Numeracy Putting the Lock Back?

Numeracy Putting the Lock Back?Author(s): D. R. GreenSource: Mathematics in School, Vol. 5, No. 1 (Jan., 1976), pp. 7-9Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211489 .

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putting the lock back?

by D. R. Green C.A.M.E.T., Loughborough University

Some thoughts on the second conference on "Mathematical Shortcomings at the School/Employment Interface', held at the Shell Centre, Nottingham University, 8-10 July 1975, convened by the Institute of Mathematics and its Applications.

This conference (which Ishall refer to as "Interface II") was a follow-up to that held just one year earlier (July 1974). A very full report of the first conference (referred to as "Interface I") has been published by the I.M.A. (Ref. 1), and a personal account of its proceedings was included in Mathematics in School, Vol. 4 No. 1, (Ref.2).

The 1974 conference grew out of repeated criticisms of school mathematics by those in industry concerned about the standard of numeracy of their recruits. Interface II cannot be properly appreciated without some reference to Interface I and so I make no apology for spending some time in commenting on the earlier conference. I believe that Interface I came as something of a shock to many, like myself, concerned with secondary mathematics. The industrial representatives (mainly from the Engineering Industry) made out a good case for more serious consideration of the arithmetical skills of those pupils, probably stufdying for CSE in mathematics, who are to become Engineering trainees-and many thousands of them are, too! (23,000 in 1974). And this was not to imply that many other areas of employment do not require basic mathematical skills (e.g. nursing), but they were not well represented at that conference. "Modern mathematics", both content and method, was blamed by those from industry for a recent fall in the standard of their en-

trants. There followed a disturbing but perhaps necessary verbal battle between the "industrialists" and the "school teachers". Professor J. V. Armitage performed a small miracle in controlling the debates and extract- ing a measure of agreement, and indeed a Core Syllabus was agreed upon (Ref. 3).

The "shock" which I received at Interface I, and to which I alluded above, stemmed from the realization: (a) that school mathematics syllabuses were not, after all, so entirely divorced from the real life of many of those leaving to enter employment at age sixteen. (b) that I had no idea what mathematics had proved useful to those CSE pupils whom I had taught in previous years, and that I had not been drawn to think of this seriously before. (c) that the industralists looked upon schools as places of "training" and were not satisfied with the teachers' ideas of "general education" (d) that the teachers themselves were apparently hiding in their ignorance behind generalizations and uncon- vincing theory. (I for one felt not a little chastened for so long having accepted the simplistic view that "modern mathematics" is superior to "traditional mathematics".) (e) that those from industry were unsympathetic and ignorant of the problems of school mathematics and wished to treat Education as just another industry amenable to the usual economic analysis.

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All parties at Interface I agreed that another conference was needed the following year, and so we found ourselves assembled at Interface II. It is useful to look again at the reason for meeting. Indeed, what is the problem?

A recent edition of Skill, a paper published by the Engineering Industry Training Board (Ref. 4), can be quoted from as showing how those in one part of industry see it:- (i) "... all kinds of firms say they find that school- leavers can't do the arithmetic which trainees (a) need for training, (b) used to take for granted. The necessary 'remedial maths.', says industry, is an unnecessary extra cost of training time and money." (ii) "The educational world simply does not under- stand why it is necessary to be capable of handling (both) imperial and metric numbers freely." (iii) "... What the customer wants matters to a firm much more than somebody's unauthorized metrication policy". (iv) "Employer interviewing: "How many 64ths in an inch?' Traineeship candidate: 'I don't really know, Sir, but there must be quite a lot'." (v) "a working party ... report highlighted the usual weaknesses ... Decimals. Fractions. Division of whole numbers. Percentages. Ratios. Transposition of formulae." (vi) A previous edition of Skill (Ref. 5) included a letter from a company manager who wrote of the steady decline in school-leaver performance in recruit- ment tests for apprentices:

"... This year I collected all the scraps of paper bearing their rough working, in an attempt to follow the devious workings of their little minds. It was revealing and utterly scandalous to see the depths of their ignorance in simple fraction and decimal matters. Many fail to place the decimal point in vertical line when adding or subtracting. Others do not know their basic tables and evaluate 7x 9 by writing down 9 sevens in a vertical column then adding them up-frequently getting it wrong in the process. Perhaps it would be kinder to say "untutored" rather than "tiny" minds for much of the fault must lie in the teaching.

Question 23 produced .000327, 3-22, 3.142, 2.17 as n to 4 places of decimals. God help us, those came from boys who reached our short list!!! The "rejects" came up with 00.22, 3.1440, 2.2111, .33, -,

1-432, 1 342 etc. etc. Question 26 produced 29, 37, 40, 45, 50, and 80 inches to the metre. Question 26-- SHORT LIST BOYS!-3, 6, 9, 12, 16, 29 or 36 sq ft in

1 sq yd..." The I.M.A. report on Interface I included a section

on "Arithmetic in the Basic Training Workshop". I quote two passages from it to illustrate some of the skills needed but found lacking:

(ii) "Addition and Subtraction

q~ P 3** 2.65 1C . D

11.0

!

Fig. 1 All dimensions in inches. Tolerances: fractional --; decimal + 0.005.

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The most obvious example of the use of addition and subtraction is in dealing with dimensions. Fig 1 shows a simple stepped shaft with imperial dimensions. The shaft has fractional and decimal dimensions since this provides a convenient convention for specifying tolerances with differing degrees of "tightness". It may be necessary to find the distance from C to D during manufacture and this will involve a fraction into decimal conversion so that the appropriate addition/subtraction can be done."

(viii) "Multiplication and Division Many simple work problems involve multiplication and division. For example, if a component is 50mm long including any cutting allowance, how much bar is re- required to make 500 components. Alternatively if material is to be removed from the bar shown in Fig 2 to reduce its diameter from 50mm to 46mm by how much should the cutting tool be advanced? This type of problem causes serious difficulty for some young people who cannot divide by 2. The trainees concerned are generally from the middle CSE range, and we only discover their problem when they start to produce faulty work. In fact a trainee could use any method for the solution of the problem and provided he produced an accurate job in the time allowed we would

Original diameter /1

D

Tool advance -r, d

Finished diameter

Figure 2

not question his arithmetic. The turning tool is mounted upon a tool post which is advanced by means of a calibrated handwheel. It would be possible to calibrate the handwheel so as to avoid the need to divide by 2, but this would cause other problems."

Interface II had a very different atmosphere from that of the first conference. It was clear that all parties had come to realise the complexity of the problem, and to appreciate the needs and difficulties of the "other side". Despite the greater harmony, on reflec- tion I found the progress made disappointing. Mr R L Lindsay, the conference organiser, had made every effort to involve more industries, commerce, the nursing and medical professions, etc... but with little success. There were virtually no school teachers there and the Examination Boards had declined to attend (Ref. 6). These were serious deficiencies for it was diffi- cult to gauge the extent of the problems facing the employers, the syllabus constructors, and the classroom teachers. So what did happen?

A useful introduction was made by Mr J W G Boucher who spoke of the nature of Primary school mathematics and he made it clear that arithmetic is



still a major priority of every teacher. Talk of the abandonment of learning tables is very misleading. There followed two talks, only marginally related to the main debate in my view, but nevertheless of interest. Firstly, Mr R A Parker, who was on a one year schoolmaster fellowship at Bath University, outlined the kinds of mathematical work done by "white collar workers" in a variety of British Engineering firms. His research was concentrated on employees with O Level in Mathematics, or equivalent, as a minimum. Mr Parker emphasised the growing importance of numer- ical methods throughout the industry, and also the elementary nature of much of the mathematics used, suggesting a wastage of talent or training. Secondly, Dr J A Anderson reported that so far (and his research is still at an early stage) he has found no startling significant differences between mathematics under- graduates at Nottingham University who had studied modern mathematics courses at school and those who had followed traditional courses.

A more relevant session was that introduced by Mr N G G Webb. He first reported on the uneven availability of computer facilities and then moved on to discuss the role of the pocket calculator. It soon became clear that many participants doubted that the pocket calculator would be common in most schools for a long time to come, despite some indications to the contrary. Again, many were sceptical of their value, anyway, as an aid to arithmetical competence, mental or practical. Indeed there was talk of cal- culators leading to atrophy of arithmetical skills, al- though this was disputed by some experienced teachers. What I had thought would be an important session petered out. "The lathe operator up to his elbows in oil can't turn to a pocket calculator every time he has to do a simple calculation." End of discussion. How- ever, it would be quite wrong to dismiss so lightly the pocket calculator which is sure to have significance in both society generally and mathematics education.

The next session brought a lively report from Mrs RM Rees on research into the mathematical difficulties of students, being a useful continuation and extension of the work reported in Mathematics in School Vol. 3 No. 1 (Ref. 7).

The last main speaker, Dr A T Rogerson, did much to reassure those delegates who felt that SMP have a "take it or leave it" attitude. The 1974 conference was probably a factor which led to SMP's brochure on Manipulative Skills (Ref. 8) and Dr Rogerson con- firmed that SMP would be publishing in 1976 "drill booklets" containing additional exercises encouraging basic arithmetical and algebraic work to supplement the 1-5 and A-H texts. It was also made clear that the current SMP 7-13 PrOject was taking very seriously the problem of the development of adequate arithmetical skills.

Each talk was followed by a lively discussion session and the conference was rounded off by two further discussion periods aimed at reaching decisions as to further action to be taken. The call for a "Bullock Report" equivalent on Numeracy was mooted. It was also suggested that the O Level Mathematics Examina- tion should include a compulsory arithmetical section (or paper) with a high mark necessary on this part to qualify for an overall pass. In view of the recent grading changes this seems a non-starter but the alternative of a separate "arithmetic" grading, similar to the oral grading in Modern Languages, has some attraction.

The difficulty of legislating for CSE was noted but it was felt that a similar scheme could be encouraged where appropriate. (Some co-operation between schools designing CSE syllabuses and local industry is already taking place (Ref. 4) and may be the most

fruitful approach). Despite valiant efforts by the chair- men of both final discussion sessions, little agreement seemed to be reached as to what we, the conference members, could do. We all recognized the seriousness of the problem but also saw that at least in the short term the answer must lie at the local level. And this is where the individual teacher must come in.

Action Find out for yourself what kind of mathematics is really needed by your school-leavers. Contact the local Industrial Training Officers, and local firms and businesses. Consult your local Mathematics Adviser. Help to organize meetings of local mathematics teachers and employers. Look critically at your mathematics syllabuses and textbooks. Are you preparing your pupils adequately for future employment? Why do you teach the topics you do teach? Try to get hold of entry tests in mathematics used by local commerce and industry and show these to your colleagues and to the pupils and find out why the firms use them and what results they are getting. Reaction Well, are we seeking to put the clock back? We are to- day realizing that not all labelled "modern" must be the best and mathematics education is entering a period of consolidation rather than innovation. It was perhaps appropriate that the clock on the wall of the conference seminar room went resolutely backwards throughout the conference period! This led to some participants wondering how often the clock would be showing the correct time. For example at a correct time of

the clock showed

5.10 6.50 By a happy coincidence this problem can be solved

equally well by arguments of symmetry or by more traditional methods! It would be cynical to say,.as did one conference member, that the clock's behaviour reflected the "progress" we made-negative rather than positive-but it does remain true that little will come from our meeting unless individual schools take up the challenge. Those in industry are most anxious to help so why not meet them half way?

References 1. Mathematical needs of School leavers Entering Employment Symposium Proceedings Series No. 6. The Institute of Mathematics and its Applications, 1974. 2. Who needs arithmetic nowadays? A R Tammadge. Mathematics in School. Vol. 4 No. 1, January 1975. 3. Whatever happened to numeracy? R L Lindsay Times Education Supplement: EXTRA, p. 59. 4 October 1974. 4. SKILL, no. 16, Summer 1975. Published by the Engineering Industry Training Board, 140 Tottenham Court Road, London W1P 9LN. 5. SKILL, No. 15, New Year 1975. 6. The breakdown of membership of the conference was roughly as follows: Teacher.Trainers (Colleges and Universities) and Researchers 10 H.M.I.s and Local Advisers 5 F.E., Technical College and Armed Forces Lecturers 6 University and Polytechnic Lecturers 4 School teachers 2 SMP 1 Engineering Industry Representatives 5 British Petroleum 1 7. An Investigation of some common Mathematical Difficulties experienced by Students. Ruth Rees. Mathematics In School. Vol. 3 No. 1 January 1974. 8. Manipulative Skills in School Mathematics. SMP, 1974.

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Numeracy Putting the Lock Back?