Advanced Study On The Concept Of Mathematics Function In Middle School

In recent years,learning progression has become a hot topic in the field of education,which is of great significance to change the confusion,scattered and improper connection of knowledge.The concept of function is an important and difficult point in middle school mathematics teaching.Because of the difficulty in mastering the knowledge ontology and mathematical symbols,it is arranged in the two learning stages of junior high school and senior high school.Although this is conducive to students' learning,it is inevitable that there is a disjunction of teaching in junior and senior high schools.Therefore,how to build the learning progression of function concept is the core of the research?Function concepts are used as research objects,and learning progression theory is used as a research tool.Through the literature analysis method?questionnaire survey method?expert interview method ?and case analysis method,the learning progression of function concepts is constructed?modified and explained.The conclusions are as follows:(1)Advanced variables:cognitive thinking and cognitive perspective.Students' cognitive thinking has gone through the steps of“image perception?establishment of appearances ?stepwise abstraction?problem solving”,and the cognitive perspective has gone through the steps of“variables?movement changes?the transition from variables to correspondences ? correspondences ? system synthesis ”.(2)Determination of advanced dimension:the function concept is divided into two dimensions for model building,function concept representation and function concept application.(3)Based on the division of advanced variables and achievement level,combined with the curriculum standard,teaching materials,students' expected performance is as follows:the research of existing literature further refines the advanced dimension into knowledge preparation,preliminary understanding of function concept,reunderstanding of function concept,application of function concept and forming concept system.On this basis,a specific description is made,the advanced theoretical model of function concept learning is completed,and the rationality of the model is illustrated with a case.Based on the learning progression model of function concept learning,a teaching design model is developed in the perspective of learning progression.It can be divided into the following steps:defining the starting point of advance and reproducing the original experience;setting up advanced activities and building functional relationships;examples to consolidate knowledge and promote the occurrence of advance;exercising empirical test to judge the class of students;setting up hierarchical assignments to achieve the goal of advance.Some strategies to promote function concept learning based on advanced learning.Taking advanced learning as the carrier,attach importance to conceptual cohesion;taking functional concept as the foothold,improve knowledge advancement;taking life situation as a series,promote literacy advancement.