The Formation And Development Of Junior Middle School Student Mathematical Reasoning Ability

In Subject Standard for Senior Mathematics,logical reasoning is regarded as one of the mathematical Key Competencies.Under the background of logical reasoning,study of the formation and development process of junior middle school mathematical reasoning,provide the basis for teaching and the compilation of mathematics subject standard in Shanghai.In this paper,the ability of mathematical reasoning refers to the individual mental characteristics that can get the conjectures and conclusions by using intuition,association,observation,experiment,induction,and analogy,and prove that by deductive reasoning which based on mathematical facts and principles(definition,theorem,concept,thesis,etc.)The evaluation framework of mathematical reasoning has three dimensions which include the content,the process and the level.The content dimension refers to number and algebra,graphics and geometry,probability and statistics.Analyze the mathematics curriculum standards in 13 major countries and regions,and summarize the requirements that each grade student in junior high school should meet in mathematic reasoning ability.According to the requirements,the students will be able to reach the level of 1 in Grade 7 and achieve Level 2 in Grade 8 and Level 3in Grade 9 students.The process dimension mainly refers to the way of students’ reasoning,including observation and experiment,intuition and association,induction and analogy reasoning,syllogism,relation reference,disjunctive syllogism.The level dimension refers to the level 0 to 3 from low to high.According to the evaluation framework of mathematical reasoning for students in junior middle school,we make the corresponding test papers.After the evaluation of experts and the study of the pre-test,we finally give the test papers that can measurethe mathematical reasoning for students in junior middle school,and has high reliability and validity.At present,the formation and development of mathematical reasoning for students in junior middle school are as follows:1.The actual level of the seventh grade students reached between level 1 and level 2,slightly higher than the required level of the course standard 1;Grade 8students actually have a level 2,which is the same as the course requirements;The 9th grade student actually achieves a level between Level 2 and Level 3,which is slightly lower than the level required by the course 3.2.The ability of plausible reasoning for students in grade seven is well.The ability of deductive reasoning for students in grade eight has developed,but didn’t get the corresponding development in plausible reasoning.Students in grade nine get uniform development in both sides.