摘要:

This paper describes a highly interactive computer program, ABACUS, which exploits the potential of microcomputers in a mathematical sciences laboratory. In contrast to most educational software which demonstrates very specific points, ABACUS can be used for a variety of applications: it allows one to plot one or more functions on the same set of axes, to differentiate analytically, to compute a definite integral, to search the zeros of a function, and to solve systems of differential equations and to generate Taylor series expansions.

ISSN:0020-739X    

DOI:10.1080/0020739890200201

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Eleven different factors were considered for their influence on calculus aptitude. It was found that past high school as well as current college academic performance significantly relate to calculus aptitude.

ISSN:0020-739X    

DOI:10.1080/0020739890200202

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

I discuss the basis of an arithmetically dominated interdisciplinary project on stamping envelopes, which involves the following skills and knowledge areas: weighing, estimating weights, a little history and geography, economics and politics, marketing, accountancy and information processing, interpreting and consulting tables, deciding between alternatives by balancing cost against speed of delivery, making up face values under various constraints, awareness of knock‐on effects of industrial action, and the planning and budgeting of mail runs. I concentrate on Post Office material, but also provide ample reference to, and analogy from, other public utilities and business perspectives.

ISSN:0020-739X    

DOI:10.1080/0020739890200203

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This article describes a new system of notation that facilitates mathematical operations in base twelve. Some advantages of the base twelve system are briefly summarized, followed by a description of the dyhexal system of notation and its advantages over the conventional Hindu‐Arabic system. It is argued that the dyhexal system provides a superior system of notation as well as a useful educational device for teaching number concepts.

ISSN:0020-739X    

DOI:10.1080/0020739890200204

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

As soon as the horizontal alignment of a road to be constructed has been given, the heights of the road at specified points along its length have to be determined. In our case these heights should be such so that the most economic road profile is created. The problem becomes more complex when the road is ‘built’ on a highly anomalous ground. A mixed‐integer programming model is proposed here, which defines the heights of the road at specified points along its length, and leads to the minimization of the road's construction cost.

ISSN:0020-739X    

DOI:10.1080/0020739890200205

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A remedial programme wherein mathematical notation and structure is taught by practice with the residual syntax inherent in the hand‐held calculator was developed. Remedial topics such as the correct use of parentheses, fractions, roots, powers, radicals, and the functional notation are taught by the evaluation of appropriate expressions on a calculator. The ability to evaluate an expression correctly is directly tied to the recognition and understanding of the symbols of mathematics and their inter‐relationships. These relationships are mirrored by, and implemented on, the calculator. In a drill‐and‐practice format, this remediation was delivered by computer as part of a CAI programme encompassing the three‐course remedial sequence for first‐year mathematics students at the Memorial University of Newfoundland.

ISSN:0020-739X    

DOI:10.1080/0020739890200206

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this paper a report is given on a study comparing Hong Kong students' performance in GCE and Hong Kong A‐level mathematics. An analysis of the data seems to indicate: (1) Hong Kong students achieve higher results in GCE than in Hong Kong A‐level mathematics; and (2) a moderate direct relationship between these scores. The aim of this study is to provide information for polytechnics and universities in the United Kingdom and Hong Kong on how to handle the disparity between these two scores for students' admission. In addition, the author considers that Chinese pupils in Hong Kong on average have better academic achievement in mathematics at advanced level stage (at the age of 18) than their ‘non‐Hong Kong’ student counterparts.

ISSN:0020-739X    

DOI:10.1080/0020739890200207

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper discusses the nature of construction problems and their pedagogical value from a modern point of view. The main observation is that a solution of a construction problem is really a constructive proof of a geometrical existence theorem. We explain this idea in the first four sections, and we show, with detailed examples, how to translate any construction problem into a modern language, without even mentioning rulers and compasses. According to this translation, construction problems are logically more complex than the usual mathematical claims of high school but less complex than the ordinary theorems of analysis. They can be used, therefore, for bridging the gap between the two levels. Another possible use, as an example of a non‐numeric algorithm, is suggested in §5, where a different presentation, this time in the language of computer science, is given. The close connection between the two presentations is then emphasized. Section 7 gives some further operative conclusions, while § 8 discusses the different meanings of the ‘numbers of solutions' concept, as well as the difficult problems connected with it. Finally, the last section suggests practical methods for solving construction problems, which are strongly related to basic ideas of AI, such as, reducing a goal to subgoals and search.

ISSN:0020-739X    

DOI:10.1080/0020739890200208

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

At the sixth‐form level, Newtonian mechanics introduces the ideas of force, motion, energy, etc., and so provides an essential basis for science and engineering. This paper gives the results of a five‐year investigation into the state of health of mechanics as an A‐level discipline. The conclusions are far reaching. (1) Over the past two decades there have been substantial changes in the number and content of A‐level mathematics syllabuses. Mechanics is in decline and in urgent need of regeneration. (2) Of the students entering Leeds University to read mathematics, the majority were found to be inadequately prepared in Newtonian mechanics and the undergraduate course has been modified accordingly. (3) There is reason to suspect that entrants to science and engineering departments are also inadequately prepared. The paper goes on to suggest ways in which mechanics can be revitalized.

ISSN:0020-739X    

DOI:10.1080/0020739890200209

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Much has been written about the arithmetic and geometric series, {nx} and {xn}. Here some of the properties of the sequence of hyperpowers {nx} are studied in the interval (0,1) using the derivatives and the analytical tools such as L'Hopital's rule and Newton's method. The sequence {"x} has two subsequences {Ex} and {°x] depending on whether n is even (E) or odd (O). The former has one relative minimum point (as does the generalized parabola {*£}). The other subsequence on the other hand {°*:] has a number of points of inflection, but not relative minimum. The analytical methods are too cumbersome without the aid of computers and perhaps this is the reason why so little work has been done on these functions in the past. Eighteen different properties are mentioned and they can all be verified by students who are familiar with computers.

ISSN:0020-739X    

DOI:10.1080/0020739890200210

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor