摘要:

For those who see mathematics as an activity and not as a body of knowledge, projects and investigational work are seen as a fundamental part of the study of the subject. After reviewing some of the efforts made over the last twenty years to introduce this kind of work into the curriculum, this paper takes a detailed look at an investigation of ‘number chains’ where each link of the chain is generated in some way by its predecessor (e.g. a new number is formed by taking the sum of the squares of the digits of the preceding number). The paper then goes on to develop a versatile and flexible computer program that can be used to generate data for such chains, leaving the student free to analyse any emerging patterns. The program, written in BASIC on a Commodore PET, is made up of several modules fitted together, and only one or two of the modules need to be changed to produce a new kind of chain.

ISSN:0020-739X    

DOI:10.1080/0020739830140411

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Two classroom examples are presented which allow students the opportunity to evaluate the reality as well as the mathematical accuracy of a problem.

ISSN:0020-739X    

DOI:10.1080/0020739830140412

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

In simple linear regression analysis, measurement error in the explanatory variable causes the ordinary least‐squares estimator of the regression parameter to be biased towards zero.

ISSN:0020-739X    

DOI:10.1080/0020739830140413

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This essay is a call for applying research efforts in mathematics education to perception and understanding of mathematical symbolism. Some related work in reading research is cited along with items of psychological and psychophysical knowledge which might be used as a basis for work in this area. The author reports briefly on a study for algebraic symbolism that indicates promising results for the mathematics education community for efforts aimed in this direction.

ISSN:0020-739X    

DOI:10.1080/0020739830140414

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The availability of sophisticated computer graphics provides an extremely powerful tool for investigating the geometrical aspects of many concepts and methods in mathematics. This is particularly applicable to calculus where much of the underlying material is geometric in nature. When teaching certain topics in calculus, most notably limits of indeterminate forms and logarithmic differentiation, we routinely deal with rather complex functions which are almost impossible to graph accurately by hand. In the present paper, a survey of some of the more interesting and surprising graphs which actually arise are displayed when the corresponding functions are viewed through the eye of the computer.

ISSN:0020-739X    

DOI:10.1080/0020739830140415

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The article treats the subject of function approximations for a computer's built‐in library as a typical topic for a school mathematical laboratory. Following a brief description of how such a laboratory is envisaged as part of mathematical education, approximation by interpolation is discussed at the pre‐calculus level. Special attention is given to the removal of ‘black box’ procedures, and inherent concepts such as quality of approximation, relative error and computational efficiency are examined. Suitable examples are given, demonstrating the actual construction of library functions.

ISSN:0020-739X    

DOI:10.1080/0020739830140416

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739830140417

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The object of this paper is to present an elegant solution to a classical geometric problem by using the geometry of complex numbers.

ISSN:0020-739X    

DOI:10.1080/0020739830140418

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor