Showing papers in "International Journal of Mathematical Education in Science and Technology in 1984"
TL;DR: In this article, a few studies reported here examine perceptions of undergraduate students specifically in mathematics courses and compare them with perceptions of undergraduates in general, and compare their perceptions of good teaching with those of the general population.
Abstract: Undergraduate students' perceptions of good teaching, which have been widely investigated, have not dealt specifically with mathematics instruction. A few studies reported here examine perceptions of undergraduate students specifically in mathematics courses and compare them with perceptions of undergraduate students in general.
14 citations
TL;DR: In this paper, it was shown that the Newton-Raphson iteration for nonlinear equations can be considered as a member of a general one-parameter family of second-order methods, and a criterion for choosing the optimal parameter was derived.
Abstract: It is shown that the Newton‐Raphson iteration for nonlinear equations can be considered as a member of a general one‐parameter family of second‐order methods. Variation of the parameter can greatly increase the speed of convergence, and a criterion for choosing the optimal parameter is derived. Finally, a conjecture is proposed on the question of convergence from any initial value.
10 citations
TL;DR: The first months of the MIME Project (Micros In Mathematics Education) at Loughborough University were described in this paper, where early difficulties and setbacks are mentioned as well as the initial successes.
Abstract: † Presented at the Conference on ‘Micros in Education’ held at Loughborough University, 4‐6 April 1984. This paper describes the experiences of the first months of the MIME Project (Micros In Mathematics Education) at Loughborough. The early difficulties and setbacks are mentioned as well as the initial successes. The first part of the paper examines the educational philosophy behind the establishment of the project and details its aims, objectives and scope. Consideration is given to how these aims were put into practice and what revisions to them were necessitated by experience. The second part traces the story of the production of a unit from the author's early ideas, through the program development, to the finished product. Emphasis is given to the way the educational objectives are achieved by careful design of the program. The testing and evaluation of a unit is outlined. The third part reviews the practical programming difficulties that have been encountered; the strengths and weaknesses of the BBC...
9 citations
TL;DR: In this paper, a solution for the first non-trivial case of cubic interpolation is presented for the problem of explicitly determining a set of nodes which is optimal in the sense that it loads to minimal Lebesgue constants.
Abstract: A famous unsolved problem in the theory of polynomial interpolation is that of explicitly determining a set of nodes which is optimal in the sense that it loads to minimal Lebesgue constants. A solution to this problem is presented for the first non‐trivial case of cubic interpolation. This example has proved to be very instructive in numerical analysis courses.
8 citations
TL;DR: In this paper, a fifty variable zero/one integer programming problem is presented, where the fifty variable space in mapped to a non-uniform five dimensional subspace of the real numbers and solved with multi-stage Monte Carlo optimization applied to the subscripts of the five arrays storing the subspace values.
Abstract: A fifty variable zero/one integer programming problem is presented. The fifty variable space in mapped to a non‐uniform five dimensional subspace of the real numbers. The problem is then solved with multi‐stage Monte Carlo optimization applied to the subscripts of the five arrays storing the sub‐space values. The implications of this approach to integer programming in general and zero/one programming in particular are explored.
6 citations
TL;DR: In this paper, the authors present their undergraduate classroom experiences in teaching students how to write and how to use writing as a learning tool in mathematics education and show that there are at least two roles that writing plays: writing about mathematics and writing to learn mathematics.
Abstract: There are at least two roles that writing plays in mathematics education: writing about mathematics and writing to learn mathematics. We present our undergraduate classroom experiences in teaching students how to write and how to use writing as a learning tool.
6 citations
TL;DR: In this article, the authors applied control through promotion to an aspect of the Nigerian educational system and examined the recruitment and promotion rates that can maintain a desired size or structure of a system.
Abstract: Some transition probabilities of a Markov system may lead to undesirable consequences. For example, a ‘reasonable’ promotion rate in a given hierarchical system may lead to growth of certain grades at the expense of others. The size of a system was considered. Recruitment and promotion rates that can maintain a desired size or structure were examined. Control through promotion was applied to an aspect of the Nigerian educational system.
5 citations
TL;DR: The authors examines the causes of poor mathematics teaching and learning in primary and post-primary schools in Nigeria, and recommends measures to overcome them, among the root causes of mathematics phobia in Nigerian schools are the introduction of modern mathematics, the poor system of examination, a lack of effective teaching aids, the Universal Primary Education Scheme (UPE), a shortage of qualified mathematics teachers, the lack of adequate in-service training programmes, lack of proper incentives for mathematics teachers and an inherent fear of mathematics.
Abstract: The paper examines the causes of poor mathematics teaching and learning in primary and post‐primary schools in Nigeria, and recommends measures to overcome them. Among the root causes of mathematics phobia in Nigerian schools are the introduction of modern mathematics, the poor system of examination, a lack of effective teaching aids, the Universal Primary Education Scheme (UPE), a shortage of qualified mathematics teachers, the lack of adequate in‐service training programmes, a lack of proper incentives for mathematics teachers, and an inherent fear of mathematics.
5 citations
TL;DR: In this article, the legitimacy of traditional analysis in school is challenged and consequences for goals and methods of analysis teaching at schools are named, and some initial examples are given, as to how this could be realized with the help of the computer.
Abstract: The computer creates new opportunities for analysis instruction. Some traditional motivations for treating conceptually exacting analysis in school can, however, no longer be maintained without further discussion, for instance: calculations such as finding extreme values or areas can be easily programmed without analysis, and practical applications, as in physics or technology, use discrete methods in computer programs. This results in a crisis: the legitimacy of traditional analysis in school is challenged. This challenge is analysed, consequences for goals and methods of analysis teaching at schools are named, and some initial examples are given, as to how this could be realized with the help of the computer.
5 citations
TL;DR: An attempt has been made to present an overview of the current research work done in the area of microteaching as mentioned in this paper, which includes a list of current research resources for the use of research workers in this area.
Abstract: An attempt has been made to present an overview of the current research work done in the area of ‘Microteaching’. It also incorporates a list of current research resources for the use of research workers in this area. The study has led to some pertinent research questions which need further experimentation and investigation in the field of microteaching for their resolution.
4 citations
TL;DR: In this article, the authors identified seven sources for learning mathematics utilized by undergraduate students and their relative contributions to students' learning were evaluated and found that the three major contributors to students learning, arranged in decreasing order of importance, are: (1) the class textbook; (2) the teacher; and (3) friends and relatives serving as tutors.
Abstract: Seven sources for learning mathematics utilized by undergraduate students are identified and their relative contributions to students' learning are evaluated. Results show that the three major contributors to students' learning, arranged in decreasing order of importance are: (1) the class textbook; (2) the teacher; and (3) friends and relatives serving as tutors. A good teacher serves as the main provider of students' knowledge. If the teacher is poor, the class textbook becomes the primary source for students' learning and the weight of tutoring increases significantly. Students in more advanced courses use more textbook and tutorial help from mathematicians and less help from friends and relatives than do students in the first courses of the calculus sequence.
TL;DR: In this paper, a preliminary classification of the modes of integration within the mathematics curriculum is offered, and it is suggested that more attention be devoted to integration in the teaching of mathematics.
Abstract: An investigation of the modes of integration which can occur within the mathematics curriculum without the loss of the distinctive discipline boundary. It is suggested that more attention be devoted to integration in the teaching of mathematics. As a first step in increasing mathematics educators' awareness of this issue a preliminary classification of the modes of integration within the mathematics curriculum is offered.
TL;DR: In this article, an inventory of the level of understanding of the conditional statement can be informative to professors of mathematics to the point where change in the teaching of the subject might occur.
Abstract: Mathematical implication is misunderstood by a large proportion of students at the college level. An inventory of the level of understanding of the conditional statement can be informative to professors of mathematics to the point where change in the teaching of the subject might occur.
TL;DR: A modified mastery learning method has been adopted to teach practical mathematical skills to a class of up to 90 first year university students taking a degree course in agriculture as discussed by the authors, which showed that students performed moderately better on mathematics material taught using the mastery method compared with their test performance on material taught conventionally.
Abstract: A modified mastery learning method has been adopted to teach practical mathematical skills to a class of up to 90 first year university students taking a degree course in Agriculture. The method is described and a study of the effectiveness of the learning method is included. The study showed that students performed moderately better on mathematics material taught using the mastery method, compared with their test performance on material taught conventionally (x 2 = 4‐95, p<0‐04).
TL;DR: In this paper, the inventory problem for n different commodities with deterministic demand and an overall storage constraint is formulated, and the general solution to the problem is obtained using the method of Lagrange multipliers; however, the computation of the Lagrange multiplier and hence the optimal solution involves numerical techniques, two of which are presented.
Abstract: The inventory problem for n different commodities with deterministic demand and an overall storage constraint is formulated. The general solution to the problem is obtained using the method of Lagrange multipliers; however, the computation of the Lagrange multiplier and hence the optimal solution involves numerical techniques, two of which are presented. A specific problem with n = 9, previously solved by a different technique, is solved here with considerably less computational effort. The general problem is advocated as a vehicle for introducing students in a wide variety of disciplines to elementary methods of numerical analysis and optimization.
TL;DR: A survey of mathematical techniques and theorems which can have relevance at a moderately advanced level to certain classes of wave propagation problems is given in this paper, where some of the techniques are discussed in detail.
Abstract: A survey is made of some mathematical techniques and theorems which can have relevance at a moderately advanced level to certain classes of wave propagation problems.
TL;DR: In this article, a model for the pH of a mixture of a monoprotic acid and its associated salt leads to a cubic equation, which is shown to have real roots, one positive and two negative.
Abstract: A model for the pH of a mixture of a monoprotic acid and its associated salt leads to a cubic equation. This equation is shown to have real roots — one positive and two negative. The exact theory for cubic equations provides a simple expression for the positive root. Due to rounding errors the use of this formula can give poor results, so the use of Newton‐Raphson is considered.
TL;DR: In this paper, a first approximation for a model of student performance in solving linear equations is presented and is followed by an examination, in terms of the model, of one student's attempts to solve a particular equation.
Abstract: The paper presents a first approximation for a model of student performance in solving linear equations. General characteristics of a model are related to the extant research on equation solving. Terminology is denned and used to reconceptualize published research results. The model is presented and is followed by an examination, in terms of the model, of one student's attempts to solve a particular equation. Finally, questions for future research are posed which might lead to the elucidation of the model. The model relates levels of control (i.e., task, method, strategy, process, operation, tactic) to the features (i.e., remote and near) of equations. The control levels are viewed from an information processing perspective; a hierarchal organization is proposed with higher levels influencing activities at lower levels. The model is created to capture the school mathematics approach to solving linear equations, though it is expected that it will generalize to other contexts. † Revision of paper presented ...
TL;DR: It is shown how to expose the laboratory participants to such concepts as error bounds and control, ill‐conditioned algorithms, rates and acceleration of convergence, probabilistic reasoning and computer simulation while their attention is focused upon the computation of π.
Abstract: The article treats the computation of π as a typical subject for a mathematical laboratory. Following a brief description of the integration of such a laboratory into mathematical education, four methods of computing π are discussed at the pre‐calculus and co‐calculus levels. Emphasis is placed upon the mathematical‐educational byproducts accompanying the implementation of these methods. Thus it is shown how to expose the laboratory participants to such concepts as error bounds and control, ill‐conditioned algorithms, rates and acceleration of convergence, probabilistic reasoning and computer simulation while their attention is focused upon the computation of π.
TL;DR: In this article, a computer program based on a technique by Leake is described for ranking athletic teams in situations where the number of teams is large compared to the actual games played.
Abstract: A computer program, based on a technique by Leake [1], is described for ranking athletic teams in situations where the number of teams is large compared to the actual games played. By denoting the teams as nodes on a directed graph and representing the differences in the scores with arcs, rankings are assigned to the teams in such a way so that the inconsistencies around closed loops which one incurs, is minimal. Hence, one finds a least squares solution for the teams' rankings. A simple example is presented to clarify the program.
TL;DR: In this article, a brief survey of mathematical models for the following problems is given: pulsatile blood flows in rigid and elastic tubes, peristaltic flows in tubes and channels, gas flows in lung airways, oxygen diffusion through the living tissues, diffusion in dialysers, fluid flow in renal tubules, lubrication in human joints, and deterministic and stochastic compartment analysis.
Abstract: † Invited Lecture given at the Third International Congress of Mathematics Modelling held at University of Southern California on 29‐31 August 1981. This paper gives a brief survey of some of the mathematical models for the following problems: (i) pulsatile blood flows in rigid and elastic tubes; (ii) blood flows in arteries with stenosis; (iii) peristaltic flows in tubes and channels; (iv) gas flows in lung airways; (v) oxygen diffusion through the living tissues; (vi) diffusion in dialysers; (vii) fluid flow in renal tubules; (viii) lubrication in human joints; and (ix) deterministic and stochastic compartment analysis.
TL;DR: In this article, the solution of linear algebraic equations is treated as a typical subject for a mathematical laboratory and an algorithm for solving linear systems is presented, where no knowledge of matrices, vectors and the underlying theory is assumed.
Abstract: This article treats the solution of linear algebraic equations as a typical subject for a mathematical laboratory. Following a brief description of such a laboratory, equipped with a set of microcomputers, an algorithm for solving linear systems is presented. No knowledge of matrices, vectors and the underlying theory is assumed. Pedagogical considerations guided the choice of material, style and level of presentation, while emphasizing the learning process in a mathematical laboratory environment. Special attention is given to possible loss of accuracy, sensitivity to minor changes in the data, pivoting, pre‐scaling and computational efficiency. Since the laboratory participants are introduced to these concepts without using matrix theory, the laboratory sessions can be carried out even before the study of linear algebra.
TL;DR: The work of the Centre for Advancement of Mathematical Education in Technology (CAMET) with particular reference to the All India Mathematics Education at CAMET (AIMEC) Project over the years 1972•84, designed to change the attitudes of mathematics teachers and to improve the teaching of mathematics in secondary schools in India as discussed by the authors.
Abstract: This paper describes the work of the Centre for Advancement of Mathematical Education in Technology (CAMET) with particular reference to the All‐India Mathematics Education at CAMET (AIMEC) Project over the years 1972‐84, designed to change the attitudes of mathematics teachers and to improve the teaching of mathematics in secondary schools in India. The description includes an outline of the components of the AIMEC programme and the follow‐up activities through workshops arranged in India designed to provide a ‘multiplier effect’ utilizing both teachers trained at CAMET and CAMET staff.
TL;DR: In this paper, the authors describe how, with respect to a basis, tensors of all ranks may be represented by matrices, and propose a new definition of tensors, which enlarges the scope of tensor algebra.
Abstract: The paper describes how, with respect to a basis, tensors of all ranks may be represented by matrices. Such representation has didactic merit, and enlarges the scope of tensor algebra. It leads to a new definition of tensors.
TL;DR: The aim of this paper is to show the necessity of teaching story problems in secondary school as preparation for mathematical modelling, and to call attention to the cognitive method: a method for transforming verbally‐given problems into mathematical form, either during the teaching ofStory problems in school, or while mathematical modelling in science, business, economics or industry is being carried out.
Abstract: The aim of this paper is twofold: to show the necessity of teaching story problems in secondary school as preparation for mathematical modelling; and to call attention to the cognitive method: a method for transforming verbally‐given problems into mathematical form, either during the teaching of story problems in school, or while mathematical modelling in science, business, economics or industry is being carried out. The cognitive method concerns problems which lead to equations, inequalities or functions or their systems; so it concerns a variety of fields, including linear programming. The examples in this paper are in the field of linear programming.
TL;DR: This paper establishes algebraic conditions for the polynomial to have a pair of minima that have a common horizontal tangent, exactly that required by the Maxwell convention of catastrophe theory.
Abstract: Given a polynomial in a single variable, we can find algebraic conditions on the coefficients corresponding to geometrically apparent features of its graph. For example, in elementary catastrophe theory, a bifurcation set in the coefficient space corresponds to a flat point of inflection on the curve. In this paper we establish algebraic conditions for the polynomial to have a pair of minima that have a common horizontal tangent. This condition is exactly that required by the Maxwell convention of catastrophe theory. The first step is a proof of a result giving a factorization of the discriminant of the discriminant of a polynomial. The proof given is a direct algebraic factorization. This result provides a condition for equal critical values. To narrow down to the cases in which the equal values are both minima, a method of using a combination of Sturm sequences has been devised. The paper thus provides complete rigorous algorithm for the determination of an algebraic expression for the Maxwell set of a ...
TL;DR: In this article, the use of a wide range of elementary mathematics in the solution of a significant practical problem is discussed, which is an interesting example of the usefulness of such a broad range of mathematics in solving real-world problems.
Abstract: This is an interesting example of the use of a wide range of elementary mathematics in the solution of a significant practical problem.
TL;DR: In this paper, a class of integral equations with logarithmically singular kernels, which arise in two-dimensional boundary value problems for a potential function which takes a prescribed value on a circular arc, is given.
Abstract: The solution is given to a class of integral equations with logarithmically singular kernels, which arise in two‐dimensional boundary‐value problems for a potential function which takes a prescribed value on a circular arc. The solutions are applied to illustrative examples in electrostatics, inviscid potential flow, and low‐frequency acoustic scattering.
TL;DR: The authors discusses methods that are applicable in the solution by quadratures of linear second-order differential equations with variable coefficients, when applied to equations with constant coefficients, produce an extremely useful method in the teaching of ordinary differential equations.
Abstract: This paper discusses methods that are applicable in the solution by quadratures of linear second‐order differential equations with variable coefficients. These same techniques, when applied to equations with constant coefficients, produce an extremely useful method in the teachingof ordinary differential equations.