Research On Unit Over All Teaching Of Space Vector Based On Problem-Driven

As a vector theory system that describes the properties of low-dimensional geometric spaces,space vectors integrate algebraic and geometric properties,not only demonstrating the development process of algebra from two-dimensional to three-dimensional,but also providing a new perspective for dealing with traditional three-dimensional geometric problems,effectively establishing the connection between high school mathematics and advanced mathematics courses.Based on the experimental version,the "General High School Mathematics Curriculum Standards(2017 Edition)" strengthens the position of spatial vectors and incorporates them into the new college entrance examination,advocating the creative use of spatial vector knowledge with a comprehensive understanding of the overall knowledge However,due to the simple formal definition of space vectors,they are often only used as tools to solve geometric problems,ignoring their underlying mathematical thinking methods.Based on the teaching suggestions of "Creating appropriate teaching situations and mathematical problems,grasping teaching content as a whole,and promoting the formation and development of core literacy in mathematics" stated in the "General High School Mathematics Curriculum Standards(2017 Edition)",this study builds and implements a holistic teaching plan for spatial vector units based on problem-driven teaching theory and unit holistic teaching theory,with the goal of establishing a complete vector knowledge system in high school.The research is based on "Problem Driven Integrated Teaching of Space Vector Units".The research path is: literature review-design analysis-current situation investigation-case design-teaching practice.The specific research work is as follows:(1)By analyzing the origin,development,and characteristics of the theory of problem driven and unit holistic teaching,the theoretical basis for the study is clarified: the theory of problem driven teaching aims to enable students to experience the "re creation" of mathematical knowledge and understand the essence of knowledge and the ideas contained therein;The unit holistic teaching theory focuses on the integrity of knowledge,logical coherence,and systematic thinking,promoting students to form a complete and clear cognitive structure.(2)Based on theoretical analysis and research,summarize the overall teaching characteristics of problem driven units: systematic and in-depth analysis to clarify the main line of unit learning;Focus on core issues and point to the essence of unit knowledge;Paying attention to problem situations and implementing unit teaching objectives;Focus on the context of the problem and establish a unit logical structure;Develop multiple evaluations,enrich the value of unit teaching,and construct a framework for instructional design(3)Understand students’ learning situation in plane vectors,the current situation of space vector teaching and learning,and frontline teachers’ understanding and understanding of space vector knowledge,in order to analyze the key to the unit overall teaching design of space vector based on problem driven.(4)Sorting out the history of the generation and development of space vectors,starting from the original problem of the generation of space vectors,"How to use algebra to simply study spatial geometry problems";Based on the logical structure of the textbook and the cognitive reality of students,under the overall requirements of the curriculum standards and the overall teaching guidance of the unit,a holistic teaching design scheme for driving a problem chain is constructed around the core issue of the unit,"Vector representation of spatial geometric elements and vector operations of geometric relationships."(5)Design a controlled experiment to explore teaching and verify the feasibility and effectiveness of problem-driven unit teaching as a whole;The practical results show that problem-driven unit holistic teaching can promote students’ thinking and development of speculative ability,help students better understand and master the overall knowledge system of space vectors,and improve classroom teaching efficiency.