Knowing Mathematics for Teaching Algebra

了解数学以教授代数

• 批准号: 0337595
• 负责人: Robert Floden
• 金额: --
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-06-15 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0337595&HistoricalAwards=false
• 关键词: Knowing; Mathematics; Teaching; Algebra

Concerns about the quality of the mathematics achievement of K-12 students in the United States continue to dominate national dialogue in the academic and popular press. Students' performance in algebra is particularly worrisome, and this may be due in part to lack of appropriate teacher knowledge. The RAND Mathematics Study Panel (2003) notes the need for: clarification of the knowledge demands of teaching, tools for assessing mathematical knowledge for teaching across grade levels and mathematical domains, and deeper understanding of the ways in which prospective and practicing teachers have opportunities to acquire this kind of knowledge; they also single out algebra as a key area. Consequently, the proposed research project has three main objectives: 1. Instrument Design: To develop items and design reliable and valid instruments to measure knowledge in large scale settings for teaching algebra among pre-service and in-service secondary school mathematics teachers. 2. Framework Validation: To produce an empirically validated and comprehensive framework for knowledge for teaching algebra. 3. Status Study of Teacher Knowledge. To study the status and variation of knowledge for teaching algebra among pre-service and in-service teachers drawn from across the nation. An interdisciplinary MSU-based research team with collective expertise in mathematics, mathematics education, research design, psychometric analysis, and secondary school mathematics teaching and curriculum will lead the project, with the support of research collaborators around the country, a national advisory board, and item writers. Intellectual merit of the proposed activity: The study will contribute an empirically validated and comprehensive framework for knowledge for teaching algebra at the secondary school level, together with items and assessment instruments to measure this knowledge in large-scale settings. The result will be clarification and description of teacher knowledge in a crucial and problematic area of the K-12 mathematics curriculum. Broader impacts resulting from proposed activity: The items and assessment tools developed here will be of value for teacher educators, mathematicians who prepare teachers, designers of professional development, and evaluators interested in teacher learning in the area of algebra. Ultimately this work could have substantial impact on the improvement of secondary school algebra teaching and learning.

对美国 K-12 学生数学成绩质量的担忧继续主导学术界和大众媒体的全国对话。学生在代数方面的表现尤其令人担忧，部分原因可能是教师缺乏适当的知识。兰德数学研究小组（2003）指出需要：澄清教学的知识需求，评估跨年级和数学领域教学的数学知识的工具，以及更深入地了解未来和实践教师有机会获得此类知识的方式；他们还将代数列为关键领域。 因此，拟议的研究项目有三个主要目标： 1. 仪器设计：开发项目并设计可靠且有效的仪器，以在大规模环境中测量知识，以便在职前和在职中学数学教师进行代数教学。 2. 框架验证：为代数教学生成一个经经验验证的综合知识框架。 3.教师知识现状研究。研究全国职前和在职教师代数教学知识的现状和变化。 一个基于密歇根州立大学的跨学科研究团队将领导该项目，该团队在数学、数学教育、研究设计、心理测量分析以及中学数学教学和课程方面拥有集体专业知识，并得到全国各地研究合作者、国家顾问委员会和项目作者的支持。 拟议活动的智力价值：该研究将为中学代数教学知识提供一个经过经验验证的综合框架，以及在大规模环境中衡量这些知识的项目和评估工具。 其结果将是对 K-12 数学课程中关键且有问题的领域的教师知识进行澄清和描述。 提议的活动产生更广泛的影响：这里开发的项目和评估工具对于教师教育工作者、为教师做好准备的数学家、专业发展的设计者以及对代数领域教师学习感兴趣的评估者都很有价值。 最终，这项工作可能会对中学代数教学的改进产生重大影响。