Arithmetic for the Mature Student PDF
Preview Arithmetic for the Mature Student
CERTIFICATE OF VALIDATION The results in validating this text will be found on page xiv PERGAMON PROGRAMMED TEXTS Arithmetic for the Mature Student by F. H. GEORGE M.A., Ph. D. F.R.S.S. ( PERGAMON PRESS OXFORD • LONDON • EDINBURGH • NEW YORK SYDNEY • TORONTO • PARIS • BRAUNSCHWEIG Pergamon Press Ltd., Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W.l Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1 Pergamon Press Inc., 44-01 21st Street, Long Island City, New York 11101 Pergamon of Canada Ltd., 6 Adelaide Street East, Toronto, Ontario Pergamon Press (Aust.) Pty. Ltd., 20-22 Margaret Street, Sydney, New South, Wales Pergamon Press S.A.R.L., 24 rue des Ecoles, Paris 5e Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig Copyright © 1966 Pergamon Press Ltd. First edition 1966 Library of Congress Catalog Card No. 66-19075 i This book is sold subject to the condition that it shall not, by way of trade, be lent, resold, hired out, or otherwise disposed of without the publisher's consent, in any form of binding or cover other than that in which it is published. (2865/66) Editor's Preface THIS new series of programmed books represents a major step towards the universal availability of programmed ma- terial. It is hoped ultimately to supply books for every sub- ject that human beings may wish to learn. The text of these programmed books is not arranged in the sequence to which we are accustomed in ordinary books. The reader follows the routing directions on each page, so that in the branching type of programme he will simply se- lect, from among the alternatives offered to him at the foot of the frame, the number of the frame which he believes contains the right answer. This method has been evolved because it has great advantages, from the instructional point of view, over the usual page-to-page sequence, and it will very soon be found to be equally easy to follow. In the linear programme, the reader will generally proceed in the usual way to the frame on the immediately following page, unless he is specifically told to turn to some other frame The programmes are written in a manner which gives the reader the maximum clarity of exposition. He is taken through the subject step by step, and each step is reinforced with a question which must be answered correctly before he can proceed to the next step. It is intended that this new library of programmed books will gradually accumulate texts in every subject, including science, the arts, engineering, mathematics, specialized vii topics such as digital computers, as well as subjects with the broad sweep of architecture and planning. With the development of a large number of such pro- grammed books, it is planned to supply programmed texts that will themselves offer integrating material, and such titles as Philosophy of Science, and Dynamic Planning, will appear in due course. These texts will be closely associated with guide books that can route the student through the sets of various texts, in pursuit of some particular goal. This can be done in much the same way as a student is routed through a single text. A student wishing to achieve, say, A-level in three sub- jects, will be able to find, in the near future, the set of pro- grammed books that he needs to carry him to the required standard; though a person who wants to understand some new branch of engineering, for example, may have to select his books carefully, to compile precisely the information he requires. It is because this library hopes to satisfy people with vastly differing needs, that each volume will be autonomous. Each subject may be repeated in more than one text to give in- struction appropriate to different sorts of requirements, such as different age groups, and research is being carried out on the possibility of catering for other individual differences. It may be that the linear form of programming is more suitable for some subjects, and branching programmes more suitable for others. We shall, however, provide texts in both forms whenever there is a good case for so doing. The first batch of programmed books — due to arrive on the market in 1966 — contains texts on mathematics, science and computers, as well as topics of general interest. These will be followed up by many more programmed books written at every level of complexity, for our scope is no less than the educational needs of the community as a whole. We are confident that they will have a wide appeal, and consequently they will be presented in a flexiback binding that is economical to produce, as well as being highly durable. An important feature of these books is that they are all carefully checked and validated. This means that each text will have been read through by a number of experienced programmers, and tried out on a sample of the people for whom the book is intended. A statement to this effect, as well as a note as to what has been assumed about the rea- der's background, will be found in the Author's Preface. It is considered that this series represents a major ad- vance in publishing, in that it will gradually accumulate in- formation, properly prepared in a specialized way, that may well revolutionize teaching facilities, both in this country and overseas. In conclusion, we offer a word of warning. For the same reasons that it is impossible to achieve agreement among teachers as to the best approach to any particular subject, we do not expect that all our texts, however good, will meet with universal approval. Readers are individuals, with varying backgrounds and often with special needs, and this is why we must have many different treatments of the same subject in the field of programmed instruction. University of Bristol F. H. GEORGE ix Author's Preface IF YOU have used this kind of book before, you will know how the system works. This introduction explains how to use the book and suggests what you should write down and keep notes of as you go along. At the bottom of each section, or frame, you will find either the instruction to turn to another frame, or a series of answers to a question which you have been asked. Beside each answer will be a number. You answer the question, find the answer which agrees with yours, and turn to the frame with the number which is beside the selected answer. For example, if you are offered three answers, numbered 23, 37, 42, and you think that the answer beside 42 is correct, you should turn to 42. You will notice, however, that there are two numbers at the top of each frame. The one at the outside edge is the number of the frame; the other (at the other side on right- hand pages) is the number of the frame from which you have just come. If you choose the wrong answer to the question, you will be told that it is wrong on the frame to which you turn, and be given some more help with the problem. Then it will be up to you to correct your working, then return to the question and choose another answer. In this subject, questions are often quite long and it is not possible to include every possible mistake. If the answer you get to a calculation is not one of those given, it is probable that you have made some elementary slip xi in your arithmetic and you should check your working to find it. You will need a notebook in which to write down impor- tant formulae and principles. Often you will be told to make a note of something, but there is no reason why you should not make other notes if you wish to. You should also copy the questions. To the reader IN THIS book the material does not generally follow seri- ally in the usual way, furthermore each page may contain more than one block of information, or frames as we call them. Each frame contains several numbers. In the top outside corner is the frame number itself: in the top left-hand corner is a number showing the frame which the reader has just left. At the bottom of each frame are instructions for reaching the next frame. These may be simply: Turn to 256. Alternatively, the reader may be given a number of differ- ent frames to choose from, where the actual choice depends upon his answer to the question on that frame. The reader should have paper or a notebook for making notes or doing calculations. To obtain maximum benefit from the programme, calculations should be done before the answer is looked up, and the instructions given must be obeyed. VALIDATION CERTIFICATE The programme was validated in book form with 32 students aged between 16 years and 43 years, whose occupations included machine operators at a shoe factory, a lorry driver, a gardener, charge hands, a housewife and one person who had recently left a secondary modern school. The Pre-test was the same test as that given for the Post-test and consisted of ten questions covering the main topics in the programme. When the students had completed the Pre-test they worked through the programme and made written responses on the standard response form supplied. The students then answered the Post-test. By subtracting the Pre-test scores from the Post-test scores, the measure of learning which had taken place, was obtained. The average time taken to work through the programme was 3 hours 25 minutes. Results. Pre-test: Maximum Score 50% Minimum Score 6% Average Score 23'2% Post-test: Maximum Score 91% Minimum Score 50% Average Score 7&6% Gain: Maximum Score 66% Minimum Score 42% Average Score 53'4%
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