| Mathematical reasoning skills are fundamental in the field of mathematics and are among the basic skills that mathematics learners need to master.The ability to use types of mathematical reasoning is also an important part of it.However,few researches in China have focused on the current situation of students’ application of mathematical reasoning types,and not many have provided targeted suggestions for improving students’ use of mathematical reasoning types.Therefore,the current status of students’ use of mathematical reasoning types is a topic of interest.This thesis attempts to establish a framework and instrument for measuring the use of mathematical reasoning types,and investigates the current situation of mathematical reasoning types used by senior high school students in Shanghai High School C.It tries to explore the relationship between different types of mathematical reasoning tasks and reasoning types,and further explores the reasons for the existence of some connection between them.This study focuses on the following two questions.1.What types of reasoning types did senior high school students use when faced with different types of reasoning tasks?2.What relationship exists between each type of reasoning task and each type of reasoning and what are the reasons for this relationship?Based on the results of tests and interviews,this study draws the following conclusions:(1)When students face various types of reasoning tasks,they exhibit different types of mathematical reasoning.When faced with a memory reasoning task,over 70% of the students used both memory reasoning and algorithmic reasoning;When faced with an algorithmic reasoning task,the complexity of the algorithmic reasoning task would directly affect the students’ use of mathematical reasoning types.All students attempted to use algorithmic reasoning to solve the task when faced with a less complex algorithmic reasoning task,over 90% of students used algorithmic reasoning when faced with a moderately complex algorithmic reasoning task,and about 60% of students used algorithmic reasoning when faced with a more complex algorithmic reasoning task;when faced with local plausible reasoning tasks,about 90% of the students use algorithmic reasoning and deductive reasoning;When faced with a global plausible reasoning task,about 80% of the students used plausible reasoning to solve the reasoning task,while the rest did not use any type of reasoning;when faced with local deductive reasoning tasks,about 80% of the students used algorithmic reasoning and deductive reasoning;Only about half of the students used deductive reasoning when faced with a global deductive reasoning task;(2)When students solved each type of reasoning task,their response results will fall into the following three situations: high match-high success rate,low match-low success rate,and high match-low success rate.Students’ reasoning situations appear high match-high success when solving local plausible reasoning tasks;Students’ reasoning situations represent low match-low success when solving memory reasoning tasks.The high match-high success rate and low match-low success rate situations reflect that the degree of matching will directly affect the success of students’ mathematical reasoning when faced with reasoning tasks.The high match-low success rate situation,on the other hand,occurs mainly under the circumstance when students are solving algorithmic reasoning tasks of moderate or high complexity,global plausible reasoning tasks,local deductive reasoning tasks,and global deductive reasoning tasks.In the situation of the high match-low success rate,the common problems of students’ reasoning in solving the above reasoning tasks can be summarized into three categories,namely,intellectual errors,logical errors,and computational errors.The causes of the above problems are also analyzed in terms of subject knowledge,students,teachers,and exercises,respectively.Based on the above findings,this thesis provides some suggestions for school curriculum and teachers’ teaching,and carries out reflections and prospects to the research. |
