Teaching Research On The Shortest Path Problem In The Junior Middle School Mathematics

The shortest path problem in the junior middle school mathematics is flexible and difficult.The emphasis is on examining students’ ability to use the knowledge and skills they have learned to discover,analyze and solve problems,so as to cultivate students’ application awareness and practical ability.Through the collection and collation of the real problems in the senior middle school entrance examination in the cities of Shandong Province in the past five years,it is found that the shortest path problem appears in about half of all cities every year,which shows its importance.Most students have no way of starting with the shortest path problem,and they are afraid of difficulty.The teacher’s teaching effect is not ideal,and there is no effective teaching method to guide the teaching,which has caused confusion to the teacher’s teaching,the mastery of students is worrying.Therefore,it is necessary to study the shortest path problem in junior middle school.This paper mainly adopts the research methods of literature,investigation,experiment etc.,and carries out teaching research on the shortest path problem in the junior middle school mathematics.First of all,this paper reviews the relevant literature on the shortest path problem in junior middle school mathematics,collates and analyzes the data of the questionnaire survey,and obtains students’ difficulties in learning the shortest path problem and teachers’ deficiencies in teaching.Secondly,analyze the shortest path problems involved in the junior middle school mathematics textbooks and the senior middle school entrance examination,classify the question types and give the corresponding problem-solving methods,and then clarify its teaching orientation.Thirdly,based on Constructivist Theory,Polya’s problem-solving theory,and Zone of proximal development,corresponding teaching strategies are proposed.Fourth,the author applies the teaching strategy of the shortest path problem to teaching practice,and analyzes the effectiveness of the strategy through specific lesson examples.Intercept some fragments of the“General Drinking Horse Problem ” and “ Bridge Building Site Selection Problem ” for case studies.Through the implementation of the teaching case,it can be seen from the post-test that most students no longer have a strong sense of fear for this type of question,which greatly enhances students’ confidence in learning.After teaching experiments,it is found that the new teaching strategies have a positive impact on students’ learning:(1)Students are able to face up to the shortest path problem,especially effective technical means such as geometric sketchpads and microlecture have stimulated students’ interest and confidence in learning the shortest path problem.(2)Students can select appropriate basic models according to specific problems,and can solve extended types of problems.Finally,in view of the findings of this paper,some suggestions are put forward for the shortest path problem of junior middle school mathematics,and some practical teaching suggestions are also put forward for junior middle school mathematics teachers.