Research On The Ability Of Posing Mathematical Problems Based On Reverse Thinking

With the continuous and in-depth development of mathematics education in China,many problems that people have neglected before gradually emerge.For example,in school teaching,the development of students' problem-solving ability was valued,while the development of students' problem-finding ability and problem-posing ability were ignored,people paid more and more attention to this kind of problems.In the era of promoting the balanced development of students,we need to further understand and comprehend the value of finding and posing problems,and explore ways to cultivate the ability of finding and posing problems.The development of reverse thinking has a great influence on the whole process of students' thinking development,balanced development of students' ability of forward thinking and reverse thinking is an important way to improve students' quality.At present,students' ability of reverse thinking is generally weak,so improving the ability of reverse thinking is an important problem in mathematics education subject.The great Newton and Leibniz discovered the potential connection between differentiation and integration,so that calculus can be widely used in people's production and life,discovering the connection of the essence of things is also an important process of people's progress,so this paper is based on the comprehensive thinking of finding and posing problems and reverse thinking,it aims to search the relationship between them and explore their education laws,and then explore how to improve students' problems-posing ability with the help of the improvement of reverse thinking ability,in addition to study teaching strategies.The significance of this study has two points: first,to enrich the research perspective of problem-posing;the second is strive to further perfect feasible teaching strategies for improve students' ability of reverse thinking and problem-posing,so as to form more optimized teaching strategies.The research questions mainly have three aspects are as follows:(1)The internal relation between the ability of posing mathematical problems and the reverse thinking;(2)Investigation on the situation of posing questions by using reverse thinking;(3)How to improve students' ability of posing questions with the help of improving their ability of reverse thinking.For the questions to be studied,this paper adopts the methods of literature research,investigation,case analysis and so on.The main findings show that there is an internal relationship between problem-posing and reverse thinking,reverse thinking is an important way to find and pose problems.From the opposite side of the research problem,we can get new questions,for example,“the sum of any two prime numbers greater than 2 must be an even number not less than 6”,from the opposite point of view,“any even number that be not less than 6 can be expressed as the sum of two prime numbers”,that is the famous Goldbach conjecture;according to the author's investigation,although both teachers and students have realized that the ability of reverse thinking and posing problems play important roles,but students' ability of reverse thinking is still weak,and they don't have a strong sense of posing problem,Among them,the situation of using reverse thinking to pose mathematical problems is rare,which shows that students' development in this aspect is insufficient.On the basis of investigation and research,this paper holds that in order to cultivate students' ability of using reverse thinking to posing problems,teachers should pay attention to the method of infiltrating reverse thinking in knowledge learning to find problems in normal teaching;in addition,they should guide students to find problems through reverse thinking;teachers should pay attention to the coordination of thinking to promote the development of problem-posing ability.Because reverse thinking can also guide students to find and pose problems in knowledge-learning and problem-solving,so it is necessary to infiltrate the cultivation of reverse thinking into all aspects of teaching,and cultivate two-way thinking in knowledge learning,problem-analysis and problem-solving.