Instructional Design For The Transformation Of Quantitative Relationship "Myth Concept"

In recent years,more and more attention has been paid to the teaching and training of students' algebraic thinking and number sense in primary school mathematics learning.Researchers have found that there are some deviations in students' understanding of quantitative relations such as equality relation,approximation relation,nearness relation,but it is the common goal of teachers and students to correctly understand the relationship between quantity.The theory of concept transformation provides a theoretical basis for the transformation of students' number relationship misconceptions.Based on the above reasons,this study carried out the relevant research on the conceptual transformation of quantitative relationship.This research adopts the methods of text analysis,investigation research and case design,mainly carries out the following research: Firstly,it analyzes the content of the equality relation,approximation relation,nearness relation involved in the primary school mathematics textbooks published by Jiangsu Education Press;Secondly,it carries out questionnaire survey and interview on students,and analyzes the possibility of students' misconceptions in three quantitative relationships according to the survey results;Thirdly,it analyzes the causes of students' misconceptions from three aspects of textbook arrangement,teaching process and students' learning;Finally,it designs the teaching scheme for students' misconceptions in three kinds of quantitative relationships.Through the research,it is found that students have the following misconceptions: The myth of equal sign direction,myth of equality property,myth of equation equal sign,myth of estimated value,myth of estimation process and results,myth of approximate equal sign direction,myth of the relationship between equality and approximation,myth of the similar concepts.The main reasons for students' misconceptions may be as follows: in the arrangement of teaching materials,the presentation of the content of teaching materials is single,the content of teaching materials narrows the meaning of concepts,and the arrangement of teaching materials lacks systematicness;in the process of teaching,teachers do not understand the meaning of concepts deeply,teachers despise students' understanding of the meaning of concepts,and teachers lack effective teaching strategies;in the students' concept learning,teachers are lack of effective teaching strategies,Proactive inhibition of concept formation,mechanical memory instead of concept understanding,thinking set hinder concept acquisition.In the teaching design of the concept transformation of quantitative relationship,it is carried out from two aspects: the overall teaching design and the case teaching design.The former is the overall design for all the misconceptions of a certain quantitative relation,and the latter is the case design for a certain misconception of the quantitative relation.In the case teaching design,it is designed from two aspects.On the one hand,it is designed for the concept transformation teaching of the existing misconceptions of the sixth grade students.The concept transformation teaching design follows the principles of student-centered,misconceptions centered and situation based,according to the idea of "creating situation,causing cognitive conflict;problem leading,exposing misconceptions;developing activities" On the other hand,in view of the concept teaching design when students begin to learn concepts to prevent students from having similar misconceptions,the concept teaching design is carried out according to the idea of "introducing concepts,establishing concepts,using concepts and consolidating concepts".