初中生逻辑推理的测验研究
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摘要
基于逻辑学对于推理的分类以及心理学关于推理能力的研究成果,对国内外的逻辑推理评价研究进行梳理,结合中学数学知识的特点,提出一个测量初中生逻辑推理能力的框架,据此编制测验题.测验兼顾推理的形式与内容两方面.通过探索性因素分析检验测验的结构效度并进行修订,修订后的维度包括简单推理、选言推理、命题演算、假言推理、合情推理,其中前4个同属演绎推理.测验具有较好的结构效度和信度.
After a comprehensive analysis of existing literatures about mathematical reasoning, basing on classification of logic inference and research findings of reasoning ability in psychology, and also giving consideration to mathematical knowledge of junior high school, we proposed a framework which can be used to evaluate mathematical reasoning ability of junior high students, and designed a test. This test took into account both form and content of mathematical reasoning. With the result of exploratory factor analysis, we examined construct validity of the test and revised the test. The final dimensions were "plausible reasoning" and "deductive reasoning" which includes "simple proposition and inference", "disjunctive inference", "propositional calculus", "hypothetical inference". The test was good in construct validity and reliability.
After a comprehensive analysis of existing literatures about mathematical reasoning, basing on classification of logic inference and research findings of reasoning ability in psychology, and also giving consideration to mathematical knowledge of junior high school, we proposed a framework which can be used to evaluate mathematical reasoning ability of junior high students, and designed a test. This test took into account both form and content of mathematical reasoning. With the result of exploratory factor analysis, we examined construct validity of the test and revised the test. The final dimensions were "plausible reasoning" and "deductive reasoning" which includes "simple proposition and inference", "disjunctive inference", "propositional calculus", "hypothetical inference". The test was good in construct validity and reliability.
引文
[1]中华人民共和国教育部.普通高中数学课程标准[M].北京:人民教育出版社,2017:5.
[2]彭漪涟,马钦荣.逻辑学大辞典[M].上海:上海辞书出版社,2010:317.
[3]史宁中.试论数学推理过程的逻辑性——兼论什么是有逻辑的推理[J].数学教育学报,2016,25(4):1-16,46.
[4]华东师范大学哲学系逻辑学教研室.形式逻辑[M].上海:华东师范大学出版社,2016:2-6,89-98.
[5]胡竹菁.演绎推理的心理学研究[M].北京:人民教育出版社,2000:216-228.
[6]毕鸿燕,方格,王桂琴,等.演绎推理中的心理模型理论及相关研究[J].心理科学,2001,24(5):595-596.
[7]杨群,邱江,张庆林.演绎推理的认知和脑机制研究述评[J].心理科学,2009,32(3):646-648.
[8]克鲁捷茨基.中小学数学能力心理学[M].李伯黍,洪宝林译.上海:上海教育出版社,1983:155-159,181-185.
[9]SENK S L. How well do students write geometry proofs[J]. Mathematics Teacher, 1985, 78(6):448-456.
[10]PERESSINID,WEBBN.Analyzingmathematicalreasoninginstudents’responsesacrossmultipleperformance assessment tasks[C]//STIFF L V, CURCIO F R. Developing mathematical reasoning in grade K-12. Reston VA, 1999:156-174.
[11]HOYLESC,KUCHEMANND.Students’understandingsoflogicalimplication[J].EducationalStudiesin Mathematics, 2002, 51(3):193-223.
[12]HARELl G, SOWDER L. Toward comprehensive perspectives on the learning and teaching of proof[C]//LESTER F.Second handbook of research on mathematics teaching and learning. Information Age Publishing, 2013:24.
[13]JANSSON L C. Logical reasoning hierarchies in mathematics[J]. Journal for Research in Mathematics Education, 1986,17(1):3-20.
[14]林崇德.学习与发展:中小学生心理能力发展与培养[M].北京:北京师范大学出版社,1999:347.
[15]田中,徐龙炳,张奠宙.数学基础知识、基本技能教学研究探索[M].上海:华东师范大学出版社,2003:98-99.
[16]CHRISTOUC,PAPAGEORGIOUE.Aframeworkofmathematicsinductivereasoning[J].Learning&Instruction, 2007, 17(1):55-66.
[17]RADFORDL.Algebraicthinkingandthegeneralizationofpatterns:asemioticperspective[C]//ALATORRES,CORTINAJL,SáizM,etal.Proceedingsofthe28thConferenceoftheInternationalGroupforthePsychologyof Mathematics Education. North American Chapter, Mérida, 2006:2–21.
[18]STYLIANIDES G J. An analytic framework of reasoning-and-proving[J]. For the Learning of Mathematics, 2008, 28(1):9–16.
[19]武锡环,李祥兆.中学生数学归纳推理的发展研究[J].数学教育学报,2004,13(3):88-90.
[20]LYND.English.Mathematicalandanalogicalreasoningofyounglearners[M].LawrenceErlbaumAssociates,Mahwah NJ, 2004:47-74.
[21]喻平.数学核心素养评价的一个框架[J].数学教育学报,2017,26(2):19-23.
[22]李丹,张福娟,金瑜.儿童演绎推理特点再探——假言推理[J].心理科学,1985(1):6-12.
[23]GOSWAMIU.TheWiley-Blackwellhandbookofchildhoodcognitivedevelopment[M].2nded.Malden,MA:Wiley-Blackwell, 2011:399-419.
[24]吴明隆.问卷统计分析实务——SPSS操作与应用[M].重庆:重庆大学出版社,2010:208.
[25]王光明,廖晶,黄倩,等.高中生数学学习策略调查问卷的编制[J].数学教育学报,2015,24(5):25-36.
[26]焦彩珍,刘治宏.初中数学学习困难学生的抑制控制能力缺陷[J].数学教育学报,2018,27(1):47-51.
[27]宋爽,郭衎.家庭背景因素对初中生数学学业成就的影响[J].数学教育学报,2018,27(1):52-57.
[28]何忆捷,熊斌.中学数学中构造法解题的思维模式及教育价值[J].数学教育学报,2018,27(2):50-53.
[29]陆明明.数学教科书例题的分类及其教学建议[J].数学教育学报,2018,27(2):54-58.
[30]罗荔龄,曹广福.中学数学部分概率内容的问题与建议[J].数学教育学报,2018,27(2):65-69.
[31]唐恒钧,HAZEL TAN,徐元根,等.基于问题链的中学数学有效教学研究——一项课例研究的启示[J].数学教育学报,2018,27(3):30-34.
[32]刘春艳.理解试题内涵把好教学方向——从一道北京中考试题说起[J].数学教育学报,2018,27(3):35-38.
[33]卜文娟,温红博,刘先伟.初中学业水平考试中固定分数法标准设定的信度分析——以中考数学为例[J].数学教育学报,2018,27(3):39-44.
[34]崔宝蕊,李健,王光明.初中生数学元认知水平调查问卷的设计与编制[J].数学教育学报,2018,27(3):45-51.
[35]王红兵.针对初中毕业阶段学生范希尔几何思维水平的调查及其分析[J].数学教育学报,2018,27(3):52-56.
[36]何小亚,李湖南,罗静.学生接受假设的认知困难与课程及教学对策[J].数学教育学报,2018,27(4):25-30.
[37]张蜀青,曹广福,罗荔龄.从历史发展的视角看中学概率教学[J].数学教育学报,2018,27(4):35-40.
[38]曹春艳,吕世虎.民国时期中学数学课程内容的发展历程及其启示[J].数学教育学报,2018,27(4):41-45.
[39]关丹丹,景春丽.新高考改革背景下不分文理的数学成绩差异研究[J].数学教育学报,2018,27(4):31-34.
[40]谷晓沛,马云鹏,朱立明.高一学生函数概念数学理解水平的实证研究——以T城市为例[J].数学教育学报,2018,27(3):25-29.
[41]李渺,徐新斌,陆颖,等.高中数学教师听评课的现状及其有效性对策研究[J].数学教育学报,2018,27(1):36-41.
[42]朱立明,胡洪强,马云鹏.数学核心素养的理解与生成路径——以高中数学课程为例[J].数学教育学报,2018,27(1):42-46.
[2]彭漪涟,马钦荣.逻辑学大辞典[M].上海:上海辞书出版社,2010:317.
[3]史宁中.试论数学推理过程的逻辑性——兼论什么是有逻辑的推理[J].数学教育学报,2016,25(4):1-16,46.
[4]华东师范大学哲学系逻辑学教研室.形式逻辑[M].上海:华东师范大学出版社,2016:2-6,89-98.
[5]胡竹菁.演绎推理的心理学研究[M].北京:人民教育出版社,2000:216-228.
[6]毕鸿燕,方格,王桂琴,等.演绎推理中的心理模型理论及相关研究[J].心理科学,2001,24(5):595-596.
[7]杨群,邱江,张庆林.演绎推理的认知和脑机制研究述评[J].心理科学,2009,32(3):646-648.
[8]克鲁捷茨基.中小学数学能力心理学[M].李伯黍,洪宝林译.上海:上海教育出版社,1983:155-159,181-185.
[9]SENK S L. How well do students write geometry proofs[J]. Mathematics Teacher, 1985, 78(6):448-456.
[10]PERESSINID,WEBBN.Analyzingmathematicalreasoninginstudents’responsesacrossmultipleperformance assessment tasks[C]//STIFF L V, CURCIO F R. Developing mathematical reasoning in grade K-12. Reston VA, 1999:156-174.
[11]HOYLESC,KUCHEMANND.Students’understandingsoflogicalimplication[J].EducationalStudiesin Mathematics, 2002, 51(3):193-223.
[12]HARELl G, SOWDER L. Toward comprehensive perspectives on the learning and teaching of proof[C]//LESTER F.Second handbook of research on mathematics teaching and learning. Information Age Publishing, 2013:24.
[13]JANSSON L C. Logical reasoning hierarchies in mathematics[J]. Journal for Research in Mathematics Education, 1986,17(1):3-20.
[14]林崇德.学习与发展:中小学生心理能力发展与培养[M].北京:北京师范大学出版社,1999:347.
[15]田中,徐龙炳,张奠宙.数学基础知识、基本技能教学研究探索[M].上海:华东师范大学出版社,2003:98-99.
[16]CHRISTOUC,PAPAGEORGIOUE.Aframeworkofmathematicsinductivereasoning[J].Learning&Instruction, 2007, 17(1):55-66.
[17]RADFORDL.Algebraicthinkingandthegeneralizationofpatterns:asemioticperspective[C]//ALATORRES,CORTINAJL,SáizM,etal.Proceedingsofthe28thConferenceoftheInternationalGroupforthePsychologyof Mathematics Education. North American Chapter, Mérida, 2006:2–21.
[18]STYLIANIDES G J. An analytic framework of reasoning-and-proving[J]. For the Learning of Mathematics, 2008, 28(1):9–16.
[19]武锡环,李祥兆.中学生数学归纳推理的发展研究[J].数学教育学报,2004,13(3):88-90.
[20]LYND.English.Mathematicalandanalogicalreasoningofyounglearners[M].LawrenceErlbaumAssociates,Mahwah NJ, 2004:47-74.
[21]喻平.数学核心素养评价的一个框架[J].数学教育学报,2017,26(2):19-23.
[22]李丹,张福娟,金瑜.儿童演绎推理特点再探——假言推理[J].心理科学,1985(1):6-12.
[23]GOSWAMIU.TheWiley-Blackwellhandbookofchildhoodcognitivedevelopment[M].2nded.Malden,MA:Wiley-Blackwell, 2011:399-419.
[24]吴明隆.问卷统计分析实务——SPSS操作与应用[M].重庆:重庆大学出版社,2010:208.
[25]王光明,廖晶,黄倩,等.高中生数学学习策略调查问卷的编制[J].数学教育学报,2015,24(5):25-36.
[26]焦彩珍,刘治宏.初中数学学习困难学生的抑制控制能力缺陷[J].数学教育学报,2018,27(1):47-51.
[27]宋爽,郭衎.家庭背景因素对初中生数学学业成就的影响[J].数学教育学报,2018,27(1):52-57.
[28]何忆捷,熊斌.中学数学中构造法解题的思维模式及教育价值[J].数学教育学报,2018,27(2):50-53.
[29]陆明明.数学教科书例题的分类及其教学建议[J].数学教育学报,2018,27(2):54-58.
[30]罗荔龄,曹广福.中学数学部分概率内容的问题与建议[J].数学教育学报,2018,27(2):65-69.
[31]唐恒钧,HAZEL TAN,徐元根,等.基于问题链的中学数学有效教学研究——一项课例研究的启示[J].数学教育学报,2018,27(3):30-34.
[32]刘春艳.理解试题内涵把好教学方向——从一道北京中考试题说起[J].数学教育学报,2018,27(3):35-38.
[33]卜文娟,温红博,刘先伟.初中学业水平考试中固定分数法标准设定的信度分析——以中考数学为例[J].数学教育学报,2018,27(3):39-44.
[34]崔宝蕊,李健,王光明.初中生数学元认知水平调查问卷的设计与编制[J].数学教育学报,2018,27(3):45-51.
[35]王红兵.针对初中毕业阶段学生范希尔几何思维水平的调查及其分析[J].数学教育学报,2018,27(3):52-56.
[36]何小亚,李湖南,罗静.学生接受假设的认知困难与课程及教学对策[J].数学教育学报,2018,27(4):25-30.
[37]张蜀青,曹广福,罗荔龄.从历史发展的视角看中学概率教学[J].数学教育学报,2018,27(4):35-40.
[38]曹春艳,吕世虎.民国时期中学数学课程内容的发展历程及其启示[J].数学教育学报,2018,27(4):41-45.
[39]关丹丹,景春丽.新高考改革背景下不分文理的数学成绩差异研究[J].数学教育学报,2018,27(4):31-34.
[40]谷晓沛,马云鹏,朱立明.高一学生函数概念数学理解水平的实证研究——以T城市为例[J].数学教育学报,2018,27(3):25-29.
[41]李渺,徐新斌,陆颖,等.高中数学教师听评课的现状及其有效性对策研究[J].数学教育学报,2018,27(1):36-41.
[42]朱立明,胡洪强,马云鹏.数学核心素养的理解与生成路径——以高中数学课程为例[J].数学教育学报,2018,27(1):42-46.