Navigating Mathematical Transitions: Students' Adjustments to Fundamental Changes in Cirriculum and Pedagogy

引领数学转型：学生对课程和教学法根本变化的调整

• 批准号: 9903264
• 负责人: John Smith III
• 金额: $ 91.09万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9903264&HistoricalAwards=false
• 关键词: Navigating; Mathematical; Transitions; Students; Adjustments

Navigating Mathematical Transitions: Students' Adjustments to Fundamental Changes in Curriculum and Pedagogy Principal Investigator: Jack Smith, Michigan State University Students can experience mathematical transitions when they move from classrooms where one perspective on doing and thinking about mathematics is illustrated and practiced to others where quite different perspectives dominate. Such discontinuities in expectations can seriously challenges students, who must make sense of and adjust to them. Mathematical transitions are now more likely given the uneven implementation of curricula and teaching practices inspired by the NCTM Standards. Two important places to search for and examine these transitions are introductory algebra (in middle and high school) and calculus. Curricular materials in these content areas and the teaching practices suggested by them can vary dramatically according to: (1) the fundamental objects and processes of study (equations and symbol manipulation procedures vs. functions, multiple representations, and solutions in each representation); (2) the typical problems presented to students (commands to manipulate symbols vs. questions about varying quantities in context); and (3) the organization of classroom learning (teacher presentation and individual problem-solving vs. these in combination with small group work and whole class discussion). This project will develop a working conceptualization of mathematical transitions (i.e., major factors and how they interact) and analyze high school and college students' passage through them. Three main questions will be addressed: (1) What are the characteristics of successful (and unsuccessful) mathematical transitions?; (2) How do students navigate them?; and (3) What kinds of resources ("internal" and "external" to the student) support more successful transitions? Four school sites (two high schools and two universities) will participate. At two sites (1 high school and 1 college, curricula and teaching practices shift from the study of equations and their solution, practice with many problems, individual study, and teacher presentation to the study of functions in multiple representations, verbal and numerical "answers," work on contextualized problems, and small group and whole group work. At the other two sites, these conditions are reversed. The project will select 100 students (25 per site) and track their progress through 2+ years of mathematics. It will assess and analyze the change in their emerging career and educational goals, mathematics achievement, content learning, beliefs about mathematics and themselves as learners, daily experience and reactions to their work, and strategies for adjusting to different expectations. The project will produce a composite portrait of the experience and learning of the entire sample and a representative set of detailed case studies to illuminate the dynamics of students' experience. It will attempt to present its findings to teachers, parents, and administrators, as well as researchers.

引导数学过渡：学生对课程和教学法基本变化的调整首席研究员：杰克·史密斯，密歇根州立大学学生可以体验数学过渡，当他们从课堂上的一种观点做数学和思考是说明和实践到其他完全不同的观点占主导地位。这种期望的不连续性给学生带来了严重的挑战，他们必须理解并适应它们。由于NCTM标准所启发的课程和教学实践的不平衡实施，现在更有可能出现数学过渡。寻找和检验这些过渡的两个重要地方是代数入门（初中和高中）和微积分。这些内容领域的课程材料及其建议的教学实践可能会根据：(1)研究的基本对象和过程（方程和符号操作程序与函数，多种表示和每种表示的解）而发生巨大变化；(2)呈现给学生的典型问题（操纵符号的命令与在语境中变化数量的问题）；(3)课堂学习的组织（教师陈述和个人解决问题vs.结合小组工作和全班讨论）。该项目将发展数学过渡的概念化（即主要因素及其相互作用），并分析高中生和大学生通过它们的过程。将解决三个主要问题：(1)成功（和不成功）的数学转换的特征是什么？(2)学生如何驾驭它们？(3)什么样的资源（“内部”和“外部”的学生）支持更成功的过渡？共有4所学校（2所高中和2所大学）参加。在两个地点（1所高中和1所大学），课程和教学实践从对方程及其解的研究、多问题练习、个人学习和教师演示转向了对多种表示形式的函数的研究、口头和数字“答案”、情境化问题的研究、小组和整体小组工作。在另外两个地点，情况正好相反。该项目将选择100名学生（每个站点25名），并通过两年多的数学学习跟踪他们的进步。它将评估和分析他们在新兴的职业和教育目标、数学成就、内容学习、对数学和自己作为学习者的信念、日常经验和对工作的反应以及适应不同期望的策略方面的变化。该项目将生成整个样本的经验和学习的综合肖像，以及一组有代表性的详细案例研究，以阐明学生经验的动态。它将试图向教师、家长、管理人员以及研究人员展示它的发现。