谈谈高等数学教材内容与体系的改革

高等数学(主要指微积分)是每一所大学几乎所有专业都要开设的基础课程,其涉及面之广仅次于外国语课程,可见该课程之重要.从某种意义上说,高等数学课程对于学生后续课程的学习乃至未来一生的作为起着举足轻重的作用.目前,高等教育正处于改革的关键时期,无论是体制、课程设置以及     

概率论中的微积分方法

目前，在我国高等学校所开设的概率论课程中，多效是以微积分知识做基础的，做为微积分课程的一门后续课程——概率论，如何正确、巧妙地运用微积分方法技巧是值得重视的问题，本试图归纳一些同题来说明微积分方法在概率论中有着广泛的用途，同时希望在学习微积分、概率论时，引起注意，从而产生更多、更好的微积分方法为概率论所应用。     

微积分MOOC数据的统计分析研究

MOOC(Massive Open Online Course)即"大规模在线开放课程"已成为国内外互联网在线学习的热点.北京理工大学微积分MOOC课程自2014年在中国大学MOOC网站上线,经过2年的开课,积累了丰富的课程数据.基于微积分MOOC数据,通过统计分析的方法,研究了微积分MOOC参与者的成绩分布,最终成绩与主观作业和客观测验成绩之间的关系,并给出了课程参与者数量变化模型.还结合两个样本班级学生的期中、期末卷面成绩,对比分析了参与微积分MOOC和未参与微积分MOOC学习的学生成绩,结果表明,参加微积分MOOC学习的同学期末较期中取得的进步程度要好于未参加微积分MOOC学习的同学,且这种促进效果对课堂学习微积分有困难的同学尤其明显.     

现代信息技术条件下高等数学课程数字化教学资源建设

高等数学是高等理工科各专业学生最重要的基础课之一.通过该课程的学习,不但可以使学生具备学习后续其他课程所需要的基本数学知识,而且还可以使学生具有理解和运用逻辑关系、研究和领会抽象事物、认识和利用数形规律的初步能力,同时也培养学生的运算能力和综合运用高等数学方法去分析问题、解决问题的能力.因此,高等数学课程的学习关系到学生在整个大学期间的学习质量,高等数学是整个大学教育的重要基础,也是终身教育的重要基础.     

微分概念的历史发展及教学启示

微分的形式化定义是学生学习微分概念的主要困难.微分概念的历史发展表明,形式化的微分定义是微积分严格化的产物,朴素的微分定义更能体现微积分思想,而非标准分析给微分概念带来重生.在微积分学中应用非形式化的方法构建微分概念,以微分为主线(传统教材一般以导数为主线)进行微积分教学可以促进学生学习效果.     

基于多层次模糊评价模型的学习效果评价体系实证研究

课程是培养大学生的科学素养与人文情怀的重要载体,而科学的评价体系在课程建设中发挥着承前启后的关键作用.在建构主义学习理论的指导下,从大学生开展学习活动的视角出发,设计了包含两个一级指标、六个二级指标以及十六个三级指标的大学数学课程学习效果的综合评价体系,然后运用层次分析法和模糊评价法,对北京市某高校的五百多名大学生进行了数学课程学习效果的实证研究.研究发现,丰富的学习情景有助于学生全面掌握数学的基础知识,跨学科教学才能真正培养学生的核心能力.     

中国科大微积分课程分层教学的设计与实践

报告了中国科大对微积分课程所作的分层教学设计与实践,利用新生入学考试的数学成绩,高分数段的学生选拔进入英才班,实施上不封顶的英才教学;中间段的学生学习普通微积分课程;对于低分数段的学生,设计了一套教学目标保持不变、进度相对缓慢、进程可以自由选择的基础微积分课程.     

探讨数学分析课程的教学改革和教学质量的提高

数学分析课程是数学类专业学生进校后首先学习的重要的基础课,它的理论、计算方法以及分析数学思想的形成,对后续课程产生了深远的影响.为了提高课程的教学质量,作者通过多年的思考和实践,提出教改的四方面:一把握当代大学生的新特点、新变化,提倡"快乐"的教学;二提高数分教学艺术;三综合运用各种教学方法和手段,不断提高教学效果;四数分课程学习效果考核的多样化.     

算术观点下的林氏微积分与传统教科书中微积分比较分析

微积分是大学里普及程度非常高的一门学科,数学系学生、理工科学生、文科学生都需要学习,传统教科书中的微积分复杂度较高,使很多学生望而生畏.而算术观点下的林氏微积分复杂度保持在乘法表的水平,大大降低了微积分的门槛,且直击微积分的核心:牛顿—莱布尼茨公式.以《数学分析》中的微积分部分为例,与林群的微积分做对比,以期为大学微积分的教学改革提供思考.     

几道关于连续函数介值性质的应用题

通过与日常生活相关的几个实际问题,说明闭区间上连续函数介值性质的应用.借此很容易将数学建模思想渗透到微积分教学中去,可以激发学生学习微积分的兴趣,培养学生的应用能力.     

An incentivized early remediation program in Calculus I

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea that a lack of prerequisite knowledge is a significant hurdle for students, but also that participation in the remediation program is correlated with student success. In addition, the program allows for the very early identification of students at high risk of failing. The program is easy to implement, and it would be adaptable to a variety of other courses for which prerequisite knowledge is essential for success including science courses, engineering courses and other mathematics courses.     

Improving student learning in calculus through applications

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.     

学生学习成绩相关性的研究

从大学生学习成绩出发,应用广义线性回归模型研究了学生学年间成绩的相关性,揭示了大学一年级,尤其是一年级的二学期是影响学生后期学习的关键阶段.进一步应用聚类分析,得到学生成绩在大学一年级就已经埋下了两极分化的隐患,应用判别分析得出了两极分化的关键课程.该结论为教育教学和学生管理提供决策依据.     

Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

The Effects of Non‐CAS Graphing Calculators on Student Achievement and Attitude Levels in Mathematics: A Meta‐Analysis

Forty‐two studies comparing students with access to graphing calculators during instruction to students who did not have access to graphing calculators during instruction are the subject of this meta‐analysis. The results on the achievement and attitude levels of students are presented. The studies evaluated cover middle and high school mathematics courses, as well as college courses through first semester calculus. When calculators were part of instruction but not testing, students' benefited from using calculators while developing the skills necessary to understand mathematics concepts. When calculators were included in testing and instruction, the procedural, conceptual, and overall achievement skills of students improved.     

The impact of taking a college pre-calculus course on students’ college calculus performance

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.     

Interpreting a graph and constructing its derivative graph: stability and change in students’ conceptions

This present study investigated engineering students’ conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the incorporation of computers for the purposes of seeing the power of visualization, investigating worked examples given in steps and solving various questions related to the worked examples, assisting conceptual understanding, and/or providing feedback besides lectures in the classroom. Students were tested before and after being exposed to instruction on differentiation and integration by a diagnostic test measuring their understanding of major aspects of calculus. Follow-up interviews were conducted with 18 students. Analyses of the results revealed that A-level student's performance was improving more than non-A-level students, particularly in computer groups. The analyses of the students’ written and oral responses in all groups indicated that prototypes, poor understanding of the notion of limit, confusion between the process and the product, and difficulties in using graphical information to give meaning to symbolic representation account for the errors and the misconceptions identified.     

Individualized additional instruction for calculus

College students enrolling in the calculus sequence have a wide variance in their preparation and abilities, yet they are usually taught from the same lecture. We describe another pedagogical model of Individualized Additional Instruction (IAI) that assesses each student frequently and prescribes further instruction and homework based on the student's performance. Our study compares two calculus classes, one taught with mandatory remedial IAI and the other without. The class with mandatory remedial IAI did significantly better on comprehensive multiple-choice exams, participated more frequently in classroom discussion and showed greater interest in theorem-proving and other advanced topics.     

The generation and use of graphical examples in calculus classrooms: The case of the mean value theorem

We analyzed video data of five instructors teaching the Mean Value Theorem (MVT) in a first-semester calculus course as part of a broader project investigating how active learning strategies were being implemented and supported in calculus courses. We sought to identify the ways examples of functions that did or did not satisfy the conclusion of MVT were generated and used in instruction. Using thematic analysis, we identified four themes that serve as characterizations of examples, which then allowed for the analysis of trends and patterns. We propose that attention to the generation and use of examples serves as one lens for considering how students can be engaged in the mathematical activity of the classroom, with implications for learning. This work contributes to an evolving notion of what is entailed in students’ active learning of mathematics and the role of the instructor in facilitating active learning opportunities.