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

This thesis is the outcome of the project entitled “the top 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)”.It is about the curricular progression of “geometry” because of its importance in school mathematics and its special educational value.There are two research questions of this thesis:(1)What are the core contents of geometry in primary and secondary school mathematics curriculum?(2)what is the curricular progression of geometry in primary and secondary school mathematics curriculum?This thesis mainly adopts the qualitative research approach,including content analysis and expert interview.Mathematics standards(syllabus),from Shanghai,the national of China,the United States,the UK,Australia and Singapore,are selected for analysis,helping to determine the core contents of geometry and the curricular progression of geometry.The expert interview has been conducted twice;the interviewed experts include high school mathematics teaching research staff,mathematics textbook editors,mathematics professors and mathematics education professors Responses to the interview schedules are used to revise the curricular progression of geometry.The conclusions of this thesis are listed below:(1)The core contents of geometry can be classified into four categories: geometric measurement,shapes and its properties,geometric transformation,and positional relationship among shapes.Each category contains specific contents,referring to table 13 in this thesis.(2)The development of geometry content from the knowledge perspective can be divided into the following four aspects: Geometric measurement is progressed as “the measurement of two-dimensional shapes ? the measurement of three-dimensional objects”.Geometric shape is progressed as “the recognition of three-dimensional objects ? the recognition of two-dimensional shapes ? the property of twodimensional shapes ? the property of three-dimensional objects”.Geometric transformation is progressed as “the recognition of transformation ? transformation operation ? the property of transformation ? the application of transformation”.The positional relationship among shapes in geometry is progressed as “the relative position between geometric elements ? the relative position between geometric shapes;twodimension ? three-dimension”.The development of geometry in the level of geometric competency is progressed as “visual level ? descriptive level ? theoretical level”,which is based on the framework of the van Hiele model of thinking in geometry.For the detail information,please see the graph 24,25,26,27.This thesis clarifies the curricular progression of geometry in primary and secondary school mathematics curriculum,presents the development of geometric core contents from simple towards increasingly complex over time.The research findings in this thesis can help mathematics teachers stand in a high perspective to grasp the contents of the geometry in primary and secondary schools.