Euclidean Geometry中的假设挖掘
Assumption Digging in Euclidean Geometry
摘要：
理论建构在数学教育中一直被忽视，尤其是在初中和高中阶段。本论文的重点是假设挖掘，这是一种类似于希尔伯特在《欧几里得几何基础》中所进行的理论建构。在学校的欧几里德几何课程是一个潜在的生产假设挖掘，因为，正如已经指出，欧几里德几何的许多课程包含无关的假设和不明确的定义。本文的重点是对印度西部两所学校的7 - 10年级学生进行的教学实验，即欧几里得几何中的假设挖掘练习。本论文的目的是确定学生参与假设挖掘的各种方式，以及教师在假设挖掘过程中所扮演的角色。虽然大多数学生参与假设挖掘的程度都是为了证明导师质疑的主张的合理性，但也有一些学生质疑导师提出的论点和主张。教员在两个方面发挥着至关重要的作用。首先，决定会议采取什么样的路径，其次，与学生的论点和怀疑态度。
英文摘要：
Theory Building has been largely ignored in Mathematics Education, especially at the Middle and High School Levels. This thesis focuses on Assumption Digging, a type of Theory Building similar to what Hilbert undertook in his Grundlagen with Euclidean Geometry. The Euclidean Geometry course in schools is a potentially productive for Assumption Digging since, as has been noted, many courses in Euclidean Geometry contain extraneous postulates and unclear definitions. This focus of this thesis is a teaching experiment with 7th-10th grade students in two schools in Western India, which is an Assumption Digging exercise in Euclidean Geometry. The goal of this thesis is to ascertain the various ways students engage in Assumption Digging, and the role played by the instructor in the Assumption Digging sessions. While most of the student engagement with Assumption Digging was at the level of justifying claims which the instructors questioned, there were a few instances of students questioning arguments and claims made by the instructors. The role the instructors played was crucial in two ways. Firstly, deciding what path the session took and, secondly, engaging with student arguments and skepticism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
