CAREER: Understanding and Cultivating the Development of Students' Competencies in Justifying and Proving

证明是数学学科和实践的核心。 在学校里，在欧几里德几何领域之外很少遇到数学证明。 最近的数学教育改革努力要求学校在整个数学课程中为所有学生提供机会和经验。 然而，我们对小学生学习猜想、证明和数学证明的方式知之甚少。 更具体地说，已知最少的年级是第6至第8级。 考虑到这一点，本中学验证研究的目标如下： 理解学生在证明和证明方面的能力的发展： 了解促进这些能力发展所需的条件和教学方法; 编制教师培训和专业发展材料，旨在提高教师对证明的理解，并支持他们培养学生证明和证明的能力。

Proof is central to the discipline and practice of mathematics. In school mathematics proof is rarely encountered outside the realm of Euclidean geometry. Recent reform efforts in mathematics education call on schools to provide all students with opportunities and experiences throughout the mathematics curriculum. Yet little is known about the ways grade school students learn to conjecture, to justify and to prove mathematically. More specifically, the grade-levels where least is known are 6th through 8th. With this in mind then, the objectives of this middle school proof study are as follows: Understand the development of students' competencies in justifying and proving: To understand the conditions and pedagogy necessary to promote the development of those competencies; and To develop teacher preparation and professional development materials designed both to enhance teachers' understandings of proof and to support them in fostering the development of students' competencies in justifying and proving.