The Research On The Influence Of Auxiliary Line To The Geometry Problem In Senior High School

In current mathematical learning,the spatial geometric problems in high school are aconundrum.Providing correct auxiliary lines and problem representations is vital in geometryproblem solving.Thus,the quality of auxiliary lines and problem representations will directly affectthe problem solving.The main purpose of geometry teaching is to teach students how to use auxiliarylines and representations to solve the geometric problem correctly,add auxiliary lines and establishrepresentations to the spatial geometric problems.With the development of a psychologyexperiment,we are able to use a method which combines eye movement with geometric problemssolving and provide objective physiological indicators for the effect of various auxiliary lines onproblem solving.Thus,it leads to an indicator of cognitive fatigue which has a profound significanceon measuring students’learning efficiency and teachers’teaching effectiveness.This study selected48sophomore high school students in Kaifeng.Then36effectiveparticipants were gained.According to good or bad scores performance,we make groupingexperiment respectively.The research one focuses on discussing the figure of Eye Movement of highschool students in solving different types of auxiliary lines on spatial geometric problems.Theresearch two explores the figure of the representation of high school students in solving differenttypes of auxiliary lines on spatial geometric problems.Based on previous studies and eyemovements,we discusses the effect of different types of auxiliary lines,different gender participants and good or poor students on the discrepancy of high school students to solve the spatial geometricproblems.Also we deep analyze the effect of different types of auxiliary lines,gender subjects andgood or poor students on the representation of spatial geometric problems among high schoolstudents.The conclusions are as follows:First,the good or poor students differed evidently in terms of eye movement indicators insolving the different type’s high school space geometries which share different auxiliary lines. Thespecific performance is that the excellent students use much less time and frequency than the poorstudents significantly in the average solving time, average fixation count, average backsight time,average fixation duration.Second,there did exist some discrepancies in the indicators of eye movements when the subjectswere solving problems containing different auxiliary lines. The specific performance is whensubjects solves the high school geometry problems, the students who use core auxiliary line usesignificantly much less time and frequency than the students who use interference auxiliary line inthe average solving time, average fixation count, average backsight time, average fixation duration.Third,the distinction of gender is not significant,namely,the different gender subjects did notdemonstrate the significant distinction in the eye movement indicators.Forth,there existed a distinction of representation strategies between good and poor students intheir solving the spatial geometric problems sharing different types of auxiliary lines.The goodstudents are apt to use visualize strategies while the bad students are apt to use content repeatingstrategies.There was no significant distinction among representation strategies when subjects utilizing different representation strategies solved the various kinds of auxiliary lines of spatialgeometric problems and the changes of type of auxiliary lines do not give rise to the changes in thecoinciding representation strategies.After subjects solved the high school geometry problems with different types of auxiliary line,the subjects within cognitive tirelessly team use significantly much less frequency than highcognitive tired team; the subjects within low cognitive tired team use significantly much lessfrequency than high cognitive tired team; the papillary diameter of subjects within cognitivetirelessly team is significantly bigger than high cognitive tired team; the papillary diameter ofsubjects within low cognitive tired team is significantly bigger than high cognitive tired team.