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.     

常用软件在《空间解析几何》教学上的实践

本文根据《空间解析几何》的学科特点和教学任务,介绍了常见教学软件在该学科上的应用及注意问题,积极探讨信息技术和《空间解析几何》这一学科的最佳结合形式,达到优化课堂教学,提高学生认知水平、认知能力和数学素养的目的。     

用几何画板解决函数最值问题教学的探讨

利用几何画板,动态演示一类含参数函数的参数运动变化过程,使学生直观理解变化,降低题目本身的内在负荷,从而减轻学生学习时的认知负荷, 促进对参数变化的深入了解.     

平面几何问题证法的探讨

本文通过对近年来全国高中数学联赛中的两道初等几何问题的多种证法(即:纯初等几何法、解析几何法和复数法)的探讨,介绍了通过建立高斯复平面,把复杂的初等几何问题转换成复数计算的思想方法.并通过三种方法的比较,展示复数法的优越性,对中学初等几何教学有一定的参考价值.     

一个重要极限的证明策略

极限理论是数学分析中研究函数的重要工具,是学好高等数学的理论基础之一,而函数极限limx→0 sinx/x=1是高等数学中常用到的一个重要极限。综合运用不同知识,给予证法比较,以期有助于复习巩固所学知识,从而提高教学质量。     

Teachers’ perspectives on “authentic mathematics” and the two-column proof form

We investigate experienced high school geometry teachers’ perspectives on “authentic mathematics” and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it, provided he return to complete the argument later. Prompted by this episode, the teachers in our focus groups revealed two apparently contradictory dispositions regarding the use of the two-column proof form in the classroom. For some, the two-column form is understood to prohibit a move like that shown in the video. But for others, the form is seen as a resource enabling such a move. These contradictory responses are warranted in competing but complementary notions, grounded on the corpus of teacher responses, that teachers hold about the nature of authentic mathematical activity when proving.

浅谈《微分几何》课程的教与学

根据高等教育必须充分体现＂以应用为目的,以必需够用为度＂的原则,结合自己对微分几何课程的教学实践,从教师教和学生学两方面进行探讨,并提出了具体的教学方法及学生的学习方法,通过本文的论述希望能为教师及学生学习微分几何提供一些参考。     

高师院校“解析几何”教改探索

“解析几何”是高师院校数学专业的一门重要且传统的专业基础课程。随着高等教育的改革与发展,解析几何课程的教学方法与模式越来越有必要做出一些调整和改革。文章从教学内容、教学方法、教学评价三个方面对该门课程的教学模式与方法进行了有益的探索。     

《解析几何》CAI软件的开发与应用

《解析几何》多媒体CAI软件适合高等院校的教师、学生及成人教育选用,根据解析几何的教学基本要求确定教学内容,按照正常的教学规律:预习→听课→复习→作业→答疑→小结等作为学生掌握课程内容的学习路线.软件在页面设计、内容导航、学习自查、答疑、以及师生交互、生生交互等方面均充分利用了网络技术的特点,便于学生进行网络学习.软件有多种应用形式:可供教师在多功能教室进行群体教学,显著提高教学质量;可供个体远程上网学习、测试、评估、互动;它是一个丰富的高校师生数学学习资源库.     

高等几何的点线接合命题对初等几何的指导作用

以实例说明高等几何的点线结合命题对初等几何的高观点指导作用和在实践中广泛的应用,表明高等几何不仅在提高观点方面有独特作用,而且在论证方法,思考问题等方面具有独特的巧妙、灵活等特点.