Concept Teaching Design Of Mathematics In Senior High Schools On The Basis Of APOS Theory

The mathematics concept is the basic component element of the curriculum content of the mathematics subject,and it is the key for students to understand mathematical thought and master skills in solving mathematical problems.With the constantly deepening of the new curriculum reform,the core position of mathematics concepts in the course teaching has been increasingly prominent as well.However,due to the high abstractness of the concept itself,coupled with the lack of active construction of the learning process and competence of students,students' understanding of the concept stays more at the level of instrumental use,leading to a more learning difficulty,and becomes an obstruction for students to further develop.Therefore,it's of great significance to explore the teaching mode of concept effectiveness and optimize the teaching design.On the basis of the constructivism learning theory-APOS(Actions,Processes,Object and Schemas)theory,this research tries to conduct a study on the concept teaching design of mathematics in senior high schools.This research dialectically dissects the guiding function of APOS theory on mathematics concepts teaching in senior high schools from the perspective of theory guiding practice and practical reflection.This research is mainly discussed in detail from two dimensions of theoretical research and practice research.In terms of practice research:(1)Through the methods of questionnaire survey and individual case interview,this research clarifies the present situation of concept teaching,and provides reference for teaching strategies.(2)Taking Exponential Function and Its Properties and Logarithmic Function and Its Properties as examples,this research makes a primary exploration on teaching design,and further practices the concrete application of APOS theory in concept teaching.(3)On the basis of teaching design,this research conducts the implementation of teaching,dissects the typical fragments of APOS theory class application,reflects on the teaching process and comes up with the optimization scheme.(4)Through an experimental comparative study between the APOS theory teaching and traditional teaching within the duration of two months,in accordance with the analysis of quantity of classroom observation and quality inspection data of two times,it can be seen that the average score of APOS theory teaching class is apparently higher than that of traditional teaching class.Students' degree of participation in classroom teaching is higher,and their completion quality of homework after class is better;Test 1 independent sample T Test P=0.007<0.05,and Test 2 independent sample Test P<0.001.The differences between the two test scores are prominent and gradually becoming larger,which further clarify the positive role of APOS theory in teaching.In terms of practice research:(1)Through the methods of questionnaire survey and individual case interview,this research clarifies the present situation of concept teaching,and provides reference for teaching strategies.(2)Taking Exponential Function and Its Properties and Logarithmic Function and Its Properties as examples,this research makes a primary exploration on teaching design,and further practices the concrete application of APOS theory in concept teaching.(3)On the basis of teaching design,this research conducts the implementation of teaching,dissects the typical fragments of APOS theory class application,reflects on the teaching process and comes up with the optimization scheme.(4)Through an experimental comparative study between the APOS theory teaching and traditional teaching within the duration of two months,in accordance with the analysis of quantity of classroom observation and quality inspection data of two times,it can be seen that the average score of APOS theory teaching class is apparently higher than that of traditional teaching class.Students' degree of participation in classroom teaching is higher,and their completion quality of homework after class is better;Test 1 independent sample T Test P=0.007<0.05,and Test 2 independent sample Test P<0.001.The differences between the two test scores are prominent and gradually becoming larger,which further clarify the positive role of APOS theory in teaching.This study found that:(1)The teaching design based on the APOS theory can promote teaching results to some extent;(2)The teaching classroom based on the APOS theory is more able to motivate students' enthusiasm for study and enhance their learning initiative;(3)The four phases of APOS theory are the psychological construction process that students must go through to understand mathematics concepts,which are closely connected.However,each class is not required to strictly follow the four phases to advance.It's suitable for a period of time of knowledge construction.