Influencing Factors And Solving Strategies Of Mathematics Heuristic Teaching Validity

Based on the heuristic teaching in mathematics teaching,this study attempts to study the factors that influence the validity of heuristic teaching and puts forward corresponding teaching strategies.In this study,the index system of influencing factors of mathematical heuristic teaching was constructed from the theoretical perspective,and on the basis of influencing factors,the coding table of effective teaching behavior of mathematical heuristic was constructed,and the high-quality classrooms of 12 teachers in China were analyzed by video.Based on the concept of mathematical heuristic teaching validity,through video analysis,this paper summarizes and proposes the characteristics of effective teaching behavior of mathematical heuristic,and explores,discovers and puts forward the solution strategies to improve the validity of mathematical heuristic teaching according to the influencing factors and specific characteristics.The research mainly solves the following two problems:(1)The index system of influencing factors of mathematics heuristic teaching is constructed from the theoretical perspective,and the reasons for choosing "three dimensions and seven elements" are discussed.(2)Taking the high-quality courses of 12 teachers in China as the object,this paper analyzes and discusses the characteristics of teachers’ mathematical heuristic effective teaching behavior in high-quality courses,and proposes solutions based on the influencing factors.The main research conclusions of this study include: First,the relationship between the "three dimensional seven elements" of mathematical heuristic teaching and its function in heuristic teaching."Three-dimensional" refers to questions based on subject knowledge,students’ cognitive engagement,and teacher feedback.Their relationship is as follows: questions based on subject knowledge is an important object to activate students’ cognitive participation,teacher feedback is an important behavior to activate students’ cognitive participation again,and student cognitive participation is a specific response to questions based on subject knowledge and teacher feedback,and questions based on subject knowledge and teacher feedback influence each other.Their function in mathematics heuristic teaching is to activate students’ thinking repeatedly.The "seven elements" refer to question type,question explanation,question situation construction,students’ cognitive preparation for learning,students’ internal learning motivation,questions and questions.Second,the high degree of teacher’s stimulation in heuristic teaching can affect the active participation of students.In the case of high level of teacher stimulation,more students would actively question or question the answers of other students and express their own views on the basis of fully mastering the basic knowledge.Third,teachers frequently use questioning to motivate students and aim at the achievement of teaching objectives in high-quality classes.Teachers will focus on students’ mathematical ideas as a starting point,repeatedly use continuous specific questions,open questions and other ways to ask students to guide students to a higher level or more open thinking,and to achieve the teaching goals.Based on the research results,five suggestions are put forward for teachers to improve the validity of mathematical heuristic teaching:(1)Design appropriate problem situation for students.(2)Questionnaire is based on students’ mathematical ideas.(3)Give students some time to think.(4)Help students understand the problem in various ways.(5)Grasp the difficulty of the problem and the proportion of high level problems and low level problems.