Research On The Application Of Conversion Thought In Function Teaching In Senior High School

Mathematics is a very important subject in senior high school curriculum,with strong abstraction and logic.When solving mathematical problems,students often use various methods to solve problems,among which the idea of conversion is a very useful one.The idea of conversion can simplify complex problems,handle unfamiliar problems familiarly and analyze abstract problems concretely.Using the idea of conversion can greatly improve the correct rate of solving problems,stimulate students’ interest in mathematics and make them feel the joy of success,so this paper chooses senior high school function teaching to study,and the specific research contents are as follows:First of all,under the guidance of learning transfer theory,metacognition theory,Bruner’s discovery learning theory and constructivist learning view,this study adopts the research methods of literature research,questionnaire survey and interview to understand the research status of conversion thought at home and abroad,and defines the core concepts.Simply put,conversion thought is to transform the problems to be solved through observation,analysis,analogy,association and other thinking processes,follow relevant principles,and come down to some problems that have been solved or are relatively easy to solve.Secondly,the five principles and four types of conversion thought are discussed in detail.The principles of conversion thought include: simplification principle,concretization principle,standardization principle of form,familiarity principle and contradiction principle when it is difficult.The types of conversion thought include: the transformation of general and special,the transformation of number and shape,the transformation of principal and secondary,and the mutual transformation of equality and inequality.Relevant examples are given in each part to prove it.Thirdly,the important role of reduction thought is deeply analyzed from four aspects:function concept,function property,function problem solving and sequence.On the one hand,the formation of function concept comes from the development of mathematics itself,on the other hand,it is abstracted from real life,and reduction thought plays an important role in it.Function property is an important aspect of studying function,which has not only special properties,but also general properties,and at the same time,properties can be transformed into each other.The nature of the original function can be obtained from the nature of the derivative function.When solving a function,the idea of reduction can reduce the difficulty of operation and simplify the operation process,which is generally reflected in three aspects: transforming abstraction into intuition,transforming directness into indirection,and transforming irregularities into rules.For this special function,we need to use the idea of reduction to transform it into a special sequence with arithmetic or equal ratio through construction.At the same time,the terms and sums of the sequence can also be transformed.arithmetic progression’s general term formula can be regarded as a linear function,and geometric progression’s general term formula and summation formula can be regarded as exponential functions.Therefore,the study of sequence problems can be transformed into the study of corresponding functions.Finally,through interviews and questionnaires,some teachers and high school students are taken as the research objects to study the application status of conversion in high school mathematics.High school teachers can realize the important role of conversion in solving problems,but the infiltration in the teaching process is limited,and most students’ conversion ability still needs to be improved.