An Investigation of Pedagogical Factors Influencing Student Understanding of Geometric Proof

影响学生理解几何证明的教学因素的调查

• 批准号: 9980476
• 负责人: Sharon McCrone
• 金额: $ 40.94万
• 依托单位: Board of Trustees of Illinois State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-04-01 至 2004-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9980476&HistoricalAwards=false
• 关键词: Investigation; Pedagogical; Factors; Influencing; Student

The purpose of the three-year study is to develop an empirically grounded theoretical model that relates pedagogy to student understanding of geometric proofs. By engaging in the logical reasoning that is associated with mathematical proof, students develop vitally important critical thinking skills. In addition, proof is fundamental to the discipline of mathematics because it is the convention that mathematicians use to establish the validity of mathematical statements. This study focuses on geometric proof because geometry is traditionally the course in which students are first required to construct proofs. Despite the fact that student difficulty with proof has been well established in the literature, existing empirical research on pedagogical methods associated with the teaching and learning of geometric proof is insufficient. This research study, focuses on the effects of curriculum and pedagogy on student understanding of geometric proof.In order to assess the effectiveness of the pedagogical methods used by participating teachers, the project focuses on two components of student understanding of proof, namely, students' beliefs about what constitutes a proof and students' proof-construction ability. Specifically, the project has four objectives:1. To document student understanding of proof in order to update and expand existing research in this area;2. To characterize evolving student beliefs about what constitutes a proof (using Dreyfus and Hadas' (1987) six principles) in proof-based geometry classes and to link these characterizations to aspects of the pedagogy including sociomathematical norms, nature of the activities, and teacher beliefs;3. To characterize students' evolving proof-construction ability in proof-based geometry classes and to link these characterizations to aspects of the pedagogy including sociomathematical norms, nature of the activities, and the teacher's instructional philosophy; and4. To describe the effects of participation in a research study focused on their classrooms on teachers' practice and perspectives that guide their practice. In order to achieve these objectives, the principal investigators will spend two years in the classrooms of several teachers recording the beliefs and proof construction ability of the students as well as the beliefs held and the pedagogical methods used by the teachers. Teachers will read and reflect on the existing research on geometric proof, will work collaboratively with the researchers to develop instructional materials, and will implement these materials in their classrooms. In addition, the study will focus on the sociomathematical norms established in each of the classrooms, as these norms relate to students' understanding of proof. Data will be analyzed as it is collected as well as in the third year of the study in order to develop models that describe how pedagogical interventions influence student understanding.Findings from this project will be disseminated to the mathematics education research and teaching communities. Research findings will have implications for curriculum, pedagogy, and teacher enhancement

这项为期三年的研究的目的是开发一个基于经验的理论模型，将教学法与学生对几何证明的理解联系起来。 通过参与与数学证明相关的逻辑推理，学生可以培养至关重要的批判性思维技能。此外，证明是数学学科的基础，因为它是数学家用来建立数学陈述有效性的惯例。 本研究的重点是几何证明，因为几何是传统的课程，学生首先需要构造证明。 尽管事实上，学生的困难与证明已经建立在文献中，现有的实证研究的教学方法与教学和学习的几何证明是不够的。 本研究旨在探讨课程与教学法对学生几何证明理解的影响，并针对学生对证明理解的两个组成部分，即学生对证明构成的信念和学生的证明构建能力，评估参与教师教学方法的有效性。 具体而言，该项目有四个目标：1。记录学生对证明的理解，以更新和扩展该领域现有的研究;2。描述学生对什么构成证明的信念（使用Dreyfus和Hadas（1987）的六个原则），并将这些表征与教学法的各个方面联系起来，包括社会数学规范、活动的性质和教师信念;3.描述学生在基于证明的几何课程中不断发展的证明构建能力，并将这些特征与教育学的各个方面联系起来，包括社会数学规范，活动的性质和教师的教学理念;描述参与一项以课堂为重点的研究性学习对教师实践的影响以及指导他们实践的观点。为了实现这些目标，主要研究者将花两年时间在几个教师的教室里记录学生的信念和证明构建能力，以及教师所持有的信念和使用的教学方法。 教师将阅读和反思现有的研究几何证明，将与研究人员合作开发教学材料，并将在课堂上实施这些材料。 此外，研究将集中在社会数学规范建立在每个教室，因为这些规范涉及到学生的理解证明。 数据将在收集时以及研究的第三年进行分析，以开发描述教学干预如何影响学生理解的模型。该项目的结果将传播给数学教育研究和教学界。 研究结果将对课程、教学法和教师的提高产生影响