A Study On Error Detection And Correction Teaching Of Pre-service Mathematics Teachers

As a special learning material,errors have attracted extensive attention and high regard of researchers of mathematics education.In order to help students learn more effectively and improve the teaching quality,mathematics teachers need to understand the characterization and types of students’ errors,dissect the underlying causes,provide the corresponding solutions and develop targeted teaching strategies in their daily work.Therefore,it is an important task which cannot be neglected for mathematics teachers to deal with students’ errors.However,pre-service mathematics teachers may have insufficient teaching experience,inadequate solid expertise,and a bias in the perception of errors,all of those will affect how they deal with mathematical errors in teaching.Based on the general reality,this research aims to analyze the performances of preservice mathematics teachers from the following three aspects,which are the cognitive orientation of mathematical errors,the ability to analyze written mathematical errors and the teaching performance targeted at mathematical errors,and explore the connections and differences among them through the four research tools,namely the error orientation questionnaire,the mathematical error-detecting test,the mathematical error-detecting teaching task and the mathematical error-detecting open question.To realize the above research purpose,131 pre-service mathematics teachers were recruited and identified as the research objects in this study,and the data were collected through the combination of questionnaire,paper-and-pencil test and teaching observation.Research questions are set as follows:Question 1.How do pre-service mathematics teachers solve math error-detecting problems? How do they perform in the math error-detecting test?Question 2.How do pre-service mathematics teachers implement math errordetecting teaching?Question 3.What is the error orientation of pre-service mathematics teachers?What do they think of math error-detecting problems?Question 4.How about the connections and differences among pre-service mathematics teachers’ math error orientation,performances in math error-detecting tests,and performances in mathematical error-detecting teaching task?For research question 1,when the pre-service mathematics teachers deal with the mathematical error-detecting problems,they give out four kinds of problem-solving strategies,which are "contrast","symbolic-graphic combination","looking for counterexamples" and "backward thinking".The performances of pre-service teachers in the error-detecting test are not satisfactory,as many problems are revealed in the paper-and-pencil test.In addition to not having given out the correct explanations and amendatory schemes,some pre-service mathematics teachers make various mistakes in the process of writing.For research question 2,based on the analysis of videos,the teaching process of pre-service teachers can be divided into 5 stages of error introduction,error interpretation,error correction,error variation and error summary.Using the Analytic Hierarchy Process,different weights are given to each step,so as to calculate each preservice teacher’s total score of teaching.Generally,the pre-service teachers perform well in error interpretation and error correction,moderately in error promotion,and badly in error introduction and error summary.For research question 3,in the study of mathematical error orientation,among the positive dimensions,error learning achieves the highest average score,while error ability achieves the lowest.Among the negative dimensions,the average score of error pressure is the highest,while that of error concealment is the lowest.Pre-service teachers believe that math error-detecting problems are more "error-prone" and "uncertain" than those they usually encounter,and "working backward" is more stressed in the process of solving these problems.They also believe that the mathematical errordetecting problems have certain educational value.For research question 4,concerning the connections,there is a negative correlation between error stress,error communication and the total score of the written test.There is a positive correlation between error correction,error variation,error summary,the total score of teaching and the total score of written test.There is a positive correlation among error learning,error risk and error correction.Concerning the differences,in terms of gender,error communication shows a significant difference.In terms of grade,the total score of written test and error variation show a significant difference.Taking pre-service mathematics teachers as the research object,and mathematical error as an entry point,the research discusses pre-service mathematics teachers’ performances from three aspects,namely the orientation of mathematical errors,the mathematical error-detecting test,and the mathematical error-detecting teaching,and the relevance among them.The research is of great innovation.It enriches the existing research on mathematics teachers’ knowledge,concept and teaching.It deepens relevant research on the specific type of mathematical error-detecting problem.It is also revelatory of the training of pre-service teachers,the designing and use of mathematical error-detecting problems in teaching.