Conceiving The Main Line Of Content Development For Primary And Middle Schools’ Analytic Geometry Curriculum

Under the background of Chinese new round of curricula reform,we formulate the object of this research as conceiving the main line of content development for primary and middle schools’ analytic geometry curriculum(“main line of curriculum” for short),so as to help teachers better understand the student cognitive development with regards to analytic geometry and provide a rational reference for the effective arrangement of textbooks,which would further promote the implement of the new curriculum.The main line of curriculum here is essentially a development sequence of the curriculum content,prescribing what to learn first and what to learn next during students’ exploration of a particular topic over quite a long period.This concept is rooted in the theories of “learning progression” and “learning trajectory”,integrating the development pattern of student thinking levels with the pedagogical consideration about the convenience and appropriateness for teaching practice.To achieve this object,this research has adopted the expert appraisal and content analysis methodology;first identified four core concepts in analytic geometry: Cartesian coordinate system,equation of the straight line,conic sections and their equations and the algebraic expression of geometrical transformation;then hypothesized the learning progressions revolving around the core concepts above combined with Freudenthal’s theory of didactical phenomenology,Piaget’s,Tall’s and Van Hiele’s propositions about the stages of child’s cognitive development,as well as other relevant empirical researches;after that took the learning progressions as the framework of content analysis,comparing the arrangement characteristic among 7 countries’ curriculum standard;next revised and refined the learning progressions into a preliminary “main line of curriculum” according to the results of content analysis,by this way the consideration about the convenience for teaching could be introduced;finally examined and adjusted the preliminary line by expert appraisal.In the finally determined main line of content development for analytic geometry curriculum,the Cartesian coordinate system can be constructed through two approaches: one starts from “locating,map-making and navigating”,while the other is mainly based on “point,number and operation on the number line”.In the environment of Cartesian coordinate system,students can explore the geometrical elements of various shapes,derive the equations of plane lines,spatial lines and conic sections in integral expressions,and afterwards step gradually into the parameter equations,polar equations of lines and conic sections.Meanwhile,the “geometrical transformation” in analytic geometry is estimated to go forward along the following sequence: using sketches,symbols and words to describe a transformation process→using coordinates to describe the effect of a transformation→using linear equations,vectors and matrices to describe a transformation as an object.It is worth noting that the main line of curriculum identified in this study is hypothesized in nature,teaching experiment,additional semi-structured clinical interviews and development of paper-and-pencil assessment items can be done to examine the validity of our hypothesis,which is necessarily a subject for further research.The revised betterconstructed main line of curriculum is promised a useful tool for teacher professional development and textbook compilation.