The Study Of Curricular Progression For Algebra Content In School Mathematics Curriculum

Since the beginning of the 21 st century,a boom in the innovation of curriculums has been swept around the world.Simultaneously,China issued a novel version of national high school curriculum standards of mathematics in 2017.This thesis is the partial research achievements of the subproject—‘The Top Design of Curricular Progression of K12 mathematics' —of the Shanghai key project of educational science—‘Effective Design of Mathematics Textbooks in K12'(D1508).In mathematical education,algebra is the main and vital content from K12 to college.Furthermore,the order of algebra education and its connotations of cognitions attract many researchers' attention.To reveal the educational properties of algebra,therefore,the curricular progression of algebra education was investigated in this thesis.The main issues studied here are as follows:(1)what are the core contents of algebra in K12 education?(2)what is the curricular progression of algebra in K12 education?Qualitative methods,including text analyses,expert argumentations,and interviews,were used in this article.The specimens in text analyses are national,Shanghai's municipal,and international(including USA,UK,Singapore,and Australia)curriculum standards.The core content of algebra education containing respective knowledge points was determined by the text analyses.The group interview method was implemented in expert argumentations whose eight interviewees included high school teaching and research staff,faculty in the field of mathematics.Based on the results from expert argumentations,the prepared curricular progression of algebra content was corrected.Finally,two college mathematics educators were interviewed.According to the consequences of interviews,the ultimate curricular progression of algebra content was improved and fixed.The main consequences obtained here are as follows:(1)the core content of algebra in K12 education is algebraic expressions,equations,inequalities,matrices,and determinants,which are respectively of own core knowledge points.(2)the curricular progression of the algebra content can be separated into two parts—a light line and a dark line.The light line is the order of detailed knowledge in teaching: algebraic expressions ? equations ? inequalities ? matrices ? determinants.The detailed development timelines of knowledge points of respective core content are shown on graph 15?16?17?18?22.In the other hand,the dark line means the development timeline of cognitions and intellects based on algebra knowledge.Two lines—the number-to-symbol line and the procedure-to-structure line—the development timeline of cognitions based on algebra knowledge.The complete development stages are presented in table 14?15.In conclusion,this investigation provides a direction to compile textbooks and curriculum standards based on the research of the curricular progression of algebra.In addition,it can help teachers grasp the content of algebra in their teaching practice.