Research On The Teaching Of Foundational Mathematics Courses For Pre-service Teachers That Connect Secondary Shcool Mathematics

This thesis explores techniques to improve the teaching of fundamental mathematics to pre-service teachers based on the current curriculum structure,in order to address the urgent need for subject matter knowledge and competence in basic education mathematics teachers.Currently,young mathematics teachers encounter difficulties in connecting their knowledge with their teaching practice,especially in their lack of abilities to apply advanced mathematical concepts to elementary mathematics.To help young mathematics teachers overcome this dilemma and to shorten their growth cycle after employment,the government has explicitly proposed to enhance teacher education and cultivation.Unfortunately,current teaching methods in tertiary institutions have not successfully bridged the gap between university mathematics and primary/secondary mathematics.This has resulted in primary/secondary mathematics teachers lacking foundational knowledge.Additionally,insufficient attention has been paid to changes in secondary school mathematics teaching following curriculum reform,which has led to unsatisfactory teaching outcomes.Therefore,it is essential for teacher training to investigate the method of linking the teaching of fundamental mathematics courses in normal universities and secondary school mathematics.However,current research on this issue is still limited and lacks in-depth and systematic research.To this end,this thesis addresses the following core issues:1.For the practical demand problem of connected teaching,what are the current requirements for the subject knowledge and competency of mathematics teachers in basic education?2.The existing defects and their causes of connected teaching,what is the situation of the setting and teaching status of foundational mathematics courses in normal universities?3.The educational response strategy problem of connected teaching,how to design the teaching of foundational mathematics courses for normal university students to effectively cultivate students’ ability to control elementary mathematics from a higher standpoint?To achieve this,this study comprehensively analyses the needs of frontline mathematics teachers,their growth predicaments,national policy guidance,and teacher education responses at first,by which the research direction is thus clarified.Additionally,a systematic literature review identifies the constraints in teaching foundational mathematics courses and the limitations of existing research.Secondly,four empirical surveys have been conducted to analyse the requirements of basic education for mathematics teachers’ subject knowledge and competency.These surveys also investigate the setting and teaching status of foundational mathematics courses in normal universities,and cover significant topics,including teacher qualification exams,college entrance exam reforms,talent training plans(such as target setting,requirement refinement,and course design),and evaluations of teaching status.Based on Klein’s theory of teaching from a higher standpoint,the theory of constructivism,the theory of transformation of knowledge forms,and Zhang Dianzhou’s pedagogical views on reforming the teaching of mathematics courses for pre-service teachers,this thesis proposes a theoretical framework for teaching foundational mathematics courses to pre-service teachers.It focuses on three key modules: calculus,vectors,and probability.This study analyses the development and arrangement of topics in secondary school and university mathematics textbooks,identifying overlaps and gaps in knowledge content.Based on this analysis,targeted teaching suggestions are proposed for normal universities.Finally,a teaching model has been constructed for foundational mathematics courses for pre-service teachers that connects secondary school mathematics.Corresponding teaching design cases have been developed and taught in practice.During the problem-solving process,this research has uncovered the following results:(1)This thesis reveals the need for mathematical literacy among teachers in basic education and the current state of mathematics courses in normal universities.The national examination for a mathematics teacher qualification certificate requires candidates to have a mastery of advanced mathematics knowledge.The focus is on their ability to use this knowledge to solve elementary mathematics problems.The new college entrance examination emphasises the importance of mathematics teachers possessing a deep understanding of mathematical subjects and the ability to apply this knowledge comprehensively.Additionally,teachers must help students bridge the gap between middle school and university-level mathematics.All normal universities follow similar standards in teacher training and course settings,but there may be significant differences in teaching depth and breadth.Normal university students often lack the ability to apply advanced mathematical knowledge to elementary mathematics teaching.However,some teachers of foundational mathematics courses in normal universities have not paid enough attention to the needs of primary and secondary school teachers.This has resulted in a significant lack of connection between teaching and secondary school mathematics.(2)The thesis provides a systematic review of the history of calculus,vectors,and probability in secondary school mathematics curriculum standards.It analyses in detail the presentation of these topics in university and secondary school mathematics textbooks,identifies overlaps and missing knowledge content in the two curricula.The thesis proposes targeted teaching suggestions for teaching calculus,vectors,and probability in higher education institutions.(3)The thesis presents a teaching model that connects fundamental mathematics for pre-service teachers with secondary school mathematics.The model consists of four stages:knowledge preparation,connection with elementary and higher mathematics,infiltration of mathematical concepts,and teaching design.Its objective is to bridge the gap between pre-service teachers’ mathematical knowledge and primary/secondary mathematics teaching.This thesis presents four cases of teaching design in mathematics education,including three at the university level and one at the secondary school level.The cases cover topics such as the concept of derivative,random variable,linear correlation,base and dimension,and the teaching design of the plane coordinate system.The instructional designs have been implemented and received positive feedback on their effectiveness.(4)This thesis contributes to the improvement of the theory behind teaching the Fundamental Mathematics Courses for Pre-service Teachers in tertiary institutions by presenting a new teaching theory.The theory highlights the significance of connecting fundamental mathematics courses to secondary school mathematics in terms of content,ideas,and methods.This approach integrates knowledge from universities,secondary schools,and even primary schools,enabling pre-service teachers to view elementary mathematics from a higher standpoint.In conclusion,this thesis analyses the deficiencies and challenges of teaching foundational mathematics at university and proposes effective articulation teaching strategies to adapt to the needs of primary and secondary mathematics teaching.The feasibility of these strategies is verified through empirical studies,providing an important reference for the training of mathematics teachers to meet the needs of basic education.