Collaborative Research: Investigating Issues of the Individual and the Collective along a Continuum between Informal and Formal Reasoning

协作研究:沿着非正式和正式推理的连续体调查个人和集体的问题

基本信息

  • 批准号:
    0634074
  • 负责人:
  • 金额:
    $ 25.8万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2007
  • 资助国家:
    美国
  • 起止时间:
    2007-09-01 至 2012-08-31
  • 项目状态:
    已结题

项目摘要

Undergraduate engineering, science and mathematics majors in the United States begin their university mathematics training with several calculus courses, but then move on to such courses as differential equations and linear algebra. Mathematics majors and minors may also study real analysis or abstract algebra. Students often find the transition from taking calculus courses to taking more formal, proof-based mathematics courses particularly challenging, and often a stumbling block to further academic success. Sophomore and junior level courses such as differential equations, linear algebra, geometry, and courses introducing set theory and logic constitute a core collection of courses that have the potential to facilitate this transition. The main goals of this project are to make contributions to theory and methodology in terms of the continuum between informal and formal mathematical reasoning. In particular, the PIs will develop theoretical means for interpreting the transition to formal, proof-based mathematics courses. They do so by using four different perspectives on the nature of the individual and collective growth of knowledge. The methodological products will include strategies for data collection and data analysis that allow for insights into student learning within and between each of the four different theoretical perspectives. The mathematical context for this work will primarily be linear algebra, with insights drawn from our prior work in differential equations, geometry, and set theory.
在美国,工程、科学和数学专业的本科生开始大学数学训练时先学习几门微积分课程,然后再学习微分方程和线性代数等课程。数学专业和未成年人也可以学习真实的分析或抽象代数。学生们经常发现从微积分课程到更正式的基于证明的数学课程的过渡特别具有挑战性,并且往往是进一步学术成功的绊脚石。二年级和初级课程,如微分方程,线性代数,几何,以及介绍集合论和逻辑的课程,构成了一个核心集合的课程,有可能促进这种转变。该项目的主要目标是在非正式和正式数学推理之间的连续性方面对理论和方法做出贡献。特别是,PI将开发理论手段来解释过渡到正式的,基于证明的数学课程。他们这样做是通过使用四个不同的角度对知识的个人和集体增长的性质。方法学产品将包括数据收集和数据分析的策略,这些策略允许深入了解学生在四个不同理论视角中的学习情况。这项工作的数学背景将主要是线性代数,从我们以前在微分方程,几何和集合论方面的工作中汲取见解。

项目成果

期刊论文数量(0)
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会议论文数量(0)
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Chris Rasmussen其他文献

The Sierpinski smoothie: blending area and perimeter
  • DOI:
    10.1007/s10649-019-09889-4
  • 发表时间:
    2019-03-13
  • 期刊:
  • 影响因子:
    1.900
  • 作者:
    Naneh Apkarian;Michal Tabach;Tommy Dreyfus;Chris Rasmussen
  • 通讯作者:
    Chris Rasmussen
Computing in Bioinformatics and Engaged Student Learning: Student Perspectives on Anticipatory Activities and Innovative Apps
生物信息学计算和学生参与学习:学生对预期活动和创新应用程序的看法
  • DOI:
    10.1080/0047231x.2022.12290692
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Tina A. Marcroft;Chris Rasmussen;Scott T. Kelley
  • 通讯作者:
    Scott T. Kelley
Effects of high carbohydrate or high protein energy-restricted diets combined with resistance-exercise on weight loss and markers of health in women with serum triglyceride levels above or below median values
  • DOI:
    10.1186/1550-2783-7-s1-p9
  • 发表时间:
    2010-09-15
  • 期刊:
  • 影响因子:
    3.900
  • 作者:
    Jonathan M Oliver;Julie Y Kresta;Mike Byrd;Claire Canon;Michelle Mardock;Sunday Simbo;Peter Jung;Brittanie Lockard;Deepesh Khanna;Majid Koozehchian;Chris Rasmussen;Chad Kerksick;Richard Kreider
  • 通讯作者:
    Richard Kreider
Comparative effectiveness of two popular weight loss programs in women III: health and fitness markers
  • DOI:
    10.1186/1550-2783-8-s1-p5
  • 发表时间:
    2011-11-07
  • 期刊:
  • 影响因子:
    3.900
  • 作者:
    Jonathan Oliver;Michelle Mardock;Brittanie Lockard;Mike Byrd;Sunday Simbo;Andrew Jagim;Julie Kresta;Claire Baetge;Peter Jung;Majid Koozehchian;Deepesch Khanna;Mike Greenwood;Chris Rasmussen;Richard Kreider
  • 通讯作者:
    Richard Kreider
Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning
  • DOI:
    10.1016/j.jmathb.2010.01.001
  • 发表时间:
    2010-06-01
  • 期刊:
  • 影响因子:
  • 作者:
    Michelle Zandieh;Chris Rasmussen
  • 通讯作者:
    Chris Rasmussen

Chris Rasmussen的其他文献

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{{ truncateString('Chris Rasmussen', 18)}}的其他基金

Making Upper Division Mathematics Courses More Relevant for Future High School Teachers: The Case of Inquiry-Oriented Dynamical Systems and Modeling
使高年级数学课程与未来高中教师更相关:以探究为导向的动力系统和建模案例
  • 批准号:
    2337047
  • 财政年份:
    2024
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Collaborative Research: Student Engagement in Mathematics through an Institutional Network for Active Learning
协作研究:学生通过主动学习的机构网络参与数学
  • 批准号:
    1624639
  • 财政年份:
    2016
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Exploring the Role of Instructors' Social Networks in Undergraduate STEM Instructional Improvement
探索教师社交网络在本科生 STEM 教学改进中的作用
  • 批准号:
    1550990
  • 财政年份:
    2015
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Collaborative Research: Developing inquiry oriented instructional materials for Linear Algebra
合作研究:开发面向探究的线性代数教学材料
  • 批准号:
    1245796
  • 财政年份:
    2013
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Collaborative Research: A Conference to Promote the Integration of Research on Undergraduate Mathematics, Physics, and Chemistry Education
协作研究:促进本科数理化教育研究融合会议
  • 批准号:
    0941191
  • 财政年份:
    2010
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Collaborative Research: Exploring Student Understanding of Physical Chemistry
合作研究:探索学生对物理化学的理解
  • 批准号:
    0816948
  • 财政年份:
    2008
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Standard Grant
Career: Differential Equations: Building a Theory of Student Reasoning and Understanding
职业:微分方程:建立学生推理和理解的理论
  • 批准号:
    0423067
  • 财政年份:
    2004
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Continuing Grant
Career: Differential Equations: Building a Theory of Student Reasoning and Understanding
职业:微分方程:建立学生推理和理解的理论
  • 批准号:
    9875388
  • 财政年份:
    1999
  • 资助金额:
    $ 25.8万
  • 项目类别:
    Continuing Grant

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