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

职业：中学课堂证明：分解核心数学实践

• 批准号: 1453493
• 负责人: Michelle Cirillo
• 金额: $ 87.4万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-15 至 2023-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1453493&HistoricalAwards=false
• 关键词: CAREER; Proof; Secondary; Classrooms; Decomposing

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.

该项目作为CAREER项目的一部分资助，将在K-12课程中教授证明的最普遍课程/主题——几何——的背景下，增加关于证明教学的知识库。鉴于证明的核心作用，以及在K-12和本科课程中教授证明的持续困难，这一主题至关重要。这项工作是新颖的，专注于一个领域的证明是研究不足，介绍学生的主题证明。在先前证明工作的基础上，该项目将解决开始教学证明的一个重要领域，这可能会在K-12和本科阶段带来更广泛的创新。该项目将产生一套资源，一套课程，可以广泛使用，并可能在PI以前的nsf支持的工作基础上广泛传播，这些工作已经广泛传播给实践者。该项目的目标是开发一种干预措施，以支持几何背景下的证明教学。本研究的前提是，如果我们引入证明，首先教学生特定的证明子目标，例如如何从给定的陈述和定义中得出结论，那么学生将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从Knowles科学教学奖学金（KSTF）获得的工作基础上，研究教师如何向学生介绍证据。本研究将以先前的工作为基础，完善一个框架，以引入KSTF研究中开发的证据。利用这一框架，研究人员将与五位高中几何教师合作，通过课程研究方法开发课程，介绍证明的子目标。PI将研究使用这些课程对学生证明能力的影响，并与没有参与干预的10名教师的学生进行比较。