Problem-solving is the core of mathematics teaching,problem-solving teaching has been the focus of experts and scholars at home and abroad.Trigonometric function,as the key knowledge module of high school mathematics,plays an important role in college entrance examination.Therefore,this paper combines Polliat’s thought of solving problems with trigonometric function,and explores relevant strategies for solving trigonometric function problems,which is of guiding significance to students’ trigonometric function solving practice.Based on Polliat’s thought of problem solving,this paper makes an analysis of the curriculum standard,textbooks and related college entrance examination questions in the trigonometric function part of Senior High School,according to the obstacles of high school students in solving trigonometric function problems,this paper sums up ten strategies of solving trigonometric function problems under the thought of Polliat,Understanding the topic stage: 1.Carding dominant condition;2.Introduction of assistive tools;3.Mining for hidden conditions.Programme development phase: 1.Look for problem connections;2.Transformation Problem Representation;3.Return to the problem itself.Implementation Programme Phase: 1.Detailed problem-solving steps;2.Check every step.Stage of retrospective reflection: 1.Optimize problem solving;2.Building problem-solving models.Then,the author studies the practical significance of the trigonometric function problem-solving strategy,and uses the strategy to solve three typical problems of trigonometric function part,and establishes the relevant problem-solving model,let the students know how to find the train of thought in solving the problem.Finally,based on Polliat’s thought of solving problems,this paper puts forward eight suggestions on the teaching of solving problems of trigonometric functions,Understanding the topic stage: 1.Create life situations,stimulate interest in problem solving;2.Improving the ability of examination with the aid of metacognition monitoring.Programme development phase: 1.Present the same kind of problem,clarify the problem connection;2.Apply trigonometric formula to find the way of solving problems.Implementation Programme Phase: 1.Analyze the intention of the steps and realize the idea of solving problems.2.Standardize writing procedures to improve error correction ability.Stage of retrospective reflection: 1.Pay attention to typical example problem,set up problem-solving program;2.Skillfully using alternative teaching to cultivate innovative thinking.Then based on the above teaching suggestions,two teaching cases of trigonometric function exercises are designed to explore its practicality and feasibility.This paper is not only a kind of extension of Polliat’s thought of problem solving,but also has an important guiding value for students’ practice and teachers’ teaching of problem solving. |