Research On The Probation And Transformation Strategies Of The High School Students' Function Misconceptions

The concept consists of knowledge,and it is also the basic unit of the form of thought.Mathematical concept is the starting point of the logic deduction of mathematical knowledge as well as the junction point in the cognitive structure of students.So the understanding and mastery of basic mathematical concepts is the foundation of learning mathematics,which determines students' mathematics Competencies accomplishment.Scientific research and instruction practice has shows that students' minds are not a blank before entering classroom learning.Students often form concepts related to mathematics themes in daily life and their own practical experience,including misconceptions which are different from the correct concepts.Misconceptions As the original state of the concept of mathematical concepts,misconceptions may hinder the understanding of new knowledge,or combine with the study to generate a new misconception.Because there are a lot of misconceptions which has greatly influenced the scientific understanding and learning of mathematics knowledge,and thus formed the students' "hearing but do not understand","understanding but cannot use”,“using but cannot do it accurately”.Based on the reasons of the above,the author take high school function learning as an example,and focuses on the following issues around the core theme of "misconception":1.What kinds of misconceptions do students have in functional concept learning? and what is the difference between different groups' understanding of function concepts?2.What are the origins and causes of the concept of these misconceptions?3.What kind of teaching mechanism strategies can effectively defense or transform the misconceptions of functions of students?To solve above problems,first of all,studied the teaching materials and curriculum standards,detailed and comprehensive combed out the high school function concept knowledge system.Then we used the literature and interview methods to collect the misconceptions that may exist in function learning.Based on this,we combined the teaching experience of first-line teachers to form a preliminary Research tools(test questions of two—tier diagnostic assessment and interview outlines).In this study,226 students of JS middle school in C city were selected for formal test.Through data recovery and processing,it was found that the research tools had good reliability and validity.The results of the study show that under the current teaching conditions,there are four misconceptions in the learning of high school students: the confusion in the concept of function category;the confusion in the symbolic representation of function concept;the inner connection of function concept knowledge system;the misunderstanding caused by the lack of connection between function and other knowledge.According to test shows that due to different grades,genders,and arts and sciences,high school students have significant differences in the understanding the concept of functions.The formation of the misconception of students is influenced by three aspects of teaching materials,teachers and students.For teaching materials : there is some improper use of examples to elicit function concepts;and after-school exercises cannot help students to better understand function concepts;Besides,the functional knowledge arrangement system needs to be improved;the history of development of function concepts lacks application.In terms of teachers: their teaching is split ignoring the generation of function concept;and they tend to utilize mechanical problem training,ignoring the strengthening and flexible application of the essence of the concept.In students' aspects: they have cognitive "inertia" and are likely to be influenced by the negative transfer of the former knowledge;The high school students' abstract thinking and reasoning ability need to be improved.To solve the "stubborn disease" in the function concepts misconception depend on both "defense" and "remedy".The defense relies on three aspects: teaching material,teachers and students.In terms of teaching materials: we need to strengthen the cohesion between junior and senior school functions;create situations to let students experience the process of "mathematicization";he function knowledge system need to be optimized with advanced learning;the exercises should be selected deliberately to promote the understanding and transformation of the function concept essence and function history should be integrated into teaching materials.In terms of teachers: In the process of concept formation,teachers enrich conceptual images with technological rationality,they create courses and flexibly apply textbooks and consciously train students to abstract thinking and reasoning ability.Students themselves need to form good learning habits.The misconceptions which has been found needs to be "remedied" in a timely.The transformation of concept mainly depends on two paths:the concept reconstruction and to enrich the concepts,which mainly include the weak reconstruction of concepts,transition function symbols on the concept of myth;strong reconstruction of concepts,building function and other sections in the connection between knowledge;concept cut and merge,altering the misconception of the function concept and complete the concepts;conceptual enrichment and unification,transforming the misconception in the inner connection of concept knowledge system.