Research On Education Of High School Mathematical Theorems Based On ACT-R Theory

Mathematical theorems are not only important parts of mathematical thinking,but also the prerequisite and basis for students to master mathematical knowledge and learn mathematics.Therefore,the study of mathematical theorems occupies an important position in mathematics teaching.ACT-R theory is essentially a cognitive learning theory,which divides knowledge into declarative knowledge and procedural knowledge.This theory acknowledges that the study of knowledge starts from declarative knowledge,then it is procedurally transformed into procedural knowledge,and finally reaches automation.Based on the ACT-R theory,this article applied the ACT-R theory to the teaching process of mathematical theorems,conducted teaching research,and used sine and cosine theorems as examples to conduct teaching design research and discussed the application of ACT-R theory to the teaching of mathematical theorems in middle schools.The main research methods in this paper were literature method,interview survey method and experimental method.First of all,the current research status of ACT-R theory was analyzed.Combined with ACT-R theory,it analyzed the value and principles that used ACT-R theory to the teaching of mathematical theorems,and divided the teaching process into four stages and ten teaching links.In the second part,interviews with teachers and questionnaires to students were conducted to investigate the current status of mathematical theorems' teaching in schools and the status of students' learning of mathematical theorems.Then selected the sine theorem and cosine theorem as examples,conducted research from the aspects of teaching goals and teaching process,and carried out educational experiments based on this.Select students from one class of senior two as experimental class for teaching.Through the analysis of the effects of teaching experiments,it concluded that the application of ACT-R theory in the teaching of mathematical theorems can better help students understand mathematical theorems and apply mathematical theorems to solve problems.And finally,made some suggestions for applying ACT-R theory to mathematical theorem teaching.The research results of this paper were mainly included the following three aspects: First,by analyzing the ACT-R theory,the five major principles of applying ACT-R theory to the teaching of mathematical theorems were summarized which contained the principle of visualization,the principle of layering goals,and the principle of combining active and passive,the principle of refinement and matching,and the principle of reflection and feedback.In the teaching of mathematical theorems,teachers must improve teaching based on these five principles.Second,based on the ACT-R theory,the teaching of mathematical theorems was divided into four stages and ten teaching links.The four stages were the declarative stage,the procedural stage,the automation stage,and the reflective feedback stage.The ten links were creating scenarios and introducing new knowledge;hierarchical goals to attract attention;guide students to explore theorems;optimize teaching and analyze theorems;explain example questions and apply theorems;compile knowledge and strengthen theorems;design variant exercises;ask students to deepen understanding;classroom feedback;practice evaluation.Third,according to teaching experiments,six suggestions were made for the teaching of mathematical theorems based on the ACT-R theory: explore the theorems from examples;establish a goal hierarchy to level the learning of the theorems;the teaching process follows four-stages progression;set up exquisite exercises and grasp the quantity and quality;infiltrate the analogy thought;and provide timely and effective feedback.