IMPACT OF EXPLICIT PRESENTATION OF SLOPES IN THREE DIMENSIONS ON STUDENTS’ UNDERSTANDING OF DERIVATIVES IN MULTIVARIABLE CALCULUS

In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of slopes in three dimensions (3D) is seen with the introduction of partial derivatives. The nature of the discussions indicates that authors seem to assume that students are able to naturally extend the concept of a 2D slope to 3D and correspondingly it is not necessary to explicitly present slopes in 3D. This article presents results comparing students that do not explicitly discuss slopes in 3D with students that explicitly discuss slopes in 3D as a precursor to discussing derivatives in 3D. The results indicate that students may, in fact, have significant difficulty extending the concept of a 2D slope to a 3D slope. And that the explicit presentation of slopes in 3D as a precursor to the presentation of derivatives in 3D may significantly improve student comprehension of topics of differentiation in multivariable calculus.     

MIGRATION OF SURPLUS AGRICULTURAL LABOR IN THE PROCESS OF ECONOMIC TRANSITION

ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｓｔｒｕｃｔｕｒｅｏｆｌａｂｏｒｉｎｔｈｅｅｃｏｎｏｍｉｃｓｏｃｉ ｅｔｙｉｓａｋｅｙｉｎｄｉｃａｔｉｏｎｏｆｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｎａｔｉｏｎ ;ａｎｄｂａｓｅｄｏｎｔｈｅｓｉｔｕａｔｉｏｎｏｆＣｈｉｎａ ,ｒｅ ｌａｔｅｓｔｏｔｈｅｍｉｇｒａｔｉｏｎｏｆｉｔｓｈｕｇｅｓｕｒｐｌｕｓａｇｒｉｃｕｌ ｔｕｒａｌｌａｂｏｒ,ｗｈｉｃｈ ,ｂａｓｅｄｏｎａ 1 998ｅｓｔｉｍａｔｅ ,ａｃｃｏｕｎｔｅｄｆｏｒａｔｌｅａｓｔ2 6%ｏｆｉｔｓ4 50ｍｉｌｌｉｏｎｒｕ ｒａｌｌａ…     

THE ROLE OF SPEAKING IN ENGLISH TEACHING

This essay discusses the role of speaking in English teaching and the qualities promoted by spoken in-teractive exercises.     

THE ROLE OF SPEAKING IN ENGLISH TEACHING

This essay discusses the role of speaking in English teaching and the qualities promoted by spoken interactive exercises.     

THE ROLE OF SELF-ACCESS IN LANGUAGE LEARNING

For English language learners who are in the college level, learning knowledge and skills from the teachers, the course books and the classroom activities can not 100 percent satisfy their individual needs or meet their various learning styles. In order to compensate this limit, they need to do self-access after class. In this paper, I will describe the relative background knowledge first and then try to illustrate the role of self-access in one＇s language learning process. Finally I will try to discuss the ways of making self-access more useful and feasible in students＂ practical study. The purpose of the present essay is to emphasize the important part self-access plays in ELT.     

最高级中的IN,OF,AMONG

在带有形容词或副词最高级的句子中,常常有一个表示比较范围的介词短语作状语,用来表达某人或某物在什么范围内最怎么样。常用的介词是IN,OF,AMONG,这三个词在用法上有所不同:一、介词IN后面常接的是表示单位、团体、组织、时间概念等单数名词或代词。HE IS THE BEST STUDENT INOUR CLASS.他是我们班成绩最好的学生。THAT WAS THE MOST EXCITINGMOMENT IN2002.那是2002年最激动人心的时刻。THERE IS A FACTORY NEAR OURSCHOOL.HE IS THE OLDEST IN IT.我们学校附近有一座工厂,他是里面年纪最…     

APPLICATION OF VIRTUAL LAMINATED ELEMENT IN THE TOPOLOGY OPTIMIZATION OF STRUCTURES

ＩＮＴＲＯＤＵＣＴＩＯＮＢｅｎｄｓｏｅａｎｄＫｉｋｕｃｈｉｉｎｉｔｉａｔｅｄｔｈｅｈｏｍｏｇｅｎｉ ｚａｔｉｏｎｍｅｔｈｏｄ (Ｂｅｎｄｓｏｅｅｔａｌ.,1 988)ｆｏｒｃｏｎ ｔｉｎｕｏｕｓｓｔｒｕｃｔｕｒｅｓ.Ａｖｅｒｙｉｍｐｏｒｔａｎｔｓｔｅｐｉｎｔｈｅｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎｉｓｔｈｅｃｈａｎｇｅｆｒｏｍｓｋｅｌｅｔａｌｓｔｒｕｃｔｕｒｅｔｏｃｏｎｔｉｎｕｏｕｓｓｔｒｕｃｔｕｒｅ .Ａｃｃｏｒｄｉｎｇｌｙ ,ｔｏｐｏｌｏｇｙｄｅｓｉｇｎｉｓｃｈａｎｇｅｄｆｒｏｍｄｅｆｉｎｉｎｇｗｈｅｔ…     

DEVELOPMENT AND PROSPECT OF GENERALHOPSITAL ARCHITECTURE IN CHINA

ＤＥＶＥＬＯＰＭＥＮＴＡＮＤＰＲＯＳＰＥＣＴＯＦＧＥＮＥＲＡＬＨＯＰＳＩＴＡＬＡＲＣＨＩＴＥＣＴＵＲＥＩＮＣＨＩＮＡＨｅＺｈｅｎｄｏｎｇ（贺镇东）（ＤｅｐａｒｔｍｅｎｔｏｆＡｒｃｈｉｔｅｃｔｕｒｅ）ＤＥＶＥＬＯＰＭＥＮＴＡＮＤＰＲＯＳＰＥＣＴＯＦＧＥ...     

EVALUATION OF ERCP IN THE DIAGNOSIS OF HEPATOCELLULAR CARCINOMA INVADING BILE DUCTS

ＩＮＴＲＯＤＵＣＴＩＯＮＭｕｃｕｎｎｅｗａｓｔｈｅｆｉｒｓｔｔｏｕｓｅＥＲＣＰ (Ｅｎｄｏ ｓｃｏｐｉｃＲｅｔｒｏｇｒａｄｅＣｈｏｌａｎｇｉｏｐａｎｃｒｅａｔｏｇｒａｐｈｙ)ｉｎｔｈｅｄｉａｇｎｏｓｉｓｏｆｄｉｓｅａｓｅｓｏｆｂｉｌｅｄｕｃｔｓａｎｄｐａｎ ｃｒｅａｓｉｎ 1 968.Ｗｉｔｈｉｍｐｒｏｖｅｍｅｎｔｏｆｅｎｄｏｓｃｏｐｉｃｅｑｕｉｐｍｅｎｔ,ｔｈｅｔｅｃｈｎｉｑｕｅｗａｓｄｅｖｅｌｏｐｅｄｒａｐｉｄ ｌｙ.ＴｈｅｒｅａｒｅｆｅｗｒｅｐｏｒｔｓｉｎｔｈｅｗｏｒｌｄｏｎｔｈｅｕｓｅｏｆＥＲＣＰｆｏ…     

USE OF PARAPHRASE IN ENGLISH TEACHING AND LEARNING

In advanced stage of English language learning,students would meet witmany difficulties in understanding English in the original.Traditionaltranslation method fails to help students to overcome these difficulties,forin translation,they might give a word-for-word version.Translation inmother tongue is able to pour the surface meaning into students'brains,butit is not able to build a bridge from the surface meaning to the implicationin deep structures,and the original language materials can hardly be explo-ited to improve students'command of expression techniches.To avoid the     

UNIVERSITY STUDENTS’ VIEWS OF THE ROLE OF MATHEMATICS IN THEIR FUTURE

We report on an international study about mathematics students’ ideas of how they will use mathematics in their future study and careers. This builds on our previous research into students’ conceptions of mathematics. In this paper, we use data from two groups of students studying mathematics: those who participated in an in-depth interview and those who completed an open-ended questionnaire. We found that their responses could be grouped into four categories: don’t know; procedural skills; conceptual skills; and professional skills. Although some students held clear ideas about the role of mathematics, many were not able to articulate how it would be used in their future. This has implications for their approach to learning and our approach to teaching.     

FORMATION MECHANISM OF MnBi PHASE IN Bi/MnBi EUTECTIC IN SITU COMPOSITE

Bi/MnBi eutectic in situ composite was produced by unidirectional solid-ification technique.The eutectic has a quasi-regular structure,in which the MnBi fi-bre is V-shaped in cross section and rod-like in longitudinal section,the aspect ratio isabout 300.The formation mechanism of this V-shaped MnBi phase was studied bycrystallographic analysis.The conclusion is that the(1120)face is the closest packedone while the(1010)face is the next.     

TRANSIENT SALIENCY EFFECT OF SYNCHRONOUS MACHINE IN THE STUDY OF POWER SYSTEM MODELLING

This paper develops a new mathematical model of electrical power system,in which the transient saliency effect of synchronous machine is taken into account.Thecomputation results show that the new model has higher precision and less computationlabor.So it is suitable for the analysis and controller design of transient power system.     

IN‐SERVICE TRAINING IN GERONTOLOGY: A CASE STUDY OF STATEWIDE NEEDS ASSESSMENT

This report describes the design and conduct of a statewide training needs assessment based on joint state agency and university planning. Sample findings are presented for both the statewide population (N = 736) and various job function groupings. Differences in expressed training needs across job function groups are examined, and strategies for providing effective and efficient training are discussed.     

CONSTRUCTION AND EXPRESSION OF BACTERIORHODOPSIN MUTANT IN HALOBACTERIUM HALOBIUM

ＣＯＮＳＴＲＵＣＴＩＯＮＡＮＤＥＸＰＲＥＳＳＩＯＮＯＦＢＡＣＴＥＲＩＯＲＨＯＤＯＰＳＩＮＭＵＴＡＮＴＩＮＨＡＬＯＢＡＣＴＥＲＩＵＭＨＡＬＯＢＩＵＭＷａｎｇＪｉａｎ（汪俭）；ＭｅｉＱｉ（梅祺）；ＬｕＣｈｕｎｌｉｎ（卢春林）（ＤｅｐａｒｔｍｅｎｔｏｆＢｉ...     

PRESERVICE ELEMENTARY TEACHERS’ GROWTH IN KNOWLEDGE OF MODELS IN A SCIENCE CAPSTONE COURSE

We used four different methods to determine the best means of assessing over 200 preservice elementary teachers’ growth in knowledge of models and their use in K-8 classrooms while participating in the Science Capstone course that focused on the unifying themes of models in science. Each assessment method probed a different aspect of models (from growth in scientific use to need for greater emphasis on the role and use of models) and each used a different method of gathering student responses (Likert-type responses to concept maps). We determined that growth in student knowledge was demonstrated by all instruments, but some instruments were more useful than others for determining preservice elementary teachers’ prior knowledge as well as growth in knowledge of models necessary for K-8 teachers.     

THE USE OF FACULTY RANK IN THE COMMUNITY‐JUNIOR COLLEGE SYSTEM OF FLORIDA

This investigation was undertaken to determine the extent to which academic ranking of faculty exists in the community‐junior college system of Florida and whether the use of academic rank is on the increase or decrease. A questionnaire was submitted to each of Florida's 28 two‐year colleges. Responses were received from all the institutions included in this study, which is a replication of an earlier study done in 1974. Eight of Florida's 28 community‐junior colleges use some form of academic rank. Most of these award the traditional rank of instructor, assistant professor, associate professor, and professor. In general, promotion is determined by degree, advanced graduate credit, experience, effective teaching, professional growth, and service. Six of the eight colleges have adopted a salary schedule related directly to the rank held.