摘要:

In this work, we examine a questionnaire for prospective secondary school teachers (students in their final year of Mathematics, graduates in Mathematics and graduates in other science subjects). We study the relationship between their own conceptions, beliefs and attitudes and the role the teacher set out in the ‘Ley de Ordenacion General del Sistema Educativo’ (the new law that orders the Spanish educational system) and we include a comparison of different students’ opinions. Our results show that there are no notable differences among these students. However, students’ notions of the role of the teacher contrast sharply with the role proposed in the current educational reforms.

ISSN:0020-739X    

DOI:10.1080/0020739980290301

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Roth's removal theorem is a fundamental result in linear algebra which gives necessary and sufficient conditions for Sylvester's matrix equation to have a solution. Here we show that Roth's theorem is true for lambda matrices and integer matrices thus greatly extending the area of validity of this fundamental result.

ISSN:0020-739X    

DOI:10.1080/0020739980290302

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The current interest in fractals suggests the study of some examples in school geometry courses. The tetrahedron fractal and the octahedron fractal are worth investigating in detail.

ISSN:0020-739X    

DOI:10.1080/0020739980290303

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In this paper the Weber problem withnexisting facilities in the Euclidean plane is considered. The solution pointX*(x*,y*)can be distinct from the existing facilities (isolated point) or coinciding with one of them (coinciding point), so that there aren+ 1 different types of possible solutions. In the paper the space of the weights is partitioned inton +1 regionsRjcorresponding to them, and a graphic construction of theRjis given for the casesn= 3 andn =4.

ISSN:0020-739X    

DOI:10.1080/0020739980290304

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

To say that the teaching of calculus has not changed much since the time of Newton and Liebnitzmaybe overkill; however, as far as this researcher knows, neither at present nor at any time in the past, have there been textbooks that teach calculus as the logical extension of algebra. The intent of this paper is to discard the blinders that have hampered the traditional teaching of calculus and, conceptually, re‐examine some of the intuitive ideas that underlie this subject matter. In particular, this paper examines the various indeterminant forms that arise through the blind application of algebraic operations. Furthermore, to exactly two of these indeterminant forms there exists an interpretation that is one of the fundamental operations that comprise the subject matter normally referred to as ‘calculus’, and to a third there is associated a fundamental number that is the most important constant of calculus.

ISSN:0020-739X    

DOI:10.1080/0020739980290305

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The study addresses the problem of how to present the setting up of definite integrals of real functions like Jbaf(x)dx.In modelling, infinitesimal considerations dating back to the less rigorous times of calculus are still successfully used. On the other hand, students are given a rigorous definition of the definite integral in the calculus course. Different pedagogical solutions to this gap between theory and practice have been presented by teachers. This paper suggests one unified solution based on the error analysis of the termf(x) dx.The starting point here is the interpretation mentioned by some authors that the infinitesimal derivations can be seen as a streamlined or abbreviated version of the use of the rigorous definition of the definite integral. In setting up definite integrals, the termf(x) dxis then an approximation to the quantity to be calculated on the generic subinterval [x,x + dx],where dx is now a positive number, not an infinitesimal. The effect of the corresponding approximation errors in the unabbreviated derivation based on the definition of the definite integral must vanish. This issue is addressed in this paper. General results are given that ensure that the error inf(x)dxis really insignificant guaranteeing thatjbaf(x)dxis the exact value for the quantity to be calculated. The aim of these results is to give rigour and confidence to the student when learning to set up definite integrals.

ISSN:0020-739X    

DOI:10.1080/0020739980290306

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In this paper we study a particular case of the generalized d'Alembert wave equation with two independent variables, a spatial dimensionxand a temporal dimensiont,at a fixed point(x = a, t = b)of the Castelnuovo spacetime, a projective representation of the de Sitter universe that generalized Minkowski spacetime. We find a d'Alembert wave equation associated with this point, and give the complete solution for the special case of an observer at the origin of spacetime coordinates.

ISSN:0020-739X    

DOI:10.1080/0020739980290307

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In recent years much work has been don; on modelling the growth of malignant tumours with a view to predicting their development and optimizing the effect of chemotherapy on their alleviation. One approach has been to treat the tumour as a non‐linear system and the drug treatment as a control strategy. This has led to the use of calculus of variations and optimization techniques to produce optimal and sub‐optimal drug regimes. This paper uses the Gompertz equation as a model of tumour growth and attempts to minimize final tumour size in the presence of drug constraints. The optimization technique is novel in that it uses the genetic algorithm method to devise optimal drug regimes where individual regimes are encoded as ‘chromosomes’ and evolution is simulated in order to improve treatment strategies.

ISSN:0020-739X    

DOI:10.1080/0020739980290308

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A research method consisting of written tests and interviews was used to explore first‐year students’ understanding of fundamental calculus concepts. The analysis of the written and verbal responses to test items revealed significant misconceptions on which students’ mathematical activities were based. This paper describes some of the common errors and misconceptions relating to students’ understanding of the ‘rate of change’ concept.

ISSN:0020-739X    

DOI:10.1080/0020739980290309

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The paper describes a test, covering 155 third‐year undergraduates in 15 different institutions, to examine the extent to which certain core first‐year material is retained and understood. The topics considered explore ideas such as the definition of differentiability, the principle of mathematical induction, understanding of basis and dimension, and perceptions about the real numbers. Also included are a question in mechanics and one on elementary aspects of group theory. As well as recording the students’ results (according to the criteria set out below), the paper includes an; lysis of the answers given by the students to each question and also some of their comments, as recorded on their scripts. Their misconceptions indicate that the foundations laid in the first year, on which their subsequent knowledge is built, is often very flimsy. Data collected include information on the final degree award of most of the test group. It is found that even among those students who subsequently achieved good degrees, the retention of first‐year material is demonstrably weak and suggests some cause for concern among those who teach them.

ISSN:0020-739X    

DOI:10.1080/0020739980290310

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor