Research On The Flexibility Teaching Of Math Problem Solving Program Based On Metacognitive Strategy

Nowadays,quality-oriented education reform is advancing continuously,but quality-oriented education and knowledge education are not contradictory,but mutually reinforcing.In order to meet the requirements of today's society for talents,we need to reform the content and methods of knowledge teaching.Procedural knowledge is very important for solving high school math problems.We use procedural flexibility as an index to measure the depth of procedural knowledge.We believe that individuals who can solve the same problem with multiple correct procedures and select the most appropriate program are flexible problem solvers.Metacognitive strategy includes planning strategy,monitoring strategy and adjustment strategy.Almost all students use metacognitive strategy intentionally or unintentionally when solving problems.According to the literature,metacognitive strategies have a positive effect on students' procedural flexibility,but the specific mechanism has not been studied.The program flexibility of high school students in solving mathematical problems is related to their development of thinking.Therefore,it is necessary to study the program flexibility of high school students.As an instrumental knowledge,the second chapter of the compulsory mathematics course of senior high school,Quadratic Function,Equation and Inequality,is a multi-solution problem related to it,which is suitable to be used as a carrier to study the program flexibility of senior high school students.Therefore,we choose multiple-solution problems in Chapter 2 to compile a test paper to test the flexibility of high school students' math problem solving program.We grade and analyze the flexibility of students' program according to the pre-determined scoring standards.Then,students were selected for interviews to understand the reasons behind the selection process and the role of metacognitive strategies.Through tests and interviews,we came to the following conclusions:1.High school students have a good level of program flexibility when solving multi-solution problems of one math problem.Very few students have an excellent level of program flexibility,but less than half of the program flexibility is average.2.There are mainly two kinds of reasons for students to choose programs--algorithm and expectation.Among them,algorithms include three categories:adhere to a predefined algorithm or process,according to the external authority to solve the problem,do not consider the future and change the state of the problem;There are three types of expectation:the behavior to achieve future state,the behavior to avoid future state,and efficiency.3.The planning strategy in metacognitive strategy promotes the flexibility of students' program mainly by helping students to identify problems and transfer knowledge;The monitoring strategy runs through the problem solving process,continuously helps students adjust the process to achieve the optimal solution,and helps students to choose the most appropriate method;The adjustment strategy allows students to reflect on and summarize the problem solving process,which is conducive to the next problem solving and promotes the sustainability of the flexible development of the program.Finally,based on the conclusion of survey and interview,the teaching design,implementation and evaluation of metacognitive strategies to promote students' program flexibility are made.In order to make teaching more scientific and standard,we summarize and conclude on the basis of existing research,and combine with the concrete reality,give a series of relevant teacher behavior framework and teacher teaching principles,and carry out classroom teaching accordingly.The purpose of this paper is to study the flexibility of high school students' math problem solving program,and to get a series of relevant conclusions and give the teaching design,implementation and evaluation.This paper may provide some references for the researchers who are interested or in need in the study of program flexibility,so as to jointly promote the development of mathematics teaching in senior high school.