Study On Triangle Function Teaching Based On ACT-R Theory

With the promulgation and implementation of the 2019 new high school mathematics textbook,great changes have taken place in the trigonometric function part,which requires teachers to adjust their teaching in time according to the changes.Trigonometric function is the carrier of cultivating students' thinking of combination of number and shape and the core quality of mathematics.It is also an important branch of the main line of function in high school mathematics curriculum.Students will have various problems when learning trigonometric function.The reason is that students do not understand the essence of knowledge.Therefore,it is very important to explore an effective trigonometric function teaching mode and improve teaching efficiency.ACT-R theory is a simple cognitive theory,which advocates simplifying complex problems,so that students can experience the generation process of knowledge and master the essence of knowledge.Therefore,it is of theoretical significance to apply ACT-R theory to guide trigonometric function teaching.Firstly,using the literature method,this paper studies the ACT-R theory and trigonometric function teaching and learning,and determines the research questions as follows:(1)what problems do students have in learning trigonometric function in the current classroom? Why?(2)How to apply ACT-R theory to improve students' problems in learning trigonometric functions?Secondly,through interview and test methods,this paper investigates the teaching and learning situation of trigonometric function in the real classroom,analyzes the attribution,and provides an empirical basis for the proposal of teaching strategies and the design of teaching cases.The survey results show that teachers generally do not pay enough attention to the curriculum standards and teaching design,and the reserve of educational theory is insufficient.Students' mastery of the declarative knowledge of trigonometric functions is not enough,and problems also occur in the process of transforming declarative knowledge into procedural knowledge,resulting in failure to achieve the degree of automation of knowledge,unable to solve comprehensive problems,and errors such as careless examination and calculation errors.Then,using the method of case analysis,this paper studies two teaching designs guided by ACT-R theory,analyzes the key points of teaching design based on ACT-R theory,and combined with the survey results of the current situation of trigonometric function teaching and learning,puts forward the teaching strategy of trigonometric function based on ACT-R theory from three stages:(1)declarative stage: select reasonable examples to clarify the exploration problems of trigonometric function;Establish learning objectives and guide students to analyze and solve strategies;Decompose the target hierarchy and establish the knowledge inquiry process of trigonometric function;The goal is solved layer by layer to form new declarative knowledge;(2)Procedural stage: knowledge coding to promote the transformation of declarative knowledge;Reflect and improve,and preliminarily master the production rules;(3)Automation stage: exquisite practice to promote the automation of production rules;Refine the model and achieve the automation of production rules.Finally,based on the above teaching strategies,taking the concept of trigonometric function and induction formula as examples,the teaching design based on ACT-R theory is given.