Research On The Design Of Teaching Quadratic Functions In Junior High School Based On Freudenthal’s Educational Ideas

The content related to quadratic functions in junior high school involves a large number of concepts,theorems,formulas and calculations,which is an important vehicle for cultivating students’ mathematical ability and developing their mathematical thinking.However,due to the simple formal definition of the quadratic function in junior high school and the conclusive summary of the function properties,it is easy to cause the teaching and learning of the quadratic function to float on the surface of knowledge,which is not conducive to revealing the essence of knowledge.The four aspects of Freudenthal’s educational ideas include "mathematical reality","mathematization","re-creation" and "reflection".Through analysis,it is found that the integration of Freudenthal’s educational ideas into the teaching of quadratic functions in junior high school means that the focus of teaching will shift from the transfer of knowledge and skills to the cultivation of mathematical ideas and consciousness,which precisely meets the need to change the status quo of teaching quadratic functions in junior high school.Therefore,this study mainly explores how to integrate Freudenthal’s mathematical education ideas into the teaching of quadratic functions in junior high school to form a new teaching perspective.First,through the observation and analysis of the classroom record of quadratic functions in junior high school,this study identifies the problems in the teaching of quadratic functions:(1)the rationality of some problem situations set in the teaching process is questionable;(2)the teaching process emphasizes the development of students’ geometric intuition and neglects the cultivation of students’ algebraic reasoning ability;(3)the quadratic function is only used as a tool for problem solving,and the teaching of students’ model concept is not enough.At the same time,through the quadratic function test papers and student interviews,we summarized the obstacles that existed in students’ learning of quadratic functions:(1)they did not grasp the essence of knowledge,and their understanding of knowledge was superficial;(2)old and new cognition easily conflicted;(3)information extraction ability was poor,and there were thinking stereotypes;(4)the connection between knowledge was not sufficiently understood,and there were obstacles to the application of knowledge transfer.Then,this study also analyzes the attribution of students’ learning obstacles from both teacher and student levels.Secondly,this study traces the quadratic function to its roots from the perspective of parabolic motion,sorts out the process of generation and development of the quadratic function in history,and searches for teaching insights of the quadratic function.In addition,this study analyzes and considers the teaching content of quadratic functions in junior high school in the context of the People’s Education Press edition of junior high school mathematics textbooks,the 2011 edition and the 2022 edition of the compulsory education mathematics curriculum standards,so as to grasp the teaching content and the important nuclei of quadratic functions in junior high school.On this basis,with the goal of improving the current situation of teaching quadratic functions,this study analyzes how to apply Freudenthal’s ideas of "mathematical reality","mathematization","re-creation" and "reflection" in the teaching design of quadratic functions,and proposes the use of "problem situations" as a node to integrate Freudenthal’s four ideas in teaching.At the same time,the study gives two basic aspects of instructional design based on Freudenthal’s educational thinking,centering on the questions of "what to teach" and "how to teach".Finally,based on the investigation and analysis,this study presents the design of teaching quadratic functions in junior high school based on Freudenthal’s educational ideas and conducts a corresponding teaching experiment.Analysis of the post-experimental quiz results,student responses,and student interviews revealed that the teaching of quadratic functions in junior high school based on Freudenthal’s educational ideas has some positive significance for improving students’ performance and developing their inquiry and problem-solving abilities.