High School Students' Understanding Level Of The Definite Integral And Teaching Experiment Based On The Theory Of APOS

In mathematics,many of the concepts have a duality,not only mathematical object is static,or dynamic procedure.Therefore,students can understand a mathematical concept from both static and dynamic aspects.Definite integral as a typical duality concept,which contains the variety of comprehension.To study students' understanding level and find what barriers are in students' learning is important to teachers teaching and students ' learning.Paper used literature analysis to establish the framework for understanding of definite integrals with the APOS theory,combined with test class of questionnaire results,surveys students' understanding level.getting following conclusions: in activities stage,90% of students can achieve excellent level;in process stage,only not to 25% of students can reached excellent level,52% of students are in medium level;in object stage,reached excellent of students has 18%,reached good level of students probably about 34%,medium level of has 32%;in schema stage,few students can achieve the best level,11% students are at a good level,70% of students are in the Middle;Finding that students will have such following barriers: unlimited,limit and other concepts in higher mathematics concepts and functions,integral nature,abstract symbols;Based on this,proposing the corresponding teaching strategies.Based on students understanding obstacles and teaching strategies,designed the teaching of definite integral according to APOS theory,and implemented in experimental class.Comparison the questionnaire results between the experimental class and the test class,combining with students' interviews,which are in experimental class,analyzing and evaluating experimental teaching effects.The result shows that the experimental class is better than the test class,which means that the teaching of definite integral according to APOS theory can promote students ' understanding.Accordingly,this paper propose teaching suggestions for each phase,and improve the framework for understanding of definite integrals with the APOS theory.