Study On The Curricular Progression Of Vector In Secondary School Mathematics

Many countries have stepped up the pace of curriculum reform in recent years.The curriculum standards of the United States,Australia and other countries have been released successively.China's national high school mathematics curriculum standard is also released in 2017.This thesis is the periodicity research result of the subtopics-one “The design of curricular progression of primary and secondary school mathematics”,which is under the big project of fundamental educational scientific research in Shanghai 2015 entitled “Effective design of mathematics textbooks in primary and secondary schools(No.D1508)”.This thesis focuses on the curricular progression of “vector” because of the importance of vector in secondary school mathematics and its special educational value.This thesis has two research questions:(1)What are the core contents of vector in secondary school mathematics curriculum?(2)What is the curricular progression of vector in secondary school mathematics?This thesis mainly adopts the qualitative research methods,including content analysis and interview method.The object of content analysis contains mathematics curriculum standards from Shanghai,the national of China,the United States,the UK,Australia and Singapore.Through comparative analysis of these curriculum standards,similarities and differences among them are reported.The similarities provide the basis for the establishment of the curricular progression of vector,and the differences is used to solicit the opinions of experts in the interview.The interview was conducted twice,in the form of a group interview by experts.There were 13 experts involved in the interview,including high school mathematics research staff,the textbook writers,math educators and mathematicians in different research directions in university mathematics department.Their opinions and suggestions on vector content provide the most direct basis and viewpoint for revising the curricular progression and forming the final curricular progression of this thesis.Considering the logical order of vector,the literature analysis on curriculum theory and students' cognitive development,results of the curriculum standards comparison,and the experts' opinions and suggestions,the conclusions of this thesis are as follows:(1)The core contents of vector in secondary school are: the concept and representation of vectors,the operation of vectors,the property of vectors,the application of vectors.Each core content includes specific topics.(2)According to the different representation of vectors,the development of vector content on the knowledge level presents two distinct lines,namely “the line of geometry” and “the line of algebra”.The two lines are divided into two parts: the two-dimensional vector and the three-dimensional vector.In each part,they are developed in the sequence of “an operation of vectors ? properties”.Joining the concept and application of vector,the vector content is developed in the following sequence “the concept and representation of two-dimensional vectors ? addition of vectors ? properties ? subtraction of vectors ? properties ? multiplication of a vector by a scalar ? properties ? scalar product in vectors ? properties ? the application of vectors ?the concept and representation of three-dimensional vectors ? linear operation of vectors ? properties ? scalar product in vectors ? properties ? the application of vectors”.Since the three-dimensional vector is an extension of the two-dimensional vector,several operations can be explained together when the students can accept it.In fact,“the line of geometry” and “the line of algebra” of vectors are intertwined,and “the line of algebra” is based on “the line of geometry”.In order to visually present the development trend of vector content and the connection between vector content,hexagon is used to present the curricular progression of vector content.This thesis also discusses the mathematical thoughts and methods underlying the concrete knowledge of vector,and designs the teaching process of vector content based on the APOS theory.This thesis clarifies and clearly presents the curricular progression of vector in secondary school mathematics curriculum.The research findings in this thesis provide the design ideas for writing the mathematics curriculum standard and the textbooks,and help math teachers to grasp the contents of the vector in secondary school from a high perspective.