Research On Teaching Design Of 'Permutation And Combination' Based On APOS Theory

After the implementation of the new curriculum reform in 2013,the content and structure of ordinary high school mathematics have been innovated and changed.According to the latest PEP edition of mathematics textbooks ' arrangement and combination ' chapter,located in PEP A selective compulsory third volume sixth chapter.Arrangement and combination are based on two counting principles,which are not only the focus of high school mathematics knowledge,but also an important bedding for the probability and statistical knowledge of university stage.There are many ways to solve the problem of arrangement and combination,and there are many mathematical models of arrangement and combination in real life.Learning arrangement and combination can develop students ' abstract ability and logical thinking ability,which is beneficial to solve practical problems in students ' life.From the perspective of knowledge investigation,in the past ten years of mathematics college entrance examination questions,arrangement and combination as a single test point will mainly appear in the two types of choice questions and fill-in questions.The examination of simple answers is mostly combined with knowledge points such as probability and mathematical expectation,and the score is about twelve points,which plays an important role in the whole high school mathematics.APOS theory,derived from constructivism,can guide mathematics teaching,where A represents action(Actions),P represents process(Process),O represents object(Object),and S represents schemas(Schemas).APOS theory believes that the concept of learning mathematics needs to go through these four stages.Theory is applied to teaching practice,more emphasis on students ' learning,students through the materials provided by teachers to complete the operation,process,object,schema,knowledge points from concrete to abstract internalization to their own knowledge system.Based on this,this paper applies the theory to the teaching design of ' permutation and combination ' to carry out the teaching experiment.In this paper,two classes of Grade Two parallel classes in H Middle School of X Province are selected as the experimental subjects.Class A is the experimental group,and Class B is the control group.In the process of teaching experiment progress,first of all,high school mathematics teachers in H middle school were interviewed to understand the current situation of the application of APOS theory in mathematics teaching,through the knowledge level test of high school grade 3,to understand the learning status of permutation and combination.Then,combined with APOS theory,the teaching design is carried out for the three sections of “ two counting principles ”,“ arrangement ” and “ combination ”.Class A is the experimental group,which is taught according to the teaching design of APOS theory,and class B is the control group,which is taught according to traditional Chinese teaching methods.Finally,by testing the teaching situation of the two classes,collecting and sorting out the test scores of the two classes,using SPSS26.0 software to analyze the test scores of the two classes and draw conclusions.