The Formation Mechanism And Case Study Of Intuitive Imagination Literacy

The core literacy of mathematics is a comprehensive reflection of the quality of thinking,key abilities,and emotions,attitudes,and values of mathematics.As one of the core literacy of the six major mathematical disciplines,intuitive imagination is not only the main way to find and solve problems,but also the thinking basis of mathematical reasoning and logical reasoning.Intuitive imagination literacy is gradually formed and developed in the process of mathematics learning and application,and plays an important role in plane geometry,three-dimensional geometry,analytical geometry and other content.How high school students form and develop intuitive imagination literacy is an urgent problem that needs to be solved to train and develop students' intuitive imagination literacy.The research on intuitive imagination literacy mainly focuses on the origin and history,connotation and structure,training strategies and evaluation studies of intuitive imagination literacy.It lacks the process research of intuitive imagination literacy that fits the students' cognitive laws and conforms to the learning process of students.Therefore,the research mainly solves the following questions:(1)How do students form intuitive imagination?(2)Combining actual teaching cases with the formation mechanism of intuitive imagination,how to cultivate high school students' intuitive imagination?The research adopts survey method,document method and case method,and uses mathematical image thinking theory,information processing theory,and Fan Hill theory as the theoretical foundation to construct the formation mechanism of students' intuitive imagination.Research shows that the formation process of students' intuitive imagination is in accordance with the information processing theory and has a staged nature.Students' intuitive imagination literacy gradually develops from concrete to abstract,and from low to advanced.The formation process can be divided into prototype,visual and visual.Prototype intuition is the starting point of intuitive imagination,which can be refined into physical prototypes,perception of geometric attributes,and formation of geometric representations.Representational intuition is a necessary condition for the development of intuitive imagination,which can be refined into forming mathematical intuition,forming mathematical concepts,and improving mathematical concepts.Imagination and intuition is a staged sign of the perfection of intuitive imagination,which can be refined into operating image movements,establishing a logical system,and constructing an intuitive model.Use the "parallel line and plane" teaching case to verify the rationality of the formation mechanism of students 'intuitive imagination.Based on the results of expert opinions,teacher interviews and student interviews combined with teaching records,revise the formation mechanism of intuitive imagination and propose the cultivation of high school students' intuitive Imagine literacy strategies.Through the analysis of teaching cases,the training strategy of intuitive imagination is summarized:(1)Enrich the imagery reserve and cultivate students' geometrical intuitive ability.Use familiar life prototypes to awaken students' existing cognition;introduce teaching aids and learning aids to enhance the image of knowledge;encourage students to use hand-drawn drawings to help students form appearances.(2)Strengthen operation practice and cultivate students' spatial imagination.Pay attention to concept analysis,cultivate students 'intuition in mathematics;integrate information technology to display the full picture of geometric figures;control the pace of teaching,and test students' operational ability.(3)Construct intuitive models to cultivate students' mathematical imagination.Summarize the geometric model to cultivate students 'intuition in problem solving;exercise the variants of the problem to cultivate students' associative ability;evaluate and test by layers to help students build intuitive models.