Mathematical Problem Situational Characteristic Element Analysis And Application Research

Since the new round of curriculum reform,problem situation has become a very important research topic.In order to promote the development of mathematics education,experts and scholars have studied the situation of mathematics problem deeply.This paper mainly adopts questionnaire survey method,experimental research method and content analysis method.The research contents mainly include the following three aspects.Firstly,on the basis of relevant studies at home and abroad,a questionnaire is prepared to construct the analysis framework of mathematical problem situation.Secondly,the test volume is compiled to verify the scientificity of the framework.Finally,using the framework,this paper analyzes the characteristics of the setting of the mathematical situation in Nanjing high school entrance examination in the past eight years,and gives some teaching suggestions.The results of investigation and analysis show that:1.There are seven characteristic elements in the mathematical problem situation:situation type,text length,presentation mode,knowledge content,task level,degree of contextual interference,and degree of openness.2.The level division of situational characteristics of mathematical problems is as follows: the type of situation can be divided into four levels--individual situation,social situation,occupational situation and scientific situation.The length of text can be divided into simple--1-2 lines,medium difficulty--3-5 lines,difficult--6 lines or more.The way of context presentation can be divided into four levels--the combination of story or plot text and chart,the non-text form such as graph or table,the text form of story or plot,and the pure number symbol or phrase.Knowledge content can be divided into simple--1-2 knowledge points,medium difficulty--3knowledge points,difficult--4 or more knowledge points.The task level can be divided into three levels--knowledge understanding,knowledge transfer and knowledge innovation.The degree of contextual interference can be divided into three levels--fully detached state,semi-detached state and fully integrated state.The degree of openness can be divided into two levels--good structure and bad structure.3.The influence of the seven characteristic elements on students’ problem solving is ranked in order from large to small: knowledge content,task level,situation type,presentation mode,text length,degree of openness,degree of contextual interference.The test results verify the scientificity of the above analysis framework.The analysis results of the mathematical situation in Nanjing 2012-2019 middle school entrance examination show that:1.In the past eight years,the number of situational questions in mathematics test is less,but the score is more.There’re mainly focusing on solving problems,supplemented by multiple choice questions and fill-in-the-blank questions.The content fields of situational questions are mainly numbers and algebra besides statistics and probability.2.In the past eight years,the difficulty span of mathematics situational test questions in the middle school entrance examination varies greatly in two factors:“situation type” and “presentation mode”,while the degree of difficulty varies little in four factors: “text length”,“knowledge content”,“task level” and “degree of contextual interference”.In terms of the overall situation,the difficulty of mathematics situational test in the past eight years is not balanced among seven factors,mainly reflected in the “text length” and “knowledge content”,especially the“degree of openness”.