CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

职业：通过代数定量推理支持学生的证明实践

• 批准号: 1743356
• 负责人: Amy Ellis
• 金额: $ 5.58万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1743356&HistoricalAwards=false
• 关键词: CAREER; Supporting; Students; Proof; Practices

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra. Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

由威斯康星大学艾米·埃利斯领导的这个职业项目的目的是探索这样一个假设：中年级数学中以定量推理为重点的课程可以增强学生技能的发展和对数学证明的理解。 该项目正在通过一系列研究来解决这一假设，其中包括学生的小组教学实验、教师的专业发展工作以及将代数中的定量推理和证明联系起来的课程单元的课堂现场测试。 该项目的工作将产生：（a）对如何统一定量推理和证明这两个先前互不相干的研究方向的见解； (b) 描述通过定量推理支持学生证明能力发展的现实方法的模型； (c) 通过参与基于定量推理的证明实践，提高学生对代数的理解； (d) 深入了解中学生从初级数学向高级数学过渡时的思维； (e) 加深对教师关于证明的知识及其课堂实践的理解，旨在帮助学生提高证明的理解和技能。