A Cultivation Study Of Mathematical Symbol Sense Based On The Theory Of ACT-R

Symbol sense is one of the ten core concepts proposed by “Full-time Compulsory Education Mathematics Curriculum Standards(2011 Edition)”.At the same time,the new curriculum standard points out that the cultivation of symbol sense should be effectively integrated into mathematics classroom teaching,forming a positive tendency towards mathematical knowledge and mathematical skills,mathematical expression and mathematical thinking.American artificial intelligence expert and psychologist John R.Anderson et al.put forward “Adaptive Control of Thought-Rational”(referred to as ACT-R theory),which reveals the nature of human complex cognitive activities.Based on the ACT-R theory,this paper constructs the basic framework of teaching design for cultivating students' symbol sense,discusses the teaching suggestion of cultivating mathematical symbol sense under the guidance of the ACT-R theory,and makes a study of teaching design with the examples of “adding and subtracting fractions of different fractions” and “judging parallel lines”.The main body of the article is divided into five parts.In the first part,first of all,this paper elaborates and analyzes the theory of ACT-R,finds the theoretical basis of students' cognitive behaviors,and then organizes the related documents of symbol sense to understand the research status of symbol sense.In the second part,through the collation of the ACT-R theory and the mathematical symbol sense,the concept of mathematical symbol sense is defined,and the feasibility of cultivating students' symbolic sense based on the ACT-R theory is analyzed.In the third part,the development of test papers was used to understand and analyze the current state of symbol sense of students in compulsory education.In the fourth part,according to ACT-R theory,combined with the requirements of instructional design,this study establishes the basic framework for cultivating students' symbol sense of instructional design,and proposes teaching suggestions based on ACT-R theory to develop students' symbol sense.In the fifth part,based on ACT-R theory,the teaching design is carried out with the examples of "adding and subtracting fractions of different denominator" and "judging parallel lines",cultivates students' mathematical symbol sense from the dimensions of perception,calculation,reasoning and representation of symbols.