Research On The Application Of The Combination Of Number And Shape Ideas In Elementary School Mathematics

Mathematics is the study of the quantitative relationships and spatial forms of the real world."Number" and "shape" are the two most basic concepts in mathematics,"number",mainly refers to logical relationships,belongs to the category of mathematical abstract thinking;and "shape" mainly refers to geometric figures,belongs to the category of image thinking.Professor Hua Luogeng has summarized,“Only numbers without shapes is not intuitive,only shapes without numbers is not precise.” In the process of teaching and learning primary school mathematics,the method of combining number and shape ideas can reveal its geometric intuition.The precise portrayal of quantitative relationships and the visualization of spatial forms are cleverly and harmoniously combined to seek out ideas for solving problems,turning the difficult into the easy and the complicated into the simple.This study takes teachers’ teaching as the entry point,investigates the actual situation of the application of the number-shape combination idea method,tries to support teachers’ practice through the analysis of teaching materials and case design,and further proposes corresponding teaching strategies.This thesis is divided into six chapters,the first chapter clarifies the significance of the problem research,research questions,research ideas,etc.Chapter 2,through the literature review to understand the status of domestic and international research,relevant concepts are defined to lay the theoretical foundation for further research.Chapter 3,questionnaires and teacher interviews are used to understand the current situation of teachers’ application of the method of combining number and shape ideas,and to explore the limitations of the application of the method of combining number and shape ideas in the classroom in depth.In Chapter 4,the two types of numerical and figurative methods of thought are analyzed and characterized by their presentation in the textbook.Chapter 5,according to the characteristics of the combination of number and shape ideas in the textbook,typical contents are selected for the design of teaching materials to provide case studies to support teachers’ teaching.Chapter 6,combining the above research results,proposes teaching strategies.Through the survey,I found that there are still misconceptions and confusions in teaching practice.At the conceptual level,teachers’ understanding of the method of combining logarithmic forms with thought is biased,some teachers regard the combination of numbers and shapes as a problem solving skill,which plays down its role as a general teaching method and ignores the cultivation of higher-order thinking.At the practical level,teachers are not accurate in the orientation of teaching objectives,do not study the teaching content deeply,pay insufficient attention to students in the process,and play an insufficient role in evaluation.The application dilemma of the combination of numeral and shape is related to many factors,including the fixed teaching concept of teachers,the subject knowledge to be updated,the lack of guidance in the study of teaching materials,the utilitarian orientation of examination and evaluation,etc.Based on this,the author puts forward the improvement strategy,teachers should correct the education idea,accept the combination of numbers and shapes;Grasping the knowledge system and positioning the teaching objectives;Improving teaching methods and emphasizing multiple representations;In order to realize the application value of the thought method of combining numbers and shapes,we should change the evaluation idea and pay attention to the mutual aid of numbers and shapes.