Study On Learning Progression Of Quadratic Function Of Ninth Grade Students

Learning progression refers to the process in which students learn a core concept in a period of time.As an important part of middle school function,quadratic function is an important content throughout middle and high school mathematics curriculum.As an important part of middle school function,quadratic function is an important content throughout middle and high school mathematics curriculum.A large number of teaching practices and empirical studies show that there are many problems and difficulties in learning and teaching unary quadratic functions.In view of this,based on the concept of learning to determine teaching,it is necessary to explore students’ learning rules about unary quadratic function.This study explores the learning rules of quadratic function from the perspective of learning progression.The research questions are as follows: First,what are the rules of the learning progression of the content of quadratic function for ninth grade students? What are the differences in the rules of learning progression among different groups? Second,how to improve curriculum teaching and evaluation based on the rules of learning progression? In order to answer the first question,the researcher have carried out three sub-studies successively:(1)sub-study 1: construction of hypothetical learning progression of unary quadratic functions;(2)sub-study 2:Development of learning progression assessment tools for unary quadratic functions;(3)sub-study 3: An empirical study on the learning progression of quadratic function for ninth graders.The methods used in this study are: text analysis,survey,interview,expert consultation and statistical analysis.In the stage of constructing hypothetical learning progression,text analysis method and expert consultation method are used to construct hypothetical learning progression of quadratic function through the research and analysis of the curriculum standard textbooks and related literature of learning progression,and after the expert consultation,the hypothetical learning progression is revised;In the development of measuring tool stage,using the method of text investigation method,interview method and expert consultation method,reference the textbook examples exercises and examination topic in recent years,compiled a set of quadratic function test,through expert consultation prediction and interviews,and a better quality of eventually developed quadratic function learning progression measurement tools;In the inspection and correction learning progression stage,using the survey method and statistical analysis,a formal test was conducted for ninth grade students in three classes of three schools in Suzhou,Nantong and Shanghai,and then the collected test data encoding,uses the Rasch model for data analysis,and on the assumption of quadratic function learning progression modification.The following four conclusions are drawn in this study: First,the learning progression model of quadratic function contains six levels: Level 1,knowing the definition of quadratic function and judging whether the relationship between two variables is a quadratic function according to the image;Level 2,can preliminarily understand the basic properties of quadratic function and can determine the analytical formula by undetermined coefficient method;Level 3,Understand the concept of quadratic function and determine the properties of quadratic function through images.Level 4,know the relationship between the properties of quadratic function and can determine the properties of quadratic function by analytic formula;Level 5,can transform the different representation methods of quadratic function to each other,and initially establish the relationship with other concepts;Level 6,have a complete concept of unary quadratic function,can solve the problem of quadratic function of the composite.Second,there are differences in the level of students’ progression level using different versions of textbooks.Third,progression level differences of different gender students.Fourth,quadratic function of three representation of progression level from low to high respectively is image method,table method,analytical method;The progression level of the three analytical formulas from low to high respectively is general type,top point type,two point type.Finally,some suggestions are put forward for the curriculum development,teacher teaching and academic evaluation: In the curriculum development,students’ understanding of quadratic function does not strictly follow the straight line development,but presents a spiral upward trend.Therefore,the curriculum content of quadratic function should be designed in a spiral upward way.In addition,the practical application content of quadratic function should be added in the textbooks of Shanghai Education Edition.In the teacher teaching,teachers should step by step,pay attention to the formation process of knowledge,pay attention to the organization of review,also should strengthen the teaching of the essential characteristics of quadratic function,pay attention to the combination of numbers and shapes of the thought of infiltration,cultivate students mathematical modeling ability.In the academic evaluation,teachers should examine students’ understanding by open questions,pay attention to the problem solving ideas of low level students,and find the root of cognitive errors.