摘要:

The accumulation of ideas concerning the teaching of elementary calculus includes recommendations which are still not in widespread use. Research into students’ understanding of calculus suggests that there are many learning difficulties which current teaching methods are not helping students to overcome. The introduction of calculators and microcomputers to school mathematics classes provides us with the illustrative and computational power to practise methods based on practical investigation and intuition which should help to meet the needs of students beginning calculus and lead to greater understanding.

ISSN:0020-739X    

DOI:10.1080/0020739860170601

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This article gives details of the SIGMA project, which was set up as a response to the ‘Cockcroft’ report on secondary mathematics teaching. The project aims in the first instance to produce material to support the use of investigations and practical work in the teaching of mathematics, encouraging discussion and promoting a positive environment in the mathematics classroom.

ISSN:0020-739X    

DOI:10.1080/0020739860170602

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

For the waveform with sharp peaks which cannot be expressed explicitly as a function of the independent variable, the usual graphical methods of Fourier analysis are of little help since the accuracy of results is limited to the first few harmonics only, even if a large number of intervals/ordinates are used. This paper presents a new method for harmonic analysis of such waveforms, which are frequently encountered in various engineering analyses. Unequal, discrete intervals can be chosen on the waveform and the analysis can be performed using limited data. Even then the higher order terms can be obtained with much better accuracy.

ISSN:0020-739X    

DOI:10.1080/0020739860170603

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The standard method of repaying a mortgage is by making payments which remain constant throughout the period of the loan for a given rate of interest. This annuity scheme is analysed as regards to the real cost when inflation is taken into account and the effect that interest rate changes have on the repayments. Other mortgage repayment models are developed which allow the borrower the option of increasing or decreasing the repayments steadily without loss of income to the lender.

ISSN:0020-739X    

DOI:10.1080/0020739860170604

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The factorial structure and reliability of four Fennema‐Sherman mathematics attitude scales were investigated. The scales were administered to 204 college students in five mathematics classes and submitted to factor analysis. The scales were found to be reliable but measured three factors instead of four. The scales appeared to be generalizable to college populations, although the items may need to be reorganized. Additional research is needed to determine their usefulness for counselling or for prediction of success in math classes. Future research should consider the possibility of sex differences, also.

ISSN:0020-739X    

DOI:10.1080/0020739860170605

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Lecturers in mathematics are inclined to accept with resignation that many students will be unable to appreciate any of the finer points associated with convergence of sequences and continuity of functions. They do not, however, question their own method of communication, yet it is that method and its effectiveness which are crucial to the recipients’ mathematical well‐being. This article considers these two areas of conceptual difficulty and concentrates on the problem of the transfer of expertise and understanding. The target group comprises those students for whom the elements of formality are appropriate.

ISSN:0020-739X    

DOI:10.1080/0020739860170606

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Rigidity has shown to exert negative effects on the solution of geometrical problems. A reduction of rigidity was attempted by the instruction of a geometry‐specific heuristic problem solving model, the Geometric Proof Finder (GPF). Four groups of highly rigid students (Gl, G2, F and N) were formed within each of four ninth grade classes. Groups Gl and G2 were taught to solve proof problems by the GPF model, group F had extra practice with the regular mathematics class model, and group N received no instruction. The instruction of the GPF model reduced the rigidity, and had facilitated subsequent learning of school geometry: (1) immediate geometry achievement improved in group Gl and in the combined groups Gl and G2, but no change was observed in groups F and N; (2) at the end of the year, geometry achievement was higher in groups Gl and G2 than in groups F and N; (3) at the end of the year geometry achievement of groups Gl and G2 equalled that of their non‐rigid classmates; (4) the inferior geometry achievement of groups F and N relative to their non‐rigid classmates persisted over the year. These results render the GPF model a powerful instructional means to remedy deficient school geometry learning.

ISSN:0020-739X    

DOI:10.1080/0020739860170607

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The teaching of mathematical modelling is a growing industry. Ten years ago few, if any, institutes of higher education taught mathematical modelling as such. Today it is a subject in its own right and its advocates suggest that it might even have a place in the primary school, such has been its increase in popularity.

ISSN:0020-739X    

DOI:10.1080/0020739860170608

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The ‘common first year’, which operated over eight academic sessions in the Faculty of Applied Science of the University of Nottingham, contained a midsessional examination the results of which were non‐confidential. Some 9293 papers from 1643 students in five departments have been analysed with two aspects in mind, these being the inherent interest such a large amount of ‘real data’ provides, and the effect of classifying results by the ‘grouping’ method practised by arts‐based departments as opposed to the science‐based method of totalling the individual marks.

ISSN:0020-739X    

DOI:10.1080/0020739860170609

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Vectors can basically be defined in four ways: geometrically, analytically, axiomatically, and physically. Authors normally choose the approach best suited to that aspect of vectors they wish to elaborate on. Ambiguous and contradictory statements are common in introductory vector algebra textbooks.

ISSN:0020-739X    

DOI:10.1080/0020739860170610

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor