Introducing Indivisibles into Calculus Instruction

将不可分引入微积分教学

• 批准号: 0126141
• 负责人: Bronislaw Czarnocha
• 金额: $ 40万
• 依托单位: CUNY Hostos Community College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-04-01 至 2006-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0126141&HistoricalAwards=false
• 关键词: Introducing; Indivisibles; into; Calculus; Instruction

The PI's Bronislaw Czarnocha and Vrunda Prabhu, will conduct two year-long cycles ofteaching experiments to introduce the intuition of "indivisibles" into calculus instruction andintegrate it with standard ways of instructing via Riemann construction. They plan to studyclosely the conceptual and computational development of students who receive this instruction. ItAs part of this project, the PI's will investigate:(1) What is the process of transformation and development of the intuition of lines (theindivisibles) into a precise, mathematical concept?(2) Does the introduction of the W-C construction based on indivisibles, the interplay of thatconstruction with the standard Riemann construction, and the instruction that integrates both,strengthen students' understanding of the concept of the definite integral?In the proposed project, they will conduct and coordinate Calculus instruction at sixinstitutions, assess students' performance via tests, essays and clinical interviews, collect dataresulting from the different assessment and analyze the data in preparation for a refinement of theteaching strategy. As a general framework they will adopt Vygotsky's theory with its emphasison the cognitive processes in the zone of proximal development, which dictates importantconsequences on the instruction and assessment. Students will be guided by the activities of theclass to enable them to experience the process of mathematical thinking and to reveal its contentto the teacher. The role of the instructor will be to provide systematization of their spontaneousdevelopment grounded in the precise mathematical understanding of the concept in question. Thedirections their spontaneous thought processes take, will be under investigation during the course.The project is a balance between various aspects: (1) the natural intuition of the learner vs.the academic instruction, (2) computational mastery vs. conceptual understanding, (3) teachingand research.

他们将进行为期两年的教学实验，将“不可分割”的直觉引入微积分教学，并通过黎曼结构将其与标准的教学方法相结合。他们计划仔细研究接受这一指导的学生的概念和计算能力的发展。作为这个项目的一部分，PI将调查：(1)线的直觉(不可分割的)转化和发展成精确的数学概念的过程是什么？(2)基于不可分割的W-C结构的引入，该结构与标准Riemann结构的相互作用，以及两者的整合是否加强了学生对定积分概念的理解？在拟议的项目中，他们将在六个机构进行微积分教学，通过测试、论文和临床访谈来评估学生的表现，收集不同评估结果的数据，并对数据进行分析，为改进教学策略做准备。作为一个总体框架，他们将采用维果茨基的理论，强调最近发展区的认知过程，这决定了教学和评估的重要后果。学生将在课堂活动的引导下，体验数学思维的过程，并向教师展示数学思维的内容。讲师的角色将是提供他们的自发发展的系统化，其基础是对所讨论的概念的精确的数学理解。他们自发的思维过程的走向将在课程中得到调查。该项目是在以下几个方面之间的平衡：(1)学习者的自然直觉与学术指导，(2)计算掌握与概念理解，(3)教学与研究。