CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

该项目作为职业方案的一部分得到资助，将在K-12课程中教授证明的最普遍的课程/主题--几何--的背景下，增加关于证明教学和学习的知识库。鉴于证明作用的中心地位，以及在K-12和本科课程中持续存在的证明教学困难，这个话题至关重要。这项工作是新奇的，集中在一个未被研究的证明领域，向学生介绍证明的主题。在建立在以前的证明工作的基础上，该项目将处理开始教授证明的一个重要领域，这可能会导致K-12和本科水平的更广泛的创新。该项目将产生一种资源，一套经验教训，可广泛使用，并有可能在国际和平协会以前由国家科学基金会支持的工作的基础上广泛传播，这些工作已广泛传播给从业人员受众。该项目的目标是开发一种干预措施，以支持几何背景下证明的教与学。本研究的前提是，如果我们引入证明，首先教授学生证明的特定的子目标，如如何从给定的陈述和定义中得出结论，那么学生就会更成功地自己构建证明。这项为期5年的设计和开发研究建立在研究人员之前的工作基础上，该研究来自诺尔斯科学教学奖学金(KSTF)，目的是研究教师如何向学生介绍证据。这项研究将建立在先前工作的基础上，以完善在KSTF研究中开发的引入证据的框架。利用这一框架，研究者将与五名高中几何教师合作，通过课堂学习方法来制定课程，以引入证明的子目标。PI将研究这些课程的使用对学生举证能力的影响，并与没有参与干预的10名教师的学生进行比较。

This project, funded as part of the CAREER program, would add to the knowledge base on the teaching and learning of proof in the context of the most prevalent course/topic in which proof is taught in the K-12 curriculum, geometry. Given the centrality of the role of proof, and the persistent difficulties in teaching proof in the K-12 and undergraduate curriculum, the topic is of vital importance. The work is novel, focusing on an area of proof that is understudied, the introduction of students to the topic of proof. While building on prior work in proof, the project will tackle an important area of beginning to teach proof, which may lead to broader innovations at both the K-12 and undergraduate level. The project will produce a resource, a set of lessons, which can be used widely and are likely to be broadly disseminated based on the PI's previous NSF-supported work, which has been broadly disseminated to practitioner audiences. The goal of the project is to develop an intervention to support the teaching and learning of proof in the context of geometry. This study takes as its premise that if we introduce proof, by first teaching students particular sub-goals of proof, such as how to draw a conclusion from a given statement and a definition, then students will be more successful with constructing proofs on their own. The 5-year design and development study builds on the researcher's prior work from a Knowles Science Teaching Fellowship (KSTF) grant to study how teachers introduce proof to students. This study will build on the prior work to refine a framework for introducing proof developed in the KSTF study. Using this framework the researcher will work with five high school geometry teachers to develop lessons via Lesson Study methods to introduce sub-goals of proof. The PI will study the impact of the use of these lessons on students' ability to perform proofs, and compare to students of ten teachers who will not have participated in the intervention.