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

威斯康辛大学的艾米·埃利斯（Amy Ellis）领导的这个CAREER项目的目的是探索一个假设，即在中学数学课程中专注于定量推理可以提高学生技能的发展和对数学证明的理解。该项目通过一系列研究来解决这一假设，其中包括与学生进行的小组教学实验，与教师进行的专业发展工作，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实地测试。该项目的工作将产生：(a)对统一定量推理和证明的两个先前不相关的研究路线的方法的见解；(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)洞察中学生从初级数学过渡到高等数学时的思维；(e)增加对教师关于证明的知识的理解，以及他们旨在帮助学生在理解和掌握证明技能方面取得进步的课堂实践。

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.