【作者】 张玲；

【导师】 刘咏梅；

【作者基本信息】 江西师范大学 ， 课程与教学论， 2018， 硕士

【摘要】 类比推理是数学推理的重要组成部分,是探索发现、提出猜想的重要途径,古今中外众多新思想、新发现和新成果出现的基础便是类比推理。类比推理能力的提升是数学教学的重要目标。注重培养学生的类比推理能力是新课程标准的一个重要方面。数列是高中数学重要内容,结合数列学习情况对高中生类比推理能力测试发现,目前存在以下问题:(1)高中生在数列中的类比推理能力水平总体较低,男生和女生在类比推理能力水平上相差很小,但是仍然存在差别,对于简单的类比推理,女生强于男生,对于稍显复杂的类比推理男生要强于女生;(2)高中生在数列中的类比推理能力在一定程度上受学生的学习基础、思维的灵活性、积极主动的学习态度、良好的认知结构以及归纳总结能力的影响,在类比推理教学过程中,讲授更多的类比推理知识显得更加重要;(3)教师在讲授数列中的类比推理知识的过程中,倾向于孤立、静止的看待问题,讲题一道一道讲,形式单一,较少把题目连在一起来进行讲授,较少对相关的数列类比推理题目进行比较,发现它们之间的相同点和不同点,较少对类比推理的类型进行归纳总结。类比推理能力的提升可以从教师重视对学生类比推理能力的培养、强化数形共同呈现的教学以此加深理解、注重形成知识的系统结构、在解决问题中归纳一般类比途径,抓住类比关键点、理论联系实际等方面加强对学生类比推理能力的培养。本文共分为5章:第1章主要从课程标准、新时代对创新型思维能力的要求、当前高中生类比推理能力的现状这三个目标论述了研究的背景,并就目前高中教学中学生和老师在类比推理方面存在的问题,确定了本文的研究方向。第2章从对类比、类比推理的定义进行界定,分析类比推理的类型,并对与类比推理有关的理论进行分析与研究;接着从国内外角度对类比推理方面的研究及其现状进行综述。第3章为实证研究,通过问卷调查、访谈法等方法对当前高中生数列教学中的类比推理能力现状有一个深入的了解,根据调查结果表明:当前高中生数学类比推理能力水平整体较低。并且结合访谈的结果,分析发现,学生类比推理能力的高低主要与学生先前的学习水平、学习的主动性和积极性,思维的灵活水平等有关,同时也与教师对类比推理的重视程度有关。第4章是在调查结果的基础上,并且对数学类比推理的基本途径进行分析,进而对类比推理教学提出相应的策略,促使高中数学教师和学生在类比推理的教学和学习上有更加深刻的理解和更好的进行类比推理的教学和学习。最后一章对本文的研究结论进行总结,并且对本文研究中所存在的不足进行改进。更多还原

【Abstract】 Analogical reasoning is an indispensable part of mathematical reasoning.It is also an important way to discover and make conjectures.The basis for the emergence of many new ideas,discoveries,and achievements in ancient and modern time is analogical reasoning.The improvement of analogical reasoning ability is a vital goal of mathematics teaching.Focusing on cultivating students’ analogical reasoning skills is a necessary aspect of the new curriculum standards.The series is an important content of high school mathematics.Combined with the series learning situation,the following problems have been found by testing senior high students’ analogical reasoning ability:(1)The level of analogical reasoning of high school students is generally low,and there is a narrow gap between boys and girls in the level of analogical reasoning,but there are still differences.When performing simple analogies,girls outperform boys.However,boys accomplish better than girls when performing analogies which are slightly more complex.(2)The analogical reasoning ability of the high school students in number sequence is influenced to a certain extent by students’ learning basis,flexibility of thinking,active learning attitude,good cognitive structure,and the ability to summarize.It seems that teaching more analogical reasoning knowledge is quite important.(3)In the course of teaching analogical inference knowledge,teachers always treat problems in an isolated,static way.The problems are combined together in a simple single form.Teachers rarely link the subjects together while teaching,and they hardly compare relevant series analogous reasoning so as to find the similarities and differences between them,seldomly conclude the principle of the same type of analogous reasoning.The improvement of analogical reasoning ability can be achieved by teachers’ emphasis on cultivating students’ analogical reasoning abilities,strengthening the teaching of digital representations to deepen understanding,focusing on forming the system structure of knowledge,summarizing general analogous approaches in solving problems,and grasping analogy key points,combining theory with reality and other aspects.This thesis is divided into five chapters: Chapter one mainly discusses the background of the research from the three aspects:the objectives of new math curriculum standards,the requirements of the new era of innovative thinking ability,and the current situation of high school students’ analogical reasoning ability.The research direction of this thesis is based on teacher’s as well as students’ poor performances in analogical reasoning.Chapter two includes the definition of analogy and analogical reasoning,the author also analyzes the types of analogical reasoning,and theories related to analogical reasoning;then it reviews the researches on analogical reasoning and its present status from both domestic and international perspectives.The third chapter is an empirical study.Through questionnaires,interviews and other methods,the author had a deep understanding of the current situation of analogical reasoning ability in the series of high school students.According to the survey results,the current level of mathematical analogical reasoning ability of high school students is overall low.Combined with the results of interviews,the analysis found that the level of students’ analogical reasoning ability is mainly decided by the students’ previous learning level,the initiative and enthusiasm of learning,the flexibility of thinking,etc,what’s more,teachers’ emphasis on analogical reasoning is also a related factor.Based on the survey results,along with analyzing the basic approaches of analogical reasoning in mathematics.In the fourth chapter,the author proposes corresponding strategies for analogical reasoning teaching,to motivate high school mathematics teachers to have a more profound understanding in teaching and to push students to learn analogical reasoning better.The last chapter is a summing-up.To summarize the conclusions of the above research,and forecasts the deficiencies in the study.更多还原