Research On The Unit Design Of Problem-solving Teaching For High School Mathematics

With the comprehensive deepening of curriculum reform,unit-oriented teaching reform has taken place at this point.The unit teaching design with the theme of mathematical thinking and method solving problems is highly consistent with the new curriculum concept with the goal of mathematical core literacy.Aiming at the current teaching phenomenon of insufficient penetration of mathematics ideology and method teaching in senior high school,low participation of students,low mastery of mathematics ideology and methods,neglect of the thinking process,and ability cultivation in problem-solving teaching,this study explores the construction of a unit teaching design with the theme of solving problems by mathematical thinking and methods.This teaching design,focussing on the goal of unit teaching and taking mathematical thinking and methods as the starting point,can ensure the integrity of unit knowledge,promote students’ deep understanding of unit problems,build a "genealogy" mathematical cognitive structure,develop students’ mathematical core literacy,and help students learn to learn.This study uses the literature research method to sort out the existing research results of unit teaching design,problem-solving teaching and function,and equation ideological and method teaching,and further analyze it in combination with relevant teaching and learning theories.Through the investigation and analysis of the teaching status of functions and equations,it is found that students have functions and equations.There is a lack of holistic understanding of the nature of ideas and methods,less attention has been paid to the application conditions,types and methods of functions and equations,and the commonality of mathematical problem units between functions and equations and equations.Teachers do not have a deep understanding of functions and equations.Although they have unit consciousness,they have unit teaching settings.The understanding of the meter is not deep,and there is less penetration into basic learning ideas,paths and methods.Given these problems,this study adopts the action research method and case study method,and takes the Mathematical Problem Unit of Functions and Equations Thought and Method as an example to build a general framework for the unit teaching design of mathematical problems based on mathematical thought methods and methods and a unit teaching strategy with the theme of solving problems by mathematical thinking methods:(1)General framework of unit teaching design with mathematical thinking and method as the theme of solving problems.1.Determine the mathematical thinking method.Analyze the teaching elements in-depth,choose mathematical ideas and methods that can run through these learning contents as the skeleton of unit design,and clarify the basic problems of list elements.2.Design the question group around the method.In-depth understanding of unit objectives,the design of question groups should be closely related to ideas and methods.Questions can come from different chapters or even different fields.3.Teachers and students solve problems together.Focus on the unit question group,design the basic learning ideas of the unit,understand the commonalities of mathematical learning,and construct the overall cognitive structure of the unit.4.Review,reflect and summarise the laws.Organize students to review and reflect,summarise laws,test students’ learning effectiveness,provide feedback and guidance for improving teaching,and promote the internalization of mathematical ideas and methods.(2)Unit teaching strategy with mathematical thinking and method as the theme of solving problems: 1.Focus on the core of the unit,accurately identify and classify unit problems.Mining the relationship between different knowledge behind the problem,choosing "good questions" that can reflect the core of mathematics,activate students’ mathematical thinking,stimulate students’ creativity,and promote the overall transfer of knowledge.2.Step by step,deeply understand the problem,and grasp the essence of the problem.Based on the guidance of variant theory,we will promote students to deeply understand the structural characteristics of the problem,effectively improve students’ discrimination ability,change students’ way of thinking and solve problems,gradually and spiral up,and implement the cultivation of students’ functions and equation ideas and methods.3.Analyse carefully,solve problems with mathematical thinking and methods,and accumulate experience in mathematical activities.In the process of examining and exploring the idea of solving the problem,we permeate the idea of function and equation,and expose the idea of function and equation in the process of solving the problem.Stimulate students’ enthusiasm for learning and provide time and space for independent exploration.4.Review and reflect,and understand the law of solving mathematical ideas and methods.Guide students to comb and understand the ideas of the question,summarise the solutions,and clear the ideas and methods of functions and equations.Pay attention to reflecting on the connection and synthesis of knowledge,connect and transfer to transform new and old knowledge,deeply migrate basic learning ideas,establish deep learning models,and learn to learn.