feel the beauty of mathematics through the study of mathematics.Some scholars have pointed out that mathematics is a subject about beauty,art,and of constant reflection and development.The beauty of mathematics is embodied in the changing beauty of numbers,the balance of mathematical formulas,mathematical discovery and exploration,as well as acquisition experienced by students in the process of learning mathematics.At the same time,mathematics is also a subject of thought.Mathematicians have constantly enriched their mathematical think tanks based on their research in relevant mathematical fields and realized the continuous development of mathematical disciplines in the process of inheritance and innovation.The debate about whether mathematics is an art or a scientific discipline still exists today.Mathematics is an art reflected in the artistic language and concise formula expression,which enables the development of mathematical thoughts.Mathematics is also called a wonderful flower in the history of the discipline.Mathematics is a science.The language and expression of mathematics require accurate and concise pointing out of the corresponding intention,and the mathematical learners and researchers should have a profound understanding of the corresponding mathematical thoughts,and on this basis,achieve the precision of application.At the same time,mathematics is a life-oriented subject,and the original mathematics originates from the solving process of life problems.For example,the development of the ancient Egyptian mathematical civilization was caused by the silting and flooding of the Nile delta,forcing mathematicians to study the silting area and provide corresponding predictions.The development of mathematics is often affected by the development of social economy.Every important stage of the development of mathematics is inevitably accompanied by the needs of social development,and it also conforms to the needs of society,which has been proved in the history of modern mathematics,especially the integration of mathematics and information technology in modern society,the increasing specialization of basic mathematics research and the popularization of mathematics education,which are the manifestations of the adaptation of mathematics to social and economic development.Archimedes' original geometry and the important achievements made by modern mathematicians have made a significant contribution to the development of mathematics.In addition to the continuous efforts of mathematicians and related researchers,the current development of mathematics requires school education to cultivate talents who are interested in mathematics and able to comprehend the beauty of mathematics.The emergence of school education is undoubtedly an epoch-making event in human history,which makes the inheritance of human civilization a relatively standardized and institutionalized way.The emergence of school education enables the important achievements to be transmitted and developed in different categories.As scholars have said,our mathematics education is not to make every child become a mathematician,but to sow the seeds of mathematics in their hearts,so that they feel and understand the beauty of mathematics.The process of subject teaching should not only be knowledge transmission,it should be the process of thought comprehension and the process of mathematical knowledge leaping over mathematical thought.The study of mathematical knowledge is the basis for the comprehension and acquisition of mathematical thought and the necessary prerequisite for the realization of mathematical deep learning.The process of cultivating mathematical ideas based on the perspective of deep teaching means cultivating the main mathematical ideas in middle school from the aspects of knowledge,learning and teaching view.From the perspective of in-depth instruction,knowledge can be divided into three parts:symbolic representation,logical structure and meaning system.In the process of mathematical knowledge teaching,it should be beyond the symbolic teaching and surface teaching of knowledge,and then go deep into the internal structure of knowledge,so that students can acquire the edification of mathematical ideas on the basis of understanding the structure of mathematical subject knowledge.From mathematics knowledge to mathematics thought,is not only the mathematics teaching leap type development,simultaneously is also the teaching trend depth inevitable request.At present,the emphasis on the cultivation of students' key abilities and core qualities needs to be eventually returned to the process of instruction in various disciplines.Through the gradual infiltration of corresponding subject ideas through subject teaching,students'excellent subject thinking can be cultivated,thus promoting the improvement of subject ability and quality.Primary and secondary schools in the compulsory education stage is the golden age of the corresponding academic thoughts,this phase of mathematical thought learning especially need to cause the attention of teachers and students,the classroom teaching should be to discipline idea,namely important mathematical thought,mathematical knowledge point into a line into the surface.Students' mathematical learning process,through the infiltration of subject ideas,usually can deepen the understanding of mathematical discipline and mathematical knowledge,promote their grasp of the subject structure.Therefore,the teaching of mathematical idea is crucial to the process of mathematical instruction,and the leap from mathematical knowledge to mathematical idea is the focus of current classroom teaching.At the same time,how to cultivate students' mathematical thinking and quality of mathematical thinking in the teaching process of primary and secondary schools is also one of the issues that front-line teachers and researchers should pay attention to.