Derivative,maxima and minima in a graphical context

A deeper learning of the properties and applications of the derivative for the study of functions may be achieved when teachers present lessons within a highly graphic context, linking the geometric illustrations to formal proofs. Each concept is better understood and more easily retained when it is presented and explained visually using graphs. In this article, we explore the conditions of necessity or sufficiency of the criteria for determining the maxima and minima of a function. The implications for the teaching of derivatives and functions in undergraduate courses are discussed in light of our analysis of textbooks.     

The role of symbols in mathematical communication: the case of the limit notation

Symbols play crucial roles in advanced mathematical thinking by providing flexibility and reducing cognitive load but they often have a dual nature since they can signify both processes and objects of mathematics. The limit notation reflects such duality and presents challenges for students. This study uses a discursive approach to explore how one instructor and his students think about the limit notation. The findings indicate that the instructor flexibly differentiated between the process and product aspects of limit when using the limit notation. Yet, the distinction remained implicit for the students, who mainly realised limit as a process when using the limit notation. The results of the study suggest that it is important for teachers to unpack the meanings inherent in symbols to enhance mathematical communication in the classrooms.     

基础物理课程在学生科学素质培养中的作用

文章分3个方面（物理学在人才科学素质中的地位,＂大学物理＂和＂大学物理实验＂课程的作用和任务,＂大学物理＂和＂大学物理实验＂课程的教学定位）阐述了作者的观点：在教育部研制＂本科专业类教学质量国家标准＂之际,应该坚持将＂大学物理＂和＂大学物理实验＂课程作为理工科各专业学生必修的两门重要的通识性基础课,并且应该保证基础物理课程拥有相应的学时.     

学生学习《高等数学》困难原因调查及统计分析

为分析学生学习<高等数学>学习困难原因,提高新建本科院校<高等数学>教学效果,我们对一所新建本科院校2005级至2007级全部本科学生进行调查.本研究主要采用问卷调查方式进行,并应用统计学方法,研究学生学习<高等数学>困难原因,探讨解决办法.     

应用型本科大学物理的教学改革新思路

通过对2019年9月中国物理学会物理教育分会学术报告的观摩学习,对目前应用型本科大学物理教学改革进行了反思.文章从实践出发,对教学理念、教学方法、教学内容进行了重新审视,对如何提高学生的自主探究能力进行了讨论,并提出了创办“物理新天地”来加强师生间的沟通,为提高应用型本科大学物理教学质量提供了一种新思路.     

Reaction of bromine with 4,5-dimethyl-1,4-cyclohexadiene-1,2-dicarboxylic acid: a green chemistry puzzle for organic chemistry students

Abstract

Bromination of an alkene is a typical addition reaction covered in an introductory organic chemistry course and laboratory. In this undergraduate organic chemistry laboratory exercise, students studied the bromination of a 4,5-dimethyl-1,4-cyclohexadiene-1,2-dicarboxylic acid. The reaction has an unexpected outcome as bromination yields the aromatic product, 4,5-dimethylphthalic acid. Green chemistry modification involves application of a “bromide/peroxide reaction” with NaBr/H₂O₂ in an acidic medium as an in situ source of bromine. The experiment was carried out as a two-day exercise and the students integrated molecular modeling, interpretation of mass spectra, knowledge of stability of organic compounds, and knowledge of the reaction mechanisms of addition and elimination to explain the experimental outcome.     

形式电荷之辨析与应用

从基础的元素化学和化学结构理论入手,系统性地举例辨析形式电荷的若干相关问题,讨论其与真实电荷、化合价、氧化态和电子对之别,并举例在前沿金属配合物等领域的应用。以期对化学基础教学与推广有助。     

An investigation into the use of microcomputers to teach mathematical problem‐solving skills to 13 year olds

This is an account of an experiment to teach mathematical problem‐solving skills to 13‐year‐old students with the aid of microcomputers. Twenty‐one children worked through six microcomputer program‐generated problem situations in two and a half hours. Nine of the children worked ‘hands on’ with microcomputers. Twelve of the children were class taught, with a single microcomputer used for demonstration purposes. A comparison of pre‐test and post‐test scores on tests indicated that no significant gains in achievement were made by either group. Informal observations suggest a positive affective response. The findings are discussed at length and possible explanations for the lack of achievement are conjectured.     

An investigation into the teaching of mathematics to undergraduate economics students

This article attempts to present a novel application of a method of measuring accuracy for academic success predictors that could be used as a standard. This procedure is known as the receiver operating characteristic (ROC) curve, which comes from statistical decision techniques. The statistical prediction techniques provide predictor models and their goodness-of-fit; in addition, ROC analysis allows to assess the accuracy of the ability to discriminate from success and failures cases of a classifier or predictive model, and so it could be considered complementary to others more commonly used. Thus, the ROC curve is used to compare and interpret the relative contribution of each university entrance factor in the correct classification as success or failure of the academic performance, as well as to establish cut-off scores for admissions and counselling purposes. It is revealed that the ROC analysis allows us to identify the better university entrance factor for each subject in predicting students’ academic success.     

基于演化博弈的大学生诚信考试研究

为研究一些要素对大学生诚信考试问题中主体行为演化的影响,借助演化博弈理论这一前沿研究工具,建立了监考教师与考生交互过程的演化模型,研究了各种情形下监考教师和学生行为交互系统均衡点的存在性和稳定性,并用数值仿真展示了决策参数的不同取值和初始条件的改变对演化结果的影响.研究发现:这些影响二者行为的要素作用的大小会影响均衡点的个数及其稳定性,均衡点的稳定性会在源点、汇点和鞍点之间变化,分析表明大学生从不诚信考试中获得的收益过高,对教师不认真监考监督、处罚不力,都可能使系统的演化向不良状态进化,并最终"锁定"于这一状态,并讨论了系统向良好状态演化和跳出不良"锁定"的条件.分析对大学生考试制度的创新和设计指明了方向.