Coordinating multiple representations of polynomials: What do patterns in students' solution strategies reveal?

We investigate the strategies used by 64 advanced secondary mathematics students to identify whether a given pair of polynomial representations (graphs, tables, or equations) corresponded to the same function on an assessment of coordinating representations. Participants also completed assessments of domain-related knowledge and background skills. Cluster analysis of strategies by representation pair revealed patterns in the participants' strategy use. Two clusters were identifiable on tasks that required matching equations to graphs and graphs to tables. We identified overlap between these two clusters, suggesting that while the representation pair influenced strategy choice, there was also a general distinction between students who used more and less sophisticated strategies. However, students who used more sophisticated coordination strategies were similar to the others on measures of domain-specific knowledge or background skills. We consider implications for future investigations testing interventions to promote coordinating representations.     

不定积分求解方法研究

给出了不定积分的两种求解新方法，结合实例讨论了这些方法在不定积分求解中的可行性，对快速正确求解不定积分有一定意义。     

浅谈一元微积分学在证不等式中的应用

从一元微积分知识应用的角度,给出证不等式的八种方法:极值法、最值法、泰勒公式法、凹凸性法、被积函数放缩法、柯西积分不等式法、辅助函数积分法、上凹函数积分法。     

微积分现代形式的确立与文化意义

微积分是人类智慧的伟大成就之一,是微分学和积分学的合称,概述了微积分这一重要数学思想从萌芽到酝酿,从诞生到发展的过程。微积分给数学注入了旺盛的生命力,它不但成为自然科学和工程技术的基础,它的产生也对其他人文学科也有着重要作用。     

A Path to Designing Inquiry Activities in Mathematics

Abstract

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks for our students. Throughout the paper the use of multiple representations (graphical, numerical, symbolic, and narrative) and the distinction between facts, skills, methods, and conceptual understanding is explained and illustrated with examples. Additionally, we present evidence of student learning through excerpts from student journals and exam analysis.     

浅论青少年天文科普活动的现状与发展对策

天文学是一门古老而又年轻的科学,它不断地吸引着人们去探索,同时,能不断地开拓着人们的视野。开展青少年天文科普活动具有重大的现实意义;针对我国开展青少年天文科普活动之现状和问题,提出在天文科普教育活动中,突出把握好"五性",并以天文观测为核心,开展天文科普教育活动等对策,以实现我国天文科普教育工作的新局面。     

如何利用科技馆资源开展天文科普活动

天文科普活动是科技馆科普教育的重要内容之一.文章首先阐述了开展天文科普活动的重要意义;重点针对如何利用现有场馆资源开展天文科普活动的课题,提出“环境情境化”、“活动主题化”与“团队体系化”的工作思路;并就科技馆开展天文科普活动发展方向进行探讨.     

经典逻辑的表列方法

表列(tableau)方法是一种形式证明的方法,具有良好的通用性,适用于经典逻辑和非经典逻辑的许多系统。表列方法对于各种逻辑系统的元理论的研究,也是一种有力工具。     

Large Lecture Halls: Whiteboards,Not Bored Students

Large lecture halls are a common feature of many undergraduate mathematics programs. However, teaching effectively in a large lecture hall can be challenging. This paper discusses the use of personal whiteboards for students as a way to make large lecture halls a more productive learning environment. I discuss the logistics of using whiteboards, setting up norms, and provide examples of supporting instructional techniques. These techniques are: warmup problems, think-pair-share, group work, and student presentations. To support this exposition, I draw on personal reflections as an instructor and report from a brief student survey on their experiences using the whiteboards.     

中国古代天文档案遗存及其科技文化价值研究

自有文明史以来,中国就设有专门机构或人员进行天象观测与研究,并形成天文档案.它主要有两大类:一是天文观测记录及其所形成的星图星经等;二是历书档案.历代绵延不辍的天学机构既是天文档案的形成者又是主要管理者,其良好的保管制度和各朝天文史志的编研为我们留下了数量可观的天文档案遗存,它可分为两大类:直接遗存与间接遗存.