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1.
Lyn D. English 《Educational Studies in Mathematics》2006,63(3):303-323
This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive
mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The
children and their teachers were participating in a 3-year longitudinal teaching experiment in which sequences of mathematical
modeling problems were implemented from the 5th grade (10 years of age) though to the 7th grade. In contrast to traditional
problem solving, mathematical modeling requires children to generate and develop their own mathematical ideas and processes,
and to form systems of relationships that are generalizable and reusable. Reported here is a detailed analysis of the iterative
cycles of development of one group of children as they worked the problem, followed by a summary of the mathematization processes
displayed by all groups. Children's critical reflections on their models are also reported. The results show how children
can independently develop constructs and processes through meaningful problem solving. Children's development included creating
systems for operationally defining constructs; selecting, categorizing, and ranking factors; quantifying quantitative and
qualitative data; and transforming quantities. 相似文献
2.
数学生活化是指以生活化的素材与方式展开数学教学,包含了"生活化"和"数学化"两个维度.数学生活化是激发数学学习兴趣的途径,促进数学深刻理解的阶梯,培养抽象概括能力的素材,积累数学活动经验的载体,形成合理数学观念的基石.生活化的情境应该体现数学知识本质,引发学生数学思维,指向数学教学目标\源自真实生活情境,基于学生知识经验. 相似文献
3.
伊德面对胡塞尔对伽利略的批判而为伽利略辩护,认为望远镜具有透明性。这错失了真正的问题,即伽利略试图将经由望远镜的所见确立为唯一的实在。基督教对质料之抵抗作用的废除、存在论二分向主客二分的转换、伽利略等人对数学的强烈信心,使得数学在亚里士多德主义的自然哲学跌落的背景下上升为唯一不受欺骗的感官。望远镜经由数学的权威而获得权威,成为"独眼"。世界因此失去纵深感,生活世界的意义沉淀在图像之中。伊德正是由于忽视了望远镜背后的这些意涵,才误以为对望远镜的运用能够扭转数学化的不良影响。 相似文献
4.
5.
Bharath Sriraman 《Interchange》2006,37(1-2):151-178
This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use
of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly
diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the
Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich
mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual
counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse.
In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting
problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos.
The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher
education are discussed. 相似文献
6.
试析影响学生数学建模数学化过程的若干因素 总被引：1，自引：0，他引：1
袁红 《上海师范大学学报(哲学社会科学版)》2009,(1):113-119
为适应新一轮数学课程改革中加强应用性和创新性,重视联系学生生活实际和社会实践要求,开展数学建模教学成为当今数学教育改革的热点之一。如何有效实施数学建模教学是许多数学教师感到困惑的一大难题。而研究学生数学建模过程中所面临的困难及产生原因是教师有效实施数学建模教学的前提与关键。文章拟从初中数学课堂中实施数学建模教学的一则案例出发,初步研究发现学生在数学建模的数学化过程中,学生自身的数学阅读能力、简化实际问题能力、数学语言能力和元认知能力影响着学生的数学建模活动。从而对教师在日常数学课堂中有效开展数学建模教学活动具有积极意义。 相似文献
7.
“数学化”的数学教学及其策略探讨 总被引：1，自引：0，他引：1
刘兰英 《上海师范大学学报(哲学社会科学版)》2010,(6):104-107
“数学化”教学就是以“数学化”为核心的数学教学,其实质就是激发学生数学地组织现实世界的过程。它是有效数学教学的核心和数学课程改革的关键。文章提出了实施“数学化”教学的三条主要策略,即教学要源于数学现实又要升华数学现实,要注重培养学生的数学建模能力,以及要尊重学生差异并促其个性化地实现数学知识的“再创造”。 相似文献
8.
随着数学在经济研究中越来越广泛而深入的应用,经济理论数学化得到持续的强化,但同时对之的批评却也从未停止。其根本原因在于忽视了数学在经济研究中所发生的变化,以及经济理论乃至科学知识的本质特征。结构与生成,确定性与不确定性,有限与无限这三对范畴的辩证统一描述了经济现象和科学知识的本质特征,说明了数学是如何不断适应并推进经济理论的发展,进而确证了经济理论数学化的合理性,强化了经济理论的科学性。 相似文献
9.
半个世纪前的弗赖登塔尔数学教育思想在今天看来依然历久弥新。弗赖登塔尔教育思想的核心是“数学化”、“数学现实”与“有指导的再创造思想”,研究其内涵对今天的数学教育具有深远的现实意义。 相似文献
10.
政治经济学能否运用数学并形式化一直是一个有争议的问题.通过对政治经济学发展过程的考察本文发现,政治经济学运用数学和形式化是政治经济学自身发展的一种趋势;政治经济学运用数学应当符合政治经济学的要求,符合数学规范和形式化要求,应当正确处理政治经济学逻辑与数学逻辑的关系. 相似文献