【作者】 王宏；

【导师】 史宁中；

【作者基本信息】 东北师范大学 ， 课程与教学论， 2017， 博士

【摘要】 现代学校教育是通过各个学科的教学来实现对整体人的培养的,每个学科都有自己的核心任务。数学教育的职责使命是培养和造就有探索能力的人才。探索能力不仅包括分析问题和解决问题的能力,也包括发现问题的能力,而发现问题的能力是探索能力的最关键要素。归纳、类比等归纳逻辑推理思维都是发现问题的基本手段,这种数学核心素养强调数学教育不再仅仅是灌输、传承,而是更加侧重于启发以及对数学思想方法的理解。在过去很长的一段时间里,中国基础教育阶段的数学教育重视演绎推理,教授训练学生验证掌握已有的完善的数学结论,而同时却忽略了归纳推理(1),数学教育的偏失和不完善,其结果必然弱化数学学科的育人价值,影响学生创造力的发展。本文围绕初中数学中归纳推理实证研究这个核心,具体研究如下问题:第一,采用文本分析法,借助文献梳理演绎推理与归纳推理的关系,同时梳理归纳推理国内外研究的现状,在分析国内小学和高中数学中归纳推理研究结论的基础上,探索初中数学中的归纳推理和演绎推理的关系。第二,通过文本分析的方法,对初中教学大纲和数学课程标准中归纳推理内容以及北师大版与人教版教材归纳推理内容呈现分别进行量化比较研究。第三,对师生的归纳推理能力以及师生对归纳推理的认同感和课堂教学现状进行调查研究,第四,对调查研究结果进行归因分析。通过研究,主要有以下发现:第一,初中数学中的归纳推理和演绎推理应该是双螺旋式发展。第二,通过对两个版本数学教材中与归纳推理能力培养的相关内容呈现的量化对比研究,并结合教学实践发现两个版本教材关于归纳推理呈现没有达到《义务教育课程标准(2011年版)》(以下简称《标准(2011年版)》)的要求。第三,选取北京市、黑龙江省十所学校初中阶段学生1446人和在职初中数学教师212人,运用了试题测试法和问卷调查法。通过对初中数学教师和学生完成的调查问卷、测试题进行的统计分析结果看,师生对归纳推理的理解不清晰,对《标准(2011年版)》的要求模糊。部分老师和学生的归纳推理能力比较薄弱,亟待提高。第四,通过聚焦访谈,87%初中数学老师虽然认同归纳推理的重要价值,但是在教学中不知道如何操作,导致在初中课堂教与学过程中目标不明确效果不好。综合上述情况,呼吁教材编写部门再修改教材时严格按着《标准(2011年版)》对归纳推理的要求,并能提供更多更鲜活的案例供老师们学习参考。也建议教育行政部门和学校真正重视初中阶段学生归纳推理能力的培养。本文对调查研究结果进行了归因分析,也从多个角度提供了一些案例,希望引起更多的讨论和研究。更多还原

【Abstract】 The cultivation of the integrated man in Modern school education is implemented through the teaching of various disciplines,and each subject has its own core tasks.The responsibility of mathematics education is to train and bring up talents with the ability to explore.The exploring ability includes not only the ability to analyze and solve problems,but also the ability to find problems,while the ability of recognition of problemis the most critical factors of the exploring ability.Inductive logic thinking such as induction and analogy is the basic means to discovery problem,and this core competenceof mathematics is no longer merely instilling and inheritance,but more focused on inspiration and understanding of mathematics thinking method.In the past a very long time,the mathematics education in the the basic education stageemphasized the deductive reasoning,and trained the students to verify and grasp the existing mathematical conclusion,while ignoring the inductive reasoning.The deficiency of mathematics education will inevitably weaken the educational value of mathematical disciplines,and influence the development of students’ creativity.Taking the inductive reasoning in mathematics of junior high school as emphasis,this paper studied some questions as follows: First,by text analysis,the paper reviewed the relationship between the deductive and inductive reasoning,and teased the domestic and foreign research about the deductive and inductive reasoning,and explored the relationship between inductive reasoning and deductive reasoning in junior high schoolon the basis of the analysis of the research conclusion about the deductive and inductive reasoning in the stage of primary school and senior high school.Secondly,by text analysis,the paper made the quantitative comparison research of the contents about the deductive and inductive reasoning between the junior middle school teaching outline and mathematics course standard,as well as PEP textbooks and Bnu edition textbooks.Thirdly,the paper made the investigation about the ability and identity of deductive and inductive reasoning of teachersand students,and the current teaching situation of the deductive and inductive reasoning.Fourthly,the paper made factor analysis of the investigation outcomes.The conclusion is: First,the relationship between inductive reasoning and deductive reasoning of in junior high school mathematics is stagger;Secondly,by making quantitative comparativeresearchon contents presentation about the inductive reasoning in two versions of the textbook,and combining teaching practice,the paper found the contents presentation about inductive reasoning did not meet the requirement of the “Mathematics Curriculum Standards of Compulsory Education(2011 Edition)”(hereafter referred to as “Curriculum Standards of 2011 Edition”);Thirdly,selecting 1,446 students and 212 mathematics teachers at the junior high school in Beijing and Heilongjiang assample,the paperused test method and questionnairesurvey,and found the teachers and students’ understanding of inductive reasoning and requires of curriculum standards was not clear,and some teacher and the students’ ability of inductive reasoning were weak,and need to be improved;Fourthly,by interview,the paper found 87% of junior high school mathematics teacher identified important value of inductive reasoning,but did’t know how to operate in the teaching,consequently,the teaching goal was not clear and the effect was not good in the teaching and learning process;The paper suggested that textbook writing departmentmodify the materials should strictly obey the requirement of inductive reasoning in “Curriculum Standards of 2011 Edition”,and provide more vivid case reference for teachers to learn,and also suggested that the education administrative department and school truly pay attention to the cultivation of inductive the reasoningability of students in junior high school.The paper made factor analysis of research results,and provided some cases from several aspects,in order to cause more research.更多还原