"Knowledge Misunderstanding" And Its Correction Research In High School Students' Mathematics Learning

The purpose of high school students' mathematics learning is to correctly understand and apply mathematics knowledge,to exercise and improve their thinking ability in the process of understanding and application.Through the questionnaire survey,this study found that the mathematics learning level of some high school students is far from the requirements of their curriculum standard.In the process of understanding certain knowledge,they often feel confused or draw wrong conclusions when they follow the direction of their thinking to a deflected course,which has not been appreciated and studied intensively this phenomena.Inspired by the justification for"prejudice"of the philosophical hermeneutics,this study proposes that when high school students decode the correct information given by the teacher or the text,because of the different characteristics of the individual's knowledge structure and the tendency to choose,the information cognition with deviation or lack of the primary is formed,which is '"knowledge misunderstanding",being abbreviated to"KM".This kind of preliminary understanding of the individualization of mathematics knowledge is an intangible knowledge system.The objective of studying the KM in high school students'mathematics learning is to find the key cause for part of students to learn mathematics so difficultly,and to liberate them from the shackles of feeling shame of making mistakes in mathematics learning,so that they do not evade but actively face any problems in mathematics learning,and learn to accept and treat different ideas,discourses,and erroneous conclusions concerning mathematics knowledge with kindness,and finally maintain a more positive and open attitude toward "KM" in order to rectify the "KM",furthest.By doing so,students not only learn mathematics but also learn how to learn and enjoy learning mathematics,which is the requirements of mathematics curriculum standards.Meantime,this study reflects on the value of teachers who become researchers so as a case study to contribute high school mathematics teaching to the study of mathematics education,teaching theory and misunderstanding theoryThis dissertation first conducts literature reviews,and then defines the core concept of"knowledge misunderstanding",constructs the research approach and the techniques and methodologies of the KM and its correction in high school students' mathematics learning.With the help of the collection and analysis of teaching observation and reflection,teacher interviews,student interviews,questionnaires,etc.,and by the action research,the KM in high school students'mathematics learning is collated and corrected.Firstly,the KM is explained from different perspectives of philosophy,psychology and pedagogy.Then,the basic knowledge of mathematical concepts,formulas and exercises in the compulsory modules of high school mathematics textbooks is examined in detail,and next,the phenomenon that students are prone to generate KM and its laws and correction methods should be screened out,and then classified and attributed.KM is classified according to the text,and there are KM in teaching materials,homework,extracurricular exercises and test papers;the language factors of KM is caused by speech,semantics,symbols,graphics,etc.According to the logical relationship of the KM in the mathematical knowledge system,it is divided into two:vertical and horizontal KM.The KM is attributed to finiteness of words,the complexity of speech,the difference of semantics,the abstraction of symbols,the intuitiveness of graphics,and other objective factors,which are attributed to narrow vision,influence from life,improper metaphor,and misplaced and other subjective factors.The KM has incomplete,unclear,unstable and other characteristics,which are characterized by deficiency,ambiguity,dynamics,etc..Based on the classification,characteristics,attribution and effects of KM,this research summarizes the correction basis,principles,standards,approaches and specific methods of KM.The correction of KM is necessary,possible and feasible.The principle of correcting KM is timely,active,appropriate,tolerant and specific,etc.The correction of KM can be seen from the following three ways,focusing on the original misunderstandings,comparing differences between right and wrong,and students understanding instantly;The correction ways of KM include effective interaction,homework and test feedback,questionnaire survey and analysis,student self-study and reflection.KM correction which are based on teaching materials and the concept of KM has nine model methods which are model method,drawing method,and formula-based induction,deductive method,assimilation method,etc.,with a total of nine specific methods.However,based on the problem-solving strategy,there comes up with six methods for problem-solving,such as lowering the requirement,timely zeroing,the function self-comparison etc.Based on student self-analysis,KM correction has student communication,investigative written assignments,action salons,and mutual inspections methods.In the action research of correcting in mathematics KMS the researcher explores the deep causes for students to generate mathematical KM from the practice of mathematics teaching.Along the main line of the change attitude of students'towards KM,the improvement ability of finding and explains the origin of KM,and the significant improvement of learning performance after KM corrected,it elaborates the process of KM correction.In an action study comparing the results,the t-test data of independent samples of the two classes were analyzed,and it was concluded that there was no significant difference in the math learning performance of the two classes in the first two tests,and there was a significant difference in the third test results.The math performance level of the class concerned about KM correction was higher than that of the class using traditional methods to answer questions,and the standard deviation of the data was lower.Therefore,the correction of KM has a positive impact on the learning effect of high school students.According to the research results,the following conclusions are drawn:(1)KM can be classified according to different criteria;(2)KM has incomplete,unclear and unstable characteristics;(3)The correction of KM should follow the principles of timeliness,initiative,moderation,tolerance,and specificity.(4)The correction of KM helps students improve their learning level.This study combines misunderstanding theory with high school students'mathematics learning practice,and studies the KM of high school students in mathematics learning from the perspective of philosophy and linguistics which is a new attempt.There are still some shortcomings in the above studies.(1)The school-based teaching and research of this study is not deep enough;(2)Due to the limitations of research time,the research subjects have certain limitations;(3)Due to limited research level,the collected data has not been fully utilized.In the actual teaching,there are more KM that need continuing study in the future teaching practice to make it more comprehensive and systematic,so as to provide a direct reference for mathematics teachers to effectively correct students'KM and provide other teachers references for further teaching and research in other disciplines.