Research On The Extraction And Application Of Big Concepts In High School Mathematic

Core Literacy-led education reform has become the latest trend in global education development.The General Senior Secondary Mathematics Curriculum Standards(2017edition revised 2020)introduced the Subject Big Ideas for the first time and emphasised that the content of the curriculum should focus on the Subject Big Ideas and promote the implementation of the Subject Core Literacy.However,it does not define the basic connotation of Mathematical Big Ideas,nor does it elaborate on the extraction of Big Ideas and their specific implementation plans.Therefore,it is important to study the connotation of Mathematical Big Ideas,especially their extraction and application.This article is dedicated to actively promoting the transformation of Literacyoriented Teaching and Learning of Big Ideas.Based on cognitive structure theory,constructivist theory and Freudenthal’s theory of mathematics education,this article takes the topic of Functions,a compulsory subject in senior secondary mathematics,as an example,and focuses on the three major issues of "What are Big Ideas in Mathematics","How to extract Big Ideas in Mathematics scientifically" and "How to effectively apply the extracted Big Ideas in Teaching Design".Firstly,an attempt was made to define the meaning of "Big Ideas in Mathematics" based on literature research.Then,a quantitative and qualitative analysis of the compulsory content "Functions" is carried out using the content analysis method,mainly based on the quantitative statistical results,and a qualitative analysis of the presentation characteristics of the subject matter of Functions in the textbook and its causes.In addition,a theoretical study and a preliminary practical exploration of extraction strategies,methods and processes are conducted,mainly by combining the characteristics of mathematics disciplines,three extraction strategies are given: abstraction,connection and classification strategies,and the "top-down" and "bottom-up" strategies are described.Based on the above,16 Secondary Ideas and 5 Big Ideas are extracted,supported by brief argumentation.Finally,the theories of Inverse Teaching and Unit Teaching are effectively combined with the ideas of Big Ideas,and an instructional design model based on Wiggins and Mc Teague’s Ub D ideas is developed.The findings show that: ⒈ Mathematical Big Ideas are the "tacit knowledge" behind mathematical knowledge or the "new structure" on top of its core knowledge and have a life value.⒉ It is scientifically valid to extract Big Ideas based on "content analysis";the synergy of multiple Big Ideas extraction strategies and approaches helps to improve reliability and validity;the ideas of dynamic construction of Big Ideas helps teachers and students to construct a Big Ideas system.⒊ Focus on the role of Big Ideas at all stages of the unit’s design,constantly confirming,testing and refining each other.