POGIL in the Calculus Classroom

In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a POGIL activity, which includes a model and a learning cycle of specific types of questions. We then turn to a discussion of the particular characteristics of a classroom implementation of a POGIL activity, including facilitation strategies an instructor might use, the importance of specified student roles in groups, and different ways of reporting out. Finally, we provide some preliminary data on student pass rates in non-POGIL and POGIL calculus classrooms in the participating institutions. Throughout the paper, we use examples from student dialogues as groups were working through POGIL activities developed for Calculus I by the authors.     

在微积分中开展探究性学习的现状调查分析

目前,高等师范院校在微积分教学中,实施探究性学习的理论较为薄弱,具体实施中存在诸多问题.可以从教师、学生及客观等3方面进行归因.建议以微积分内容为载体,从内容选择、几何直观、数学思想方法、网络环境等方面开展微积分探究性学习.     

《微积分》课程的有效教学探析

《微积分》是经济数学中的必修课程。要让学生在有限的时间里从没兴趣学、难学变成乐意学、容易学,教师不仅要学会找准教学重点和难点,而且要站在学生的角度上制定灵活的教学方法。     

微积分思想方法研究

对微积分学科的知识结构有深入了解，就能进一步分析微积分的思想方法：微积分是变量数学，是辩证法与常量数学交叉且用形式逻辑表达的一门最早的交叉学科。     

高等数学新教材的改革探索与实践

“高等数学”课程是大学中最重要的基础课之一,因此,该课程教材的改革直接关系到学生的数学素质的培养。介绍了我校与上海交大合编的“高等数学”新教材的改革思路、创意、探索与实践。新教材重视数学思维方法教学,注意微积分与实际问题的联系,并引入了数学软件以训练学生数学应用能力。努力使该课程在大学生的素质和能力的培养方面发挥更大的作用。     

Bringing Engineering Design into High School Science Classrooms: The Heating/Cooling Unit

Infusing engineering design projects in K-12 settings can promote interest and attract a wide range of students to engineering careers. However, the current climate of high-stakes testing and accountability to standards leaves little room to incorporate engineering design into K-12 classrooms. We argue that design-based learning, the combination of scientific inquiry and engineering design, is an approach that can be used to meet both K-12 educators’ and engineering advocates’ goals. This paper describes an 8-week high school curriculum unit, the Heating/Cooling System, in which engineering design is used to teach students central and difficult chemistry concepts such as atomic interactions, reactions, and energy changes in reactions. The goals of the paper are to (1) describe this successful design-based unit, (2) provide guidelines for incorporating design-based learning into other science topics, and (3) provide some evidence of its value for teaching difficult chemistry concepts and increasing interest in engineering careers.     

基于深度学习思维培养的高等数学课堂教学探索

随着科技的进步,特别是近年来以深度学习为代表的算法研究的飞速发展,微积分在深度学习的算法设计以及理论推导过程中的重要性尤为凸显。本文主要研究深度学习中的高等数学基础,并在此基础上提出如何在教学过程中引入深度学习思想,把一些深度学习的学术前沿问题渗透给学生,提高其数学兴趣,培养科研能力。     

数学建模融于微积分教学的探索与实践

当前大学微积分的教学改革，应强调对数学原理和背景的介绍，强调微积分的数学建模方法和计算功能。据此提出了以“启发应用意识，提高应用能力”为宗旨的一整套教学改革方案，并进行了教学改革的实践。结果证明：这一改革方案的实施能卓有成效地提高学生学习积极性、提高学生数学知识应用能力和综合素质。     

数学文化融于微积分教学的实践与思考

数学文化是大学生文化素养的重要组成部分,如何在大学数学教学中融入数学文化尤为重要。微积分作为变量数学中的重要内容,讨论其中蕴含哪些数学文化以及怎样在其教学中渗透数学文化,不仅能帮助学生很好的领悟微积分的基本概念和思想方法,而且有助于培养学生科学、理性的思维方式和交流表达能力,提高整体文化素养。     

微积分学的产生和发展

微积分中的问题至少被几十位科学家探索过,但最杰出的贡献者是牛顿和莱布尼兹,他俩最大的功绩是将两个貌似不相关的问题联系起来,一个是切线问题(微分学的中心问题),一个是求积问题(积分学的中心问题),建立了两者之间的桥梁——"牛顿—莱布尼兹"公式。     

数项级数与反常积分关系的几个问题

探讨了数项级数与反常积分的关系，分别从收敛性、和值的计算与估计、反常积分作为级数的极限等方面提出了若干问题，并进行了较深入的分析与解答．     

微积分中蕴含的数学美

文章以法国数学家庞加莱的"数学美"的内涵为着眼点,揭示微积分中所蕴舍的数学美.     

Assessment of Classroom Environments in Reformed Calculus Education

Research was conducted to determine if current reforms in calculus education are more inclusive of students of different genders, personalities, attributional beliefs, mathematical abilities, and computer attitudes. Two types of calculus reform are examined: a computer-assisted, student-centred and inductive reform based on the Calculus and Maple (C&M) package; and a teacher-only, teacher-centred and deductive reform. Both methods emphasise student participation in the learning and employ collaborative-learning groups mixed by ability and the assessed sociometric measures, but not mixed by gender. The classroom environments of the reform classes were assessed qualitatively using free-form surveys, interviews and classroom observations, and assessed quantitatively using the College and University Classroom Environment Inventory (CUCEI). The classroom environment of reform classes was compared qualitatively to the normal lecture environment. Students assessed the classroom environment as being significantly less favourable than preferred, confirming general dissatisfaction with socio-emotional aspects of university classes, even when adopting modern educational reforms. Differences in the actual and preferred classroom environments were observed in all class sub-divisions (i.e. gender, personality) and across all environment scales of the CUCEI. The research illustrates the psychosocial diversity of reforms for university classrooms and the desirability of evaluating such reforms using a learning environment inventory as well as conventional qualitative measures.     

微积分中数学语言的时序性

微积分作为一门语言，是其它学科（尤其是物理学）解决问题的有力工具，而学生在学习微积分过程中，出现概念的困惑、语言的晦涩难懂、方法上的欠缺，甚至结束了微积分的学习，也有一部分学生不理解微积分的深刻涵义，由于微积分中许多知识隐含的时序性却不易被人注意，其实，在微积分中处处出现“时序”要素的踪影。从另一个侧面来讨论数学语言的时序性在微积分教学和学习中的作用，具体从四个方面：概念中的时序性、定理中的时序性、运算关系间的时序性、方法中的时序性进行分析。     

Bringing Inquiry to the First Two Years of College Mathematics

Abstract

In this editorial, we provide an introduction to the special issue on Inquiry-Based Learning in First and Second Year Courses. We also discuss the essential features of inquiry-based learning and provide a brief overview of the literature and evidence for its effectiveness.     

Partial Fractions via Calculus

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to calculate coefficients, reinforcing calculus connections. For irreducible quadratic factors, the simple derivative formula with complex arithmetic gives the coefficients, helping students gain facility with complex numbers. For higher multiplicity factors, we can use higher derivative formulas taken from the Laurent expansion. We conclude with examples of using the technique in different courses, highlighting precalculus and calculus classes.     

探索微积分教学中的非常规性思维

对大学数学教材中的五道例题的分析常规思维做法做了重新分析,通过非常规思维的做法。解决了计算量大、繁琐、冗长的弊端。在大学数学的课堂教学中,适当摄入非常规思维教学,有利于学生创造性思维的培养。     

外微分在微积分中的应用

引进外积和外微分的概念后,用来解释微积分中的二重积分变量变换式、场论中的格林公式、斯托克斯公式和高斯公式.     

微分在微积分课程中的作用

微分是微积分中的一个基本的重要概念,它是微分学转向积分学的枢纽.其概念和运算在微积分课程中有广泛的应用.如果能从多方面了解这些应用,就会进一步明确微分教学的目的性和重要性,并可使有关内容的教学取得更好的效果.将微分与导数、不定积分、定积分的关系作一定探讨,用以体现微分在微积分课程中的作用.