The Obstacle Analysis To Solving Mathematical Problem With Implicit Conditions For High School Students And Teaching Countermeasure

"China’s eighth basic education reform" proposed to pay attention to the cultivation of students’ ability to solve problems,"ordinary high school mathematics curriculum standards(2017 edition)" pointed out that to improve students’ ability in solving problems,in the current teaching,the main way to achieve this requirement is by exercising.The exploration of problem-solving ideas for students is based on their understanding of the topic.The topic mainly includes explicit conditions and implicit conditions.Here,the implicit conditions have certain concealment and are easy to be ignored by students.In the process of solving the problems,excavating the implicit conditions hidden behind the problem is related with students’ Abilities,such as information extraction and integration,logical thinking and reasoning,and other aspects.In the process of teaching practice,the author noticed that the negelect of implicit conditions in the topic leads many problems.For example,the process of solving problem is not rigorous,the ideas of solving problem are interrupted,the results of solving problem are wrong and so on.Therefore,it is very important for students to study and put forward specific teaching suggestions for teachers in solving mathematical problem with implicit conditions.This paper first introduces the current state of research on solving mathematical problem with implicit conditions and gives the theoretical basis of this paper.Then,on this basis,the paper classifies the topics with implicit conditions in the recent five years of national college entrance examination mathematical papers and analyzes their proportion,by editing test papers and questionnaires,combined with interviews,the following questions are mainly studied:(1)types of obstacles in solving mathematical problem with implicit conditions for high school students;(2)the correlation and difference between solving mathematical problem with implicit conditions,implicit conditional excavating ability and ordinary mathematical problem solving;(3)the difference of hidden condition ability of arts and science students and students of different genders;(4)the causes of obstacles in solving mathematical problem with implicit conditions for high school students and the causes of differences for different levels students.Then,through statistics and analysis of the collected data,the following research results are obtained:(1)the obstacles for high school students to solve problem with implicit conditions include: the obstacles of analyzing the topic,thinking obstacles,problem presentation obstacles and psychological obstacles;(2)there is a positive correlation between solving mathematical problem with implicit conditions and the ability of excavating implicit conditional and ordinary mathematical problem solving,there are significant differences in solving the problem with implicit conditions and the ability of excavating implicit conditions for different levels students;(3)there is no significant difference in the ability of excavating implicit conditions for arts and science students and the different genders of students;(4)the main causes of obstacles are:weak awareness of analyzing the topic,poor habits of analyzing the topic,mathematical formulaic,one-sided thinking,poor cognitive structure,negative effects of thinking stereotypes,etc,the causes of differences for different levels studens are mainly reflected in the aspects of analyzing the topic,cognitive structure,thinking stereotypes,reflection and review.Finally,based on the findings of the study,the following teaching suggestions are put forward: pay attention to the teaching of " analyzing the topic ",emphasize the importance of excavating hidden conditions;consolidate the basic knowledge and construct the framework of knowledge;teaching based on the error samples,so that students are alert to the implicit conditions in the topic;Scaffolded teaching inquiry to guide students to excavate implicit conditions.