数学史在数学概念教学中的应用研究

1数学史在数学概念教学中的应用研究摘要内容摘要：新一轮课程改革无疑是对传统数学教学的挑战，从理念到内容，从方法到模式，蕴含着古今中外杰出数学人才成长史、数学演变史、数学思维发展史的数学文化在数学教学中的价值逐渐得到认同，数学课程应当反映数学的历史、应用和发展趋势，反映数学与社会发展相互作用、相互推动的关系，反映数学科学的思想体系、美学价值，已经成为数学教育教学研究的共识。在高中数学教学中渗透数学的科学价值、应用价值、人文价值，进行数学愉快教学，让学生学会体验、欣赏数学，帮助学生培养热爱数学知识、自主进行数学技能训练，在数学文化的熏陶中逐步将知识、技能内化为一种数学性格，生成良好的数学素养，是高中数学教学的新视点，本文结合数学史范例，从高中数学新课程改革的角度探讨数学文化在高中数学教学的渗透，并通过实验证明，数学文化背景下教与学理念和形式的人文化、多样化，课题的研究对高中数学教学有着极大的促进作用，将对学生的终身数学学习的兴趣和能力产生深远的影响，有利于完善学生的数学人格，促进他们身心的健康发展。关键词：数学文化数学素养数学教学研究性合作学习2AbstractContent:Anewwaveofcoursereformisundoubtedlyachallengetoconventionalmathteaching.Fromtheideastocontents,frommethodstomodels,withthedevelopmentstoriesofmanyoutstandingmathematicaltalentshistory,withtheevolvementhistoryofmathematics,andwiththehistoryofmaththinking,themathculture’svalueinmatheducationisgraduallyrecognizedandaccepted.Themathcourseshouldreflectmath’shistory,math’sapplicationanddevelopmenttrend,andmath’sinteractionandco-developmentwiththesociety,andreflectmathscience’sideologysystemandaestheticvalues.Thishasbecomeacommonrecognitioninmatheducationresearch.Itisanewviewpointthatteachersteachcoursesinanenjoyablewaywithmath’ssciencevalues,practicalvalues,andhumanityvalues.Meanwhile,teachershelpstudentsexperienceandenjoymath,helpthembegintolovemathknowledgefromthebottomoftheirhearts,helpstudentsobtaintheirmathtechniquesbythemselves.Inthisway,studentsgraduallyintegrateknowledgeandtechniquesintoamathcharacteristic,andobtainexcellentmathaccomplishments.Thepaperintroducesexamplesofmathhistory,fromtheanglesofmathscoursereformexploresmathculture’sinfluenceinhighschoolmathcourseteaching.Thepaperproveswithexperimentsthat,ithasgreatlypromotedhighschoolmathcourseteaching,withthehumanityanddiversificationofconceptsandformsofteachingandproject.Itisalsobeneficialtostudents’personalitydevelopmentandtheirdevelopmentinphysicalandmentalhealth,profoundlyinfluencedstudents’interestsandabilitiesinlearningmaththroughouttheirlives.Keywords:Mathematicsculture;Mathematicsskillset;Mathematicsteaching;Researchingcooperationandlearning3目录引言···········································································11新课程背景下关于数学的思考···········································12问题的提出································································1第1章树立数学文化观···························································41.1数学与文化··········································································41.1.1关于数学··········································································41.1.2数学文化的概念界定···························································41.2数学文化观··········································································51.2.1数学文化在中学数学教学中的迷失和回归································51.2.2在中学数学教学中树立数学文化观·········································6第2章数学文化的形成和发展·········································72.1数学发展史概述····································································72.1.1古代数学时期····································································72.1.2变量数学时期····································································92.1.3近、现代数学时期······························································92.1.4我国现代数学的发展··························································102.2数学文化的发展···································································122.2.1几何、微积分、非欧几何与数学文化·····································122.2.2自然、综合国力与数学文化·················································132.2.3人的发展与数学文化··························································14第3章高中数学教学渗透数学文化教育的必要性················163.1渗透数学文化教育是高中新课标的要求····································163.2渗透数学文化教育是素质教育的重要内容·································163.3渗透数学文化教育可以有效激发学习数学的热情························183.4渗透数学文化教育有助于全面认识数学的价值··························19第4章高中数学教学渗透数学文化教育的实施···················214.1通过介绍数学史来渗透数学文化教育·································214.2创新教学方法，传播数学文化········································234.2.1发掘数学的内蕴，展示数学的美学价值····························234.2.2重视数学思维的培养，崇尚数学的理性精神······················244.2.3营造良好的课堂文化氛围，体现数学的人文精神·················264.3渗透数学思想方法，提高学生数学素养······························2744.3.1运用数学思想方法的创新属性培养数学创新意识·················274.3.2运用数学思想方法的辩证特点培养正确的世界观、完善认知结构··············································································284.3.3在课堂教学中实施化归、构造函数等数学思想方法的渗透·······284.4开展研究性合作学习，体验感悟数学文化的价值····················30第5章高中数学教学渗透数学文化教育的实验研究···············365.1实验的目的·····························································365.2实验的理论依据························································365.2.1普通高中数学新课程标准···········································365.2.2学习理论·····························································365.3实验设计·······························································365.4实验结果分析··························································37结语··········································································40参考文献····································································41附录1········································································43