摘要:

The paper discusses some of the factors which have to be considered in constructing an adequate description of the understanding of mathematics. It examines three models of understanding which have appeared during the last three years. The evolution of the concept of understanding mathematics is traced from early ‘all‐or‐none’ dichotomies to models based on a classification of mathematical understanding into multiple categories. While it is recognized that the ultimate test for a model of understanding is its usefulness in the classroom, it is suggested that categorizations based directly on educational practice are fraught with conceptual difficulties. Reference is made in this connection to the role of language and of mathematical concepts; limitations of the ‘levels’ approach are indicated. Understanding is characterized as a state of cognition; the distinction between understanding and knowledge is emphasized.

ISSN:0020-739X    

DOI:10.1080/0020739800110101

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Two possible designs are described for the estimation of the size of populations using the capture‐recapture technique. It is shown that the principle of maximum likelihood applied to one design leads to a biased estimator with infinite expectation and variance, but that applied to the other design it leads to an unbiased estimator; a value for the variance is given in this case. A simulation is described which can be used in the classroom to demonstrate the contrast between the two designs.

ISSN:0020-739X    

DOI:10.1080/0020739800110102

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The paper demonstrates a graphic approach to different numeric problems of the calculus with the aid of a computer with graphic output and a function‐plotting program.

ISSN:0020-739X    

DOI:10.1080/0020739800110103

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The distribution of the number of customers served during a busy period for an M/M/1 queue is derived. The method used is a simple one, and although it cannot claim to be as powerful as many of the other techniques to be found in the literature for dealing with this problem, it does have the virtue of using only elementary ideas and concepts, and so allows this interesting topic to be introduced to undergraduates.

ISSN:0020-739X    

DOI:10.1080/0020739800110104

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Mathematics is often referred to as a language. This paper attempts to explore the implied meanings of such statements and to outline a rationale for utilizing the language‐structure of mathematics in mathematics instruction.

ISSN:0020-739X    

DOI:10.1080/0020739800110105

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Any course in numerical mathematics must set out to help the student to interpret the numerical results obtained from calculations. The characteristics of round‐off error, stability and ill‐conditioning of the results must be considered before the results are accepted. Although the effects of the above can be shown in theory, it is more difficult to recognize them in practice, and it is considered that graphical presentation of these effects can assist the student greatly.

ISSN:0020-739X    

DOI:10.1080/0020739800110106

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The purpose of this study was to test the relative efficacy of two modes of instruction for promoting learning and retention of selected geometrical concepts. The subjects in this study consisted of 119 students from three seventh and two eighth grade mathematics classes in Pittsburgh, Pennsylvania. The students in each class were randomly assigned by ability, to either the individualized group or the traditional group. The experiment consisted of five 45‐minute periods per week for approximately six weeks. A 53‐item achievement test was administered to each group at the conclusion of the experiment. The retention test (55 items) was administered three weeks after the completion of the experiment. The results of the study did not indicate a significant effect on learning or retention due to the mode of instruction. There was however a slight trend favouring the individualized group.

ISSN:0020-739X    

DOI:10.1080/0020739800110107

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Concern about certain of the difficulties encountered by undergraduate students in learning mathematics is discussed. Three attitudes of present‐day undergraduates to study are examined. These attitudes, which contribute substantially to the difficulties encountered by students, are:arabican expectation to assimilate new ideas without mental effort;arabica reluctance to devote time to study and to practice;arabicthe lack of persistence necessary to tackle exercises of a non‐trivial nature.

ISSN:0020-739X    

DOI:10.1080/0020739800110108

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Some easily stated numerical and arithmetic problems are described to be explored experimentally with a computer or programmable calculator. The experimental results might induce theoretically inclined students to do some number‐theoretic research with analytic tools and methods well within most undergraduate programmes in mathematics

ISSN:0020-739X    

DOI:10.1080/0020739800110109

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

This paper surveys various approaches of mathematical relaxation in the solution of decision‐making problems. A particular mathematical programming problem is considered in detail and it is demonstrated how a relaxed formulation provides a convenient framework for problem formulation

ISSN:0020-739X    

DOI:10.1080/0020739800110110

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor