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.     

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.     

一元函数微积分的一些应用

该文主要介绍了极限、导数、微分中值定理以及不定积分的一些应用,并得出了相关结论。     

分数阶离散卡尔曼滤波

分数阶微积分在控制系统的应用日益广泛,随着分数阶动态模型的引入,需要求解分数阶估计问题的方法。文章从分数阶线性动态系统模型出发,以概率论为基础,导出分数阶的卡尔曼滤波器,得到其递推模型。     

构建微积分教学的新思路和新方法

我国大学数学教育改革侧重课程体系的建设,而对教学理念、教学方法的改革尚没有全面同步实施。通过改善单一的教学环境、突出实际情境的教学、建立新型教学平台和构建新的评价理念等方面综述了加拿大St.Francis Xavier大学微积分教改实验的特色及我们对构建微积分教学新思路和新方法的建议。