A Research On Teaching Practice Of Mathematical Reasoning In Primary School

Reasoning is a hot topic in mathematics education and among related scholars in recent years.It is an important part of the mathematical core literacy "reasoning ability" which is concerned by the education stage;it is also closely related to innovation awareness.It should be an important stage to cultivate students’ reasoning when students are in primary school.However,now it mainly focuses on junior and high school students.Therefore,the implementation of reasonable reasoning on the elementary school students was investigated and studied from the teaching materials,teachers and students;some feasible teaching suggestions and teaching designs are put forward.Firstly,the current research status of reasonable reasoning is well known by reviewing all the available literature on reasonable reasoning in primary school at home and abroad.The logical meaning in this paper is defined by summarizing the relevant historical meaning of reasonable inference and distinguished from deductive reasoning.In elementary school,it is divided into three categories: incomplete inductive reasoning,analogical reasoning and statistical reasoning,and examples are given to illustrate the patterns and characteristics of different types of reasoning ability.In this paper,the theoretical knowledge of reasonable reasoning is analyzed,and the relationship between relevant theories and reasonable reasoning is summarized.Then,the author sorted out the compulsory education mathematics curriculum standard(2011 edition)and the primary school mathematics textbooks published by Beijing Normal University Press and find that students’ experiences are emphasized and that students acquire knowledge and develop thinking ability by observing,operating,induction,analogy,speculation and other activities.Three characteristics are known by teasing out the primary school mathematics textbooks published by Beijing Normal University Press.First,the reasoning content is mainly distributed in the third,fourth and fifth grades,and inductive reasoning is mainly examined,followed by analogical reasoning and the least statistical inference.Second,there is a lack of rationality and regularity in the setting of reasonable reasoning content,and the chapters are not evenly distributed.Third,the logical thinking mode of the textbook of the northern teacher edition is mainly presented as: special case-obtaining general rule-special case test,and levels of reasonable reasoning are differed to low,medium and high grades.Thirdly,some problems are found by interviewing mathematics teachers in elementary school.Mathematics teachers in elementary schoolhave insufficient understanding of reasonable reasoning and lack awareness of cultivating students’ ability of reasoning.But the classes where the teachers consciously apply reasonable reasoning are more likely to use the reasoning method to solve the problem.The middle periodof the primary school should be the best time to cultivate students’ reasonable reasoning.At the same time,the test volume was prepared to test the students in grade four of primary school to understand their reasonable reasoning level;statistical software SPSS was used to analyze the correlation between test scores and gender and math scores.The following three characteristics are found.First,the ability of incomplete inductive reasoning is the best,followed by the overall reasoning ability and analogical reasoning ability.Second,elementary school students lack awareness of reasonableness,and don’t know the method of reasoning;knowledge is complex or not;all above can affect the solution of students’ reasoning problems.Third,there is no significant difference between male and female students in reasoning,and there is a high positive correlation between math achievement and reasoning ability.Finally according to the survey result of the teaching materials,teachers and students,concrete teaching suggestions for reasonable reasoning teaching in primary school are put forward.And combining the suggestions and the primary school mathematics textbooks published by Beijing Normal University Press,three reasoning teaching designs are designed.