A Case Study Of Cultivating Senior High School Students’ Mathematical Reflection Ability Based On Error Management

The General Senior High School Mathematics Curriculum Standards(2017 Edition)clearly states that “the students ability to find and propose problems,analyze and solve problems from the perspective of mathematics should be improved”.Cultivating students’ "four abilities" is inseparable from in-depth analysis and reflection on mathematical learning activities,which shows that the research on cultivating students’ mathematical reflection ability is of great value.In mathematics learning activities,learning mistakes are inevitable,especially in solving problems.Although the mathematics wrong question is an important resource reflecting the students’ lack of learning activities,the current students can only correct and collect mathematics wrong questions,and lack the in-depth analysis on wrong questions.This research takes the wrong questions analysis as the cornerstone,further excavates the wrong questions,strengthens the reflection on the wrong questions,and seeks ways to improve students’ ability of mathematics reflection.This study uses questionnaires,literature methods,think aloud protocols,interviews,physical analysis and case studies to solve two problems.First,to investigate the status of high school students’ error management and the status of mathematical reflection ability,analyze the improvement strategies.Second,to analyze typical cases and study the error management-based basic process to develop students’ methods of improving mathematical reflection ability.Main conclusions of the study: First,through the questionnaire survey,this paper finds that high school students pay more attention to the wrong question resources,hold positive correction attitudes,but lack effective management actions and strategies.High school students have a medium level of mathematical reflection ability and have a preliminary sense of mathematics reflection,but most students do not have good reflective habits and clear reflective skills.And then,through the analysis of the literature and the questionnaire,this paper draws the basic process of mathematical error management: Question analysis→reflection on the cause of wrong→extension.That is to say,analyze the question and the knowledge points,summarize the purpose of the question and the question-solving strategy,and analyze the type of question-solving error.Secondly,reflect on the direct causes and underlying causes of errors in the process of solving questions and future considerations.At last,draw inferences from one example,change the purpose of the question and make achievements from the question.There are two main points in the innovation of the research: First,combine the wrong management with the mathematical reflection ability.This research is based on the basic process of mathematical error management,and through the guidance of the management and reflection process of the specific wrong question of typical case to find the method of cultivating the ability of high school students to reflective ability on mathematics.Second,the study uses the think aloud protocols to judge the changes in students’ ability to reflect on mathematics,and to make the recessive process explicit.It is an improvement over the previous method that only depended on the rise and fall of math scores to judge the change of mathematical reflection ability.