Theory Research And Practice Of High School Mathematics Problem-solving Teaching

As a new model of education, problem-solving teaching is receiving more and more attention andits related studies had been made some progress with the new round of depth development of reform ofbasic education in China."Problem-solving" teaching has also entered into the mathematics classroom, itposees challenge to traditional mathematics teaching mode and produces good results. However, due to thebroad and vague of problem solving theory itself, as well as some one-sided understanding of the teachingstrategies of teachers, and many other reasons, result in "problem-solving" teaching a lot of problems andmisunderstandings at the operational level. Therefore, using new teaching and educational concepts andtheories of modern mathematics education study on mathematical problem solving teaching method is veryimportant. In view of the current problems existing in the teaching of problem solving, exploratory practiceand reflection are of great significance to further refinement and improvement of mathematics"problem-solving" teaching strategies and more effective teaching practice.Since America Mathematics Teachers’ Federation proposed "problem-solving" is the core ofmathematics education in1980,the problem solving is listed as one of the main research topics byCongress of Mathematics Education, countries around the world have been carrying out research onteaching of mathematical problem-solving. Most of our nation’s research is the appropriate presentationand introduction of related study abroad, and make a wide range of research at the theoretical level ofproblem solving teaching, formed certain characteristics.on study."Problem-solving" has not onlydeveloped students’ problem-solving ability, but has a broader teaching guiding ideology and a significanceof fundamental reform. For students, the purpose of problem solving is to make students to learnmathematical thinking,enable studentsexperience the whole process from the discovery of the problem to solving the problem,and guide the students to creatively apply mathematical knowledge to solve variousproblems of non-simple exercises, including practical problems and problems from the internalmathematics, so as to improve their cognitive structures. For educators, problem-solving is a teaching mode,make students as sceptics, discovers, explores, and other roles, discovery knowledge, analysis, solveproblem, construct, develop skills of problem solving. Mathematics teaching must enable students toacquire knowledge through their own initiative inquiry activities, and maste the re-creation methods inlearning. Problem-solving teaching allows students to maximize the independent exploration, autonomouslearning, cooperation and exchange in the learning process.This article summarized the problem solvingteaching mode on the basis of the researches of others, the teaching program include:(1) Create problemsituation;(2) Guide students to characterize the problem properly, of implement the explorationindependently;(3)Organize students cooperation and exchange, solving problem;(4) Reflect and evaluate.During the teaching process of problem solving, teachers should try to accurately determine a student’sexisting knowledge level and research capacity; use the contradictions between new knowledge and thestudents ’ existing knowledge of cognitive structure, present questions in the students’ power to grasp butalso set a certain amount of difficulty to inspire students ’ interest in learning and at the same time achievethe aim of enhancing students ’ self-confidence. Due to students’ knowledge basis and cognition indifferent ways, and take the problem-solving strategies differently, therefore, teachers should encouragestudents to attempt boldly, advocate diversification strategies in teaching.