Research On The Variant Teaching Of Junior Middle School Mathematics Concepts Based On The APOS Theory

With the reform of the new curriculum,more and more scholars and experts put the focus of education and teaching on the teaching process rather than the students' achievements.This reaction is reflected in the teaching of mathematics,which is reflected in whether teachers can successfully design a vivid image and motivate the classroom teaching of students.The basicity and core value of mathematical concepts determine its status in mathematical learning.Therefore,domestic and foreign scholars have carried out various experimental studies on the study of "mathematical concepts",and have germinated many theoretical branches.Among them,the APOS theory and the variant teaching theory,the former is a theory to guide students' learning,and the latter is a teacher's experience teaching theory.Teaching is composed of teacher's teaching and student's learning.The teacher's identity as a guide stands on the podium.His teaching methods and methods are various,and the variant teaching can be said to be one of the characteristics of China's mathematical education..Therefore,based on the guidance of APOS theory,this paper proposes to expand the theory in the vertical stage and expand it horizontally.This article first studies the background and development of the two theories,finds out what they have in common,and then conducts an integrated theoretical analysis based on the duality of mathematical concepts.The establishment of a schema is a long-term process,which requires students to repeat repeatedly,and to extract the essential attributes of objects through multiple experiences.Due to the different levels of students' intelligence,the time spent in this process is also different,but our classroom study time is limited.We cannot guarantee that students can independently complete multiple repetitions and reflections after class.Therefore,during the teaching process.The guiding role of teachers appears to be extremely important.The essence of variant teaching is "to reflect the changes in change." From a theoretical analysis,the combination of the two can help students better learn mathematical concepts.After the theoretical analysis,the author designs a teaching case which accords with the development of students' thinking,and then analyzes the design through classroom observation and after class interview.It is found that APOS theory can well mobilize the enthusiasm and initiative of students,so as to facilitate the subsequent development of students,and the rational use of variation in teaching design can effectively help students understand concepts,reduce those meaningless repeated operations,and improve teaching efficiency.