Grade 8 Students’ Performance In Solving Geometry Proofs By Employing Auxiliary Lines ——A Case Study From School Y In Chongqing

Auxiliary line plays an important part in junior middle school geometry teaching,and it also marks the focal and difficult point for teachers and students in the front-line teaching and learning.In recent years,there are many researches on students’ geometric thinking level or problem solving performance,but there are few researches involving auxiliary lines.The study raises the following two research questions.First,from the two dimensions of description level of auxiliary lines and completion degree of geometry proofs,how do the students of Grade 8 perform in solving geometry proofs by employing auxiliary lines.Second,is there any difference between different genders and different academic achievements in the performance of students of Grade 8 in solving geometric proof problems by employing auxiliary lines?By sorting out the theories and literature of “Thinking Levels”,“Auxiliary Line” and“Problem-solving Performance”,this thesis,based on the actual research,determines SOLO Taxonomy as its theoretical basis,and observes students’ problem-solving performance of solving geometric proofs by employing auxiliary lines from the perspectives of description level of auxiliary lines and completion degree of geometry proofs and also conducts two researches to investigate the performance of the students from two classes in Chongqing by using test methods.The pretest investigates the validity of the degree of difficulty and the length of time of the test,constructs the evaluation framework according to students’ written answers and then evaluates the written answers in the pretest.Based on the pretest,the formal test is conducted after adjusting its questions,methods of marking.In the analysis of data and results in the formal research,the result shows that there is no obvious difference between different genders in the description level dimension and completion degree dimension,but students of different academic achievements exhibit obvious difference in the two dimensions.From the perspective of the SOLO Taxonomy,the description level of most students are on the stage of level 2,the transition from level 2 to 3 or level 3,and the overall performance of students is at middle level.In terms of the completion degree of problem-solving performance,students exhibit differentiation,because students who are on the stage of the transition from level 1 to level 2 make up one third of the total number and more than half of the students can achieve level 3.From students’ written answers,the overall performance of students’ completion degree is better than the description level.This study,based on the research results,provides with three suggestions: first,teachers should give equal treatment to students of different genders and also should teach students in accordance with their aptitude according to their different test performances;second,teachers should focus on the principles of describing auxiliary lines,and promote the development of auxiliary line description;third,homework and mistakes of written answers are significant resources in class,and the bottleneck in solving geometric proofs should be considered as a chance to develop students’ geometric thinking and an emphasis of teachers’ geometric teaching.