浅谈高等几何与初等几何的关系

几何学是数学的重要组成部分之一,对提升学生观察图形的能力、空间想象力、逻辑推理的能力等具有重要的作用。高等几何和初等几何作为几何学的重要模块,在学习思维上具有很多相似之处,初等几何的学习为几何学打下了坚实的基础,高等几何是在初等几何的基础上进行延伸和扩展的一门课程。研究高等几何和初等几何之间的关系,可以更好的实现它们之间的过渡和衔接,提升学生的学习效率。     

基于初等几何的高等几何的教学研究

高等几何课程是高等师范院校数学专业学生的必修课之一,长期以来学生总认为它对中学的几何教学没有任何帮助。本文从几个方面探讨了高等几何对初等几何学习的指导作用。     

用《高等几何》的理论解决初等几何中的一些问题

《高等几何》是师范系统数学专业重要的基础课之一。本文着重举例用高等几何的理论解决初等几何中的一些问题,以便引起将要学习《高等几何》的同志和中学教学教师研究《高等几何》的同志的重视。     

高等几何在初等几何中的应用例说

高等几何在培养学生思维能力方面,具有独特的功能.学习高等几何,不仅可以用它的观点来指导初等几何的教学,为初等几何教学提供新的思维方法,更重要的是它能帮助人们对初等几何中的一些现象、规律得到更透彻的理解.随着新课程改革     

高等几何与初等几何的关系

高等几何是高等师范院校数学专业的重要基础课之一。这门课与中学的初等几何的关系是每一个从事高等几何教学的教师和毕业后从事中学几何教学的学生必须清楚的。本文从三个方面论述这一问题。     

髙等几何对初等几何教学的指导作用

采取例证分析的方法探讨仿射变换在初等几何中的应用,彰显了高等几何在论证方法、思考问题等方面具有的独特性、巧妙性和灵活性特点.旨在群论观点下进一步认识初等几何的内涵与外延,深刻理解高等几何对初等几何教学与研究的指导作用.     

“初等几何研究”课程改革与实践

随着数学教育的深入发展，高师数学教育课程的势在必行。“初等几何研究”课程的教学大纲需要重新制订，其课程体系和教学内容也需要大幅度调整，特别是将原来的“初等几何研究”课程和“高等几何”课程合并成为一门课程，并将该课程的教学目的从初等几何“研究”转到初等几何教学素质的培养上来。与此同时，编写中的教材《初等几何教学基础》也必须突出与数学教育改革思路相适应的特色。     

高等几何在初等几何中的作用

高等几何是初等几何的延深课程.高等几何为初等几何的有关内容提供了理论依据,高等几何为初 等几何的某些问题提供了解题方法,高等几何可把初等几何的某些内容拓广与延深.     

高等几何在初等几何中的一些应用

从仿射几何和射影几何的理论与方法出发,探讨了它们在初等几何中的一些应用,有利于高等几何对初等几何教学的指导作用。     

师范生学习高等几何的重要性

高等几何是师范系统数学专业重要的基础课之一.本文从高等几何对师范生在几何基础方面的观点的提高、思维的灵活性和提高学生学习兴趣三个方面阐述了高等几何有助于师范生科研能力的培养和中学数学教学质量的提高,从而显示师范生学习高等几何的重要性.     

中国小学生解决国外数学试题分析

通过中国小学生解决国外数学试题的分析 ,探讨中国基础教育现状 ,为数学教学改革提供实证研究基础。我们从国外数学测试中筛选、改编了一套小学五年级数学试卷 ,在全国九个省、市做了测验。结果显示 ,中国学生在考察基础知识的项目中表现出色 ;但在考察利用已有的生活经验解决问题的项目中 ,存在着相当的问题。因此 ,中国数学教育在重视基础知识的同时 ,应该引导学生有意义地理解数学、灵活自主地选择数学方法解决问题。     

Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes

Teaching geometry at the elementary level is challenging. This study examines the impact of van Hiele theory-based instructional activities embedded into an elementary mathematics methods course on preservice teachers’ geometry knowledge for teaching. Pre- and post-assessment data from 111 elementary preservice teachers revealed that van Hiele theory-based instruction can be effective in improving three strands of participants’ geometry knowledge for teaching: geometry content knowledge, knowledge of students’ van Hiele levels, and knowledge of geometry instructional activities. As a result, this paper offers implications for teacher educators and policy makers to better prepare elementary preservice teachers with geometry knowledge for teaching.     

高等几何教学改革的探索与实践

根据基础教育新课程改革要求及对高师数学专业培养目标的认识,结合高等几何教学,论述了其教学改革的必要性与重要性。介绍了高等几何教学内容、教学方法和教学模式改革的新做法。     

The Effect of Visual‐Chunking‐Representation Accommodation on Geometry Testing for Students with Math Disabilities

Students who struggle with learning mathematics often have difficulties with geometry problem solving, which requires strong visual imagery skills. These difficulties have been correlated with deficiencies in visual working memory. Cognitive psychology has shown that chunking of visual items accommodates students’ working memory deficits. This study investigated the effects of visual‐chunking representation as a testing accommodation for improving students’ geometry problem‐solving performance. Participants were four third‐graders with difficulties in mathematics. An adapted reversal design was employed to examine the students’ performance changes during standard testing conditions and accommodated testing conditions. During the accommodated condition, students were presented with visual‐chunking images. Results suggested that the visual‐chunking representation accommodation improved students’ performance on geometry problem‐solving tasks, and an interview confirmed students’ preference for the visual‐chunking representation approach.     

论胡塞尔关于数学起源的思想

胡塞尔的数学学习经历是建立其现象学哲学思想的一个重要的基础,在其前期的《算术哲学》中他试图通过对数学基本概念的澄清来稳定数学的基础,在晚期的《论几何学的起源》中他认为几何学自身具备明见性的特点,应该回溯几何学的最源初的开端。胡塞尔关于数学起源的思想对今天的启示是数学的生活世界是可能的,现象学还原方法是数学史学研究的一个重要方法。     

Disrupting a learning environment for promotion of geometry teaching

Creating a classroom learning environment that is suitably designed for promotion of learners’ performance in geometry, a branch of mathematics that addresses spatial sense and geometric reasoning, is a daunting task. This article focuses on how grade 8 teachers’ action learning changed the learning environment for the promotion of geometry teaching. This was an exploratory study in which a sample of 13 grade 8 mathematics teachers from the rural schools of a district in the Eastern Cape Province in South Africa participated in a project aimed at creating mathematical learning environments through action learning while supporting and promoting the teaching of geometry. The study was qualitative and data was collected using questionnaires, classroom observations and semi-structured interviews with the teachers on a participatory action research conducted in two cycles. Results indicated that 92% of teachers changed their classroom environments by modifying instructional strategies, learner -interactions, and engagements, but could not change how they managed the classrooms due to some factors related to power dynamics andthe education policy. It is recommended that teachers be workshopped on modifying their classroom learning environments while they undergo learning in action on the promotion of teaching and learning geometry in their school defining contexts.     

模型教学对几何教学的意义探究

几何是数学教学的重要组成部分,也是学习的难点。在几何教学中采用模型教学具有重要意义,能将复杂抽象的几何概念具象化,降低学生理解难度,有利于提高教学效率和教学质量,提升学生数学核心素养。文章探究模型教学对几何教学的意义,以促进几何教学的高效发展。     

Project-based geometry learning: Knowledge and attitude of field-dependent/independent cognitive style students

The authors in a convergent parallel mixed method design aimed to investigate whether and how the geometry knowledge and attitude toward geometry of students with field-dependent/independent cognitive style improve differentially within a project-based learning environment. Quantitative data were collected from 97 seventh-grade students before and after the treatment. Repeated measures multivariate analysis of covariance results, controlling for gender and prior mathematics achievement, revealed a statistically significant main effect of time but not cognitive style. Follow-up repeated measures analysis of covariance by controlling the experiment-wise alpha level indicated that field-dependent, field-mixed, and field-independent students achieved a statistically significant mean increase for all measures. The qualitative (classroom observations and interviews with some students) data provided evidence that contextualizing, visualizing, and collaborating opportunities in the project-based learning environment made contributions for mean increase.