The Application Status And Strategy Analysis Of Transformational Thinking In The Field Of “Graph And Geometry” In Primary School Mathematics

The Mathematics Curriculum Standards for Compulsory Education(2022 edition)(hereinafter referred to as the "2022 Curriculum Standards")are guided by core literacy and advocates for the design of structured curriculum content.It highlights the cultivation of students’ mathematical thoughts and methods.Transformational thinking is one of the most widely used and important mathematical ideas.Conducting related research helps teachers deepen their grasp of the material and improve their teaching,so as to help students form reasoning consciousness and structured thinking,and finally developing core literacy.The main research content of this paper is based on the characteristics of the arrangement of transformational thinking in the field of “graph and geometry” in the PEP primary school mathematics textbook(2022 edition),and proposes corresponding teaching and learning strategies based on the current application status and problems in front-line teaching.First of all,it is found that there are some problems in the research of transformation thinking in the field of “graph and geometry”,such as unclear classification and vague statistical standards.After that,the textual analysis method was used to grasp the teaching requirements of the 2022 Curriculum Standards in the field of“graph and geometry” and further analyze the organization characteristics of the PEP primary school mathematics textbook(2022 edition)to form a structured understanding of the knowledge points.Finally,from the three perspectives of transformation between plane figures,transformation between solid figures,and transformation between plane and solid figures,a specific analysis was conducted on the infiltration and characteristics of transformational thinking in textbooks,which deepened the overall understanding of the textbook knowledge system.Next,by utilizing the case study method,representative and high-quality lessons such as “Area of Triangle” “Volume of Rectangular Prism” and “Surface Area of Cylinder” were selected for in-depth analysis from three perspectives of textbook analysis.It was found that while the application of the transformation concept in the field of “graph and geometry” is widespread,there are still some issues that need to be addressed,such as inaccurate teacher understanding of the concept of transformational thinking,insufficient time for classroom operations,and irregular classroom procedures.To further explore the reasons for these issues,a questionnaire survey was designed with three dimensions to investigate: teachers’ understanding of the importance of transformational thinking,teachers’ current level of mastery of transformational thinking,and teachers’ application of transformational thinking.Subsequently,correlation analysis were conducted using software such as SPSS 26.0,combining the data from the student questionnaire survey to further clarify the problems with the application of transformational thinking in frontline teaching in the “graph and geometry” field.Through analysis,it was found that teachers face the following issues when applying transformational thinking: firstly,their understanding of transformational thinking is not deep enough,and their awareness of its application is insufficient;secondly,their mastery of transformational thinking is not sufficient,and they lack relevant theoretical guidance;thirdly,their application of transformational thinking is not comprehensive enough,and further standardization is needed.On the other hand,students also face the following issues when applying transformational thinking: firstly,they have narrow learning goals and a weak awareness of mathematical thinking and methods;secondly,their foundational knowledge is not solid enough,making it difficult for them to flexibly apply transformational thinking;thirdly,they have not developed good study habits and lack the ability to summarize transformational methods.Finally,some strategies for the application of transformational thinking were proposed.Teachers can use the following teaching strategies when applying transformational thinking: firstly,they should thoroughly explore the materials before teaching to improve their own understanding and mastery of the concept;Secondly,during teaching,they should respect their students and carefully design the teaching process and methods;Thirdly,after teaching,they should reflect on their teaching practice in a timely manner to improve their ability to summarize and apply transformational thinking.When learning about transformational thinking,students can use the following learning strategies: firstly,they should improve their understanding of the concept and recognize its value;Secondly,they should strengthen their foundational knowledge and lay a solid foundation for transformation;Thirdly,they should participate in hands-on activities to enhance their transformational ability;Fourthly,they should strengthen their reflection and summarization skills to form a strong awareness of transformation.