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

这个由威斯康星大学的艾米·埃利斯领导的职业生涯项目的目的是探索这样一种假设，即在中学数学课程中注重定量推理可以提高学生的技能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，这些研究包括与学生进行小组教学实验，与教师进行专业发展工作，以及对课程单元进行课堂实地测试，将代数中的定量推理与证明联系起来。该项目的工作将产生：(A)对如何统一两个以前相互割裂的定量推理和证明研究方向的见解；(B)描述通过量化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)深入了解中学生在谈判从初级数学向更高级数学过渡时的思维；以及(E)加深对教师关于证明的知识及其课堂实践的理解，旨在帮助学生在证明方面的理解和技能。

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.