The Optimization Design And Application Research Of High School Math Problem Solving Micro-lessons

Under the influence of "the Internet plus education," fragmented,intelligent,and personalized forms of learning and education have been developed unprecedentedly in recent years,and micro-lesson,as an important educational tool born in this era,has the characteristics of strong teaching purpose,short learning time,and easy to disseminate and view,which can better meet the needs of personalized learning,online and offline.It is a hot research topic in the field of information technology education both at home and abroad.According to the 2017 Edition of the General High School Mathematics Curriculum Standards,"emphasis is placed on the use of information technology to achieve the deep integration of information technology and mathematics curriculum." Mathematics micro-courses have gradually grown in popularity as related research and practice have grown.Primary and secondary school teachers expect to help students learn mathematics more effectively through micro-courses in the context of the "double reduction" era,but the number of problem-solving mathematics micro-courses developed in existing research is large,but the quality varies,and there are many problems: The problem-solving ideas are unclear,and there is a lack of a methodological summary;The problems of how to optimize the design of problem solving micro-lessons,how to find appropriate strategies for optimizing problem solving micro-lessons,and how to effectively apply problem solving micro-lessons must be solved in this context.This research focuses on the optimal design and application of problem solving micro-lessons in high school mathematics,and it employs a variety of research methods to conduct theoretical and practical research.In terms of theory,a literature review of the design and application of mathematics problem solving micro-lessons is conducted first,and two main research questions are raised: how to optimize the teaching design of high school mathematics problem solving micro-lessons,and whether optimally designed high school mathematics problem solving micro-lessons are effective.Second,the optimized design strategies of high school mathematics problem solving micro-lessons are discussed,based on the learning and application of Polya’s problem solving theory and mathematical multiple representation learning theory:（1）clarifying the problem,focusing on the discovery of implicit information;（2）attempting to solve the problem,focusing on the attempts of student subjects;（3）dissecting the solution,focusing on the connection of different solutions;and（4）summarizing and reflecting,focusing on the discovery of implicit information.In terms of application,the micro-lesson "2.3 Quadratic Functions,Equations,and Inequalities" from the People’s Education Publishing House’s General High School Mathematics Textbook（Compulsory Course 1）was used as an example,and the experimental teaching method was combined with questionnaires and interviews to conduct a comparative study on the effectiveness of the design strategies for optimizing the micro-lesson on mathematics problem solving.To compare the effectiveness of problem-solving micro-lessons,an experimental study was undertaken in two high school courses.The experimental class received the optimized version of the micro-lesson,while the control board received the non-optimized version of the micro-lesson.The study’s findings suggest that well-designed issue-solving micro-lessons can improve students’ problem-solving performance while also having a favorable impact on problem examination awareness,problem-solving approaches,and reflective awareness.