| Junior high school mathematics vividly reflects the characteristic that mathematics originates from real life,and the "Shortest Path Problem" is not only an important issue in real life,but also a difficult point in junior high school mathematics teaching.The situation of the "Shortest Path Problem" in junior high school is complex and changeable,and its textual expressions are relatively diverse.It is also a hot topic in mathematics in the middle school entrance examination.Therefore,combining the content structuring requirements proposed in the new mathematics curriculum standard,it is of certain significance to carry out teaching research on the relevant content of the "Shortest Path Problem" in junior high schools.It can not only structurally integrate the teaching content of the "Shortest Path Problem",help students understand the essence of the "Shortest Path Problem",but also promote the effective implementation of the new curriculum concept.Through reading relevant literature,it is found that most articles focus on analyzing the "issue of generals drinking horses",while paying insufficient attention to the "issue of bridge construction and site selection",with few in-depth analysis.In order to design the teaching content of the "Shortest Path Problem" section as a whole,on the basis of attaching importance to "issue of generals drinking horses",this paper strengthens the analysis of "issue of bridge construction and site selection",and tries to add "rotation" transformation into practical teaching.Meanwhile,with the help of the "Fermat point problem",axial symmetry,translation and rotation are integrated,and corresponding teaching practices are carried out to test the effectiveness of students’ learning and promote the structuring of the course content.In this study,first of all,it summarizes the research status of the "Shortest Path Problem" in junior high school,and defines relevant concepts;Secondly,it analyzes the essence of the "Shortest Path Problem" in junior high school and explains the theories used in teaching design and teaching experiments,such as Big Ideas,Ub D theory,and Visualization theory;Thirdly,select the content of the section "13.4 Topic Learning Shortest Path Problem" in the eighth grade volume of mathematics published by People’s Education Press.From the perspective of content structure,carry out a specific teaching case design,which is divided into three class hours in total.Each class hour involves three transformations: "axial symmetry","translation",and "rotation".Design the content of this section as a whole,and propose basic teaching strategies based on the designed cases;Finally,carry out teaching experiment to the teaching design of this paper,and prepare test questions and attitude scales.After the course is completed,they will be distributed to students for completion.The collected data will be statistically analyzed,and the teaching design will be improved and optimized.According to the teaching practice of "Shortest Path Problem" and analysis of experimental data,the following conclusions are drawn:(1)In the content structured teaching of "Shortest Path Problem" designed in this paper,the average score of the experimental class is higher than that of the control class,and the teaching effect is better than the traditional teaching mode,which can help students better solve various shortest path problems;(2)Students in the eighth grade experimental class were able to accept the relevant knowledge of rotation in advance,and there was no significant difference in the scores of the third test question compared to students in the ninth grade experimental class(who had already learned "rotation");(3)After experiencing the learning of this lesson,the students in the eighth grade experimental class have improved their thinking and knowledge to a certain extent,which further demonstrates the advantages of structured organization of the knowledge of the "Shortest Path Problem". |
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