Research On Mathematics Concept Teaching Under The Integration Of APOS Theory And Variant Teaching Theory

The study of mathematical concepts has always played an important role in mathematical learning.Teachers often give concepts first,and then transform the concepts to achieve the goal of consolidation and deep understanding of the concepts.But this approach actually ignores the procedural nature of the concept.With the promulgation of the 2017 high school curriculum standards,mathematical concept teaching should pay more attention to both its structure(object)and its operability(process).Both the APOS theory abroad and the variant teaching in China have noticed these two aspects of the concept,which can provide effective operation guidance for the concept teaching.And they have many similarities.Therefore,I tries to integrate them,hope to enhance their respective effects.First,I analyze the necessity of integration of APOS theory and variant teaching from the perspective of teaching practice and the theory’s own needs.Then,by reading relevant literature,it is found that both are closely related to the duality of mathematical concepts,so they have the possibility of integration.Next,I use the duality of the concept as an intermediate bridge to integrate the two theories.Taking the four stages of APOS theory as the main line,the author meticulously designed various variable question groups,which acted horizontally on each teaching process,to enable students to grasp the invariable essence and laws of concepts from various changes.Finally,a teaching model under the integration of APOS theory and variant teaching was formed.Based on this model as the basic frame,taking the conic curve as the entry point,three conceptual teaching schemes of conic curve were designed and taught in the practice class.Finally,in order to verify the effect of the model,three mathematical results of the experimental class and the control class were collected as quantitative analysis data.At the same time,dialogue interviews are conducted with teachers and some students as a basis for qualitative analysis.Judging from the data of mathematical results,the teaching model has no significant effect on the improvement of students ’mathematical performance.From the dialogue interviews,teachers who were interviewed showed satisfaction to the teaching effect of the lesson.They believe that the teaching model can improve students’ learning interest.It is beneficial to students’ understanding of mathematical concepts,and has a certain teaching effect.From the dialogue with the students of the three grades,students prefer this teaching model,thinking that the exploration of concepts can deepen their understanding of concepts,especially for upper-middle-level students in mathematics.However,the experimental samples are small,so the experimental results lack strong data support.At the same time,the teaching model is still in its infancy,and more problem research needs to be gradually improved in future teaching practices.