a captive audience?

A Captive Audience?Author(s): Sheila RussellSource: Mathematics in School, Vol. 13, No. 1 (Jan., 1984), pp. 31-34Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30213894 .

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A

CAPTIVE

AUDIENCE?

by Sheila Russell, Greenhead Grammar School, Keighley

In the Spring Term of 1982, seconded to the Centre for Studies in Science and Mathematics Education at the University of Leeds, I was able to make a study7 of some sixth form students in schools in Bradford. The study complements the work reported by Giles Dickins and Michael Wood.s My objective was to compare the attitudes of girls and boys to their learning experience in mathematics, and, in particular, to attempt to find explanations for the relatively small number of girls who choose to study mathematics at 'A' level.

National statistics show that far fewer girls than boys continue their studies of mathematics to 'A' level.

The Cockcroft report3 and irecent APU surveys have paid attention to the relatively poor performance of girls at mathematics. Reactions to this problem range from Muriel Eddowe's6 book Humble Pi: The Mathematical Education of Girls which gives practical guidelines to teachers who want to encourage girls, to Tom Beldon's article1 which appears to accept that the observed differences are inevitable. It must be recognised that, when mathematics becomes optional, the difference in mathematical performance between boys and girls becomes even more marked. The DES report Mathematics in the Sixth Form4 states that, in schools surveyed, on average 25 per cent of girls in the sixth form (on 'A' level courses) were studying mathematics, but 47 per cent of the boys included mathematics as an 'A' level subject.

In Bradford Upper Schools in 1981-82 there were 1 165 students on 'A' level courses in first year sixth forms, 604 boys and 561 girls. It was found that 56 per cent of these boys had chosen 'A' level mathematics, while only 22 per

-

-- -

40.-

Boys

Entries 30 Girls (Thousands)

20

10

1974 1975 1976 1977 1978 1979 1980

Fig. 1 Number of entries for 'A' level mathematics for boys and girls separately (1974-80).

cent of the girls had chosen the subject. My study attemp- ted to find some of the reasons for the magnitude of this difference. I was able to obtain responses to a questionnaire from 299 students (128 who were studying mathematics and 171 who were not), and to interview 24 of these students to explore their answers further.

In the questionnaire students were given the opportunity to write at some length about their experiences in learning mathematics. I have analysed these responses in my report, and refer to them here, as well as to the factual data I was able to collect.

Usefulness of Mathematics The students were asked to rate the subjects that they had studied at 'O' level for "usefulness". The following rank orders were produced:

Rank orders for fifth form subjects (The order listed is the overall ranking for both sexes; the numbers refer to the rank for each sex separately.) Usefulness

M F (a) Mathematics 1 3 (b) English 2 1 (c) Biology 3 2 (d) Chemistry 5 4 (e) Art 7 5 (f) Physics 4 9 (g) History 7 6.5 (h) French 9 6.5 (i) Geography 7 8

It is apparent that the girls did not see mathematics as such a useful subject as the boys did: however, examination of their written comments indicates that there are social factors at work. It appears that neither boys nor girls regard the content of the 'O' level mathematics syllabus as particularly useful, but that boys see the qualification in mathematics as more useful for their intended careers, ".. Where- as a boy is usually counselled to work towards a qualification in mathematics as a career essential, this is not always the case with girls."3 At 'A' level 59 out of the 91 boys rated mathematics as their most useful 'A' level subject, but only 9 of the 37 girls studying 'A' level mathematics did so.

A strong resentment of the apparently irrelevant nature of the mathematics studied at 'O' level was expressed, in vivid terms, by many respondents to the questionnaire. This attitude was not confined to those who had chosen subjects other than mathematics for their 'A' level courses, nor was it confined to girls.

Mathematics in School, January 1984 31



"It was not down-to-earth; the topics were almost escapist in their un-relevant aspect to the real outside life."

(boy; Ph,Ch,Geog)*

"Most of the maths we did was irrelevant to everyday living. Who needs trig and logs? Because of this I preferred to study more interesting and relevant subjects - circle theorems I found particularly hard and it got to the point where I despised them.

(girl; Eng,H,Eco)

"Much of the syllabus is apparently useless and cannot be applied to daily life, or even some jobs where one would have thought that maths would have had many practical appli- cations. I thought that if the exam was more practical results would be higher and the people taking the course would reap higher benefits."

(boy; M,F,Eng)

"I can take an interest in maths topics where I can see a practical application and how this work could help people in the real world."

(boy; Ph,M,FM)

There is evidence that some boys had chosen mathematics at 'A' level because it was the expected thing for them to do, and to some extent because of its status with teachers and peers.

"I chose maths because--- it is easy for me--- ---needed in Physics--- ---applies to Chemistry--- --- to impress."

(boy; M,Ph,Ch)

"..necessary boredom to survive before escaping out of the Colditz of school. The most enjoyable employment for me will probably be in a science-related field. Therefore it is essential that I have a good understanding of maths."

(boy; M,FM,Ph,Ch)

"People who don't choose a maths course at 'A' level are considered inferior by many of the staff."

(boy; Eng,Bio,Eco)

"I have never enjoyed maths and why I am taking a maths course at 'A' level is beyond me."

(boy; M,Ch,Bio)

"I was caught, abducted and assaulted with a knotted gown and persuaded very forcibly by my present pure maths teacher to carry on and do 'A' level."

(boy; M,Ph,Ch)

The last boy quoted had obtained a C grade at 'O' level. What he writes is in marked contrast to the comments of these two girls, who had had more success, but less "encouragement" to continue.

"Very surprisingly I managed to cope with the maths exam. I'm sure I couldn't cope with Maths'A' level or be interested in it."

(girl; Eng,F,H)

That girl got an A grade at 'O' level: the next girl got a B grade.

"if I was really good at it I would have considered it." (girl; Bio,Geog,Ch)

Out of the 154 boys who were questioned only seven with an A or B grade at 'O' level did not continue with mathematics. Of the 145 girls there were 22 with A or B

*The two, three or four 'A' level subjects of each student are given.

grades at 'O' level mathematics who chose to study other 'A' levels.

Very few of the girls studying 'A' level mathematics who were questioned expressed intentions of entering any career involving mathematics. If they did, it was almost invariably teaching. On the other hand almost all the boys who had clear career intentions at this stage were aiming for fields of work where mathematics would be used, or considered an essential entry qualification.

The study of 'A' level mathematics does not necessarily increase confidence in its usefulness:

"I am gradually coming to the view that the abstract ideas of mathematics are of no apparent use except to budding professors of higher mathematics"

(boy; M,Ph,Ch)

Enjoyment in Mathematics Some students felt that mathematics had been taught in such a way as to stifle original thinking and had found the subject boring: the girls were then more likely to choose other subjects, but it seems that the boys felt less free to do this.

Perhaps not surprisingly the most articulate comments on this aspect came from students who were studying other 'A' level subjects, because of the freedom of expression they found available to them there.

"The other subjects I have chosen do not condition you as a human robot, these I feel teach you to think while maths teaches you/conditions you to accept and conform to the social system."

(boy; Soc,Eng,Eco)

"Maths students seem narrow-minded as it is really a certain set of rules, learnt then applied, whilst history, for instance, is only 45 per cent fact and is very much based on interpretation, opinion, interest and bias. It is rare to find people having an informal chat about maths, whereas arts are discussed by everyone up to the headmaster."

(boy; H,Eng,Eco)

"The subject never really captivated me, as it was too rigid and allowed no scope for expression or individual creativity. Maths is maths, O10 people could do an essay and they will all be unique, no person can say if it's "right" or "wrong". 10 people may do a maths problem and there is only one answer."

(boy; H,Eng,Geog)

"Whereas in English or Art you adapt yourself to the subject and you can go about it in your own way with no right or wrong conclusions maths is not like that at all."

(girl; Eng,Art,Ger)

and, rather sadly,

"The pressure put on me to be methodical and logical, especially in maths, changed me. Now I am a lot more serious and much quieter as a result. I may have passed maths with a reasonable grade but I had to pay a price."

(boy; M,F,Eng)

All of the students involved in the survey would agree that mathematics is about "getting it right". While it would be foolish to deny that a correct/incorrect assessment is possible for most mathematical problems that we, as teachers, give to pupils, it seemed a pity that very few of the students I interviewed or questioned had been exposed to any other aspect of the subject. The opportunity to investi- gate problems or to discuss methods more fully might have enabled them to see the scope in mathematics for creativity and originality. Some of the girls might have been more attracted to the subject presented in this way. A recent

32 Mathematics in School, January 1984



article by Dorothy Buerk2 asks "must maths be viewed dualistically?" Many people she interviewed felt powerless in the face of mathematics because, as one woman put it, "the wicked mathematician has all the answers in the back of the book." Her article describes a study with five women who "experienced" and discussed mathematical problems as a group, where they were encouraged to make problems meaningful to them. She concludes, "My experience with the women in my study indicates that a more relativistic view of mathematics coupled with a sense of personal responsibility for their own learning, made mathematics more agreeable for them."

The girls in my survey who had chosen to do mathematics at 'A' level stood out as being more able, as evidenced by their 'O' level grades in all subjects, than the boys. They also expressed more enthusiasm for the subject than many of the boys studying mathematics. They were more likely than the boys to agree with the statement: "I really enjoy the challenge of a maths problem".(See Table below.)

The response to the statement was on a five-point scale and a low mean indicates agreement with the statement. The difference between the first two groups was significant at the 1 per cent level.

These quotations from girls studying mathematics express their enjoyment of the subject:

"I enjoyed the maths exam most because mainly I think it is so logical. Ifelt maths was for me because I am an organised person and maths is an organised subject."

(girl; Ch,Bio,M)

"I enjoyed the challenge of problems which Ifound difficult yet overcame, and also enjoyed the attention I got from my Dad whilst getting sums right."

(girl; Eco,Eng,Geog)

"I enjoyed tackling hard problems, solving them and getting the answers right. It made me feel happy and somewhat relieved to conquer something challenging."

(girl; Eng,F,Ger)

This girl explained how she could have enjoyed mathematics more:

"I found the '0' level lessons excessively boring and methodical, and only did the minimum amount. I think there should have been more challenging problems - applying methods to situations so that the process is not as obvious."

(girl; M,Ph,Ch)

"The reason I like maths is that the solution follows logic whilst a lot of other subjects you have to accept facts without there being much logic to it - there is no "parrot-fashion" revision required which adds to its charm."

(girl; M,Ch,Bio)

For girls more than boys it appears that enjoyment of the subject is a prerequisite of studying it at 'A' level.

Teachers Encouragement by their teachers, or the lack of it, was seen as important by many girls in describing their attitude to the subject. This is possibly a stronger influence for girls

than for boys. Only 14 per cent of the boys studying mathematics at 'A' level attributed their success in mathematics to the influence of the teacher, whereas 22 per cent of the girls did. (Boys were more likely to attribute their success to their own ability.)

Some comments about teachers illustrate this:

"I had a very bad teacher who was always impatient of my questions and seemed to consider me lazy and stupid when I did not understand".

(girl; Eng,F,Ger)

"He was a good teacher and he encouraged me to take Maths at 'O' level and helped me gain confidence in my work."

(girl; Art,Ph,Bio)

"I enjoyed maths at Middle School as the teacher was always very helpful and I was never shy or embarrassed to speak up and ask about something I couldn't understand. This wasn't so at Upper School where you felt a fool if you asked things."

(girl; Geog,Bio)

"The teachers gave little help to struggling souls such as myself and I basically regarded them as sadists. More could be done by some teachers to help pupils who find it difficult instead of regarding them as hopeless."

(girl; H,Eng,Eco)

"I was expected by the teacher to maintain standards set by some of the boys who were excellent at maths and should have no worries about their '0' level. Our maths teacher used to say that if a certain group of boys could understand something, all of us should be able to. As one of the 8 girls in our maths class who were all pretty much at the same level I though that he could have gone through things much better."

(girl; F,Eng)

"It was probably the attitude of the teachers which affected my preference. All my English teachers have seemed en- thusiastic and interested in their subject. Most of my maths teachers (bar one) have bored me."

(girl; Eng,Ger,F)

"I got on well with the maths teacher. He explained it well. He encouraged me when I asked about whether I would be able to do maths at 'A' level."

(girl; M,Bio,Ch)

These comments were all written in response to the request to write about "experiences of mathematics" or about "why you preferred to do other subjects". Some of the boys made similar comments about teachers, but it was particularly the girls who gave the impression that often the personality and behaviour of the teacher was a stronger influence than the nature of the subject in affecting their later choices.

Four Girls In these extracts from interviews with four of the girls, all very able, there is a common feature of lack of confidence in their ability in mathematics and a need to prove this ability to themselves. All but one claimed to enjoy mathematics, but the enjoyment was only possible once outside agencies had confirmed their "success"

Statement Group Agree Uncertain Disagree Mean

I really enjoy Boys 'A' level Maths 51% 25% 24% 2.69 the challenge Girls 'A' level Maths 62% 35% 3%0 2.19 of a maths Boys no 'A' level Maths 19% 22% 59% 3.65 problem Girls no 'A' level Maths 22% 19%0 59%0 3.63

Mathematics in School, January 1984 33



Susan, who obtained an A grade at 'O' level mathematics, wants to study medicine, and is taking Biology, Chemistry and Mathematics at 'A' level.

Susan: "In the maths lessons, when we had tests and that, I always wanted to come out top and, it sounds awful, but I always liked that. It used to spur me on even more, especially because I was getting higher marks than all the lads - because a lot of people think maths is for the lads and that used to spur me on because I wanted to do better than them." Joanne also got an A in 'O' level mathematics and wants

to study medicine. She takes Mathematics, Physics and Chemistry at 'A' level.

Joanne: "Maths at '0' level, well it was definitely just learning a method, say for quadratic equations and just applying it over and over again, but then at the end of the exercise there were one or two difficult ones and I liked having to think about it. I preferred that. I liked having to choose a method and Ifeel satisfied once I know I've done it right. I liked to come out top. I'm badly in need of confidence; just little things like that make me feel better," Narendra got a B grade at 'O' level in mathematics. She

wants to study Law, or go into the police force. She very much enjoyed mathematics but could not take it at 'A' level because at her school "you can't mix science and arts". She chose History first for 'A' level and then English and Economics.

Narendra: "I liked it when we did areas under a curve and maximum and minimum values. Most of the class found it hard. I remember going home and getting worried and thinking 'this can't be right'. It seemed too easy. And then when I got to school the answers were right. You feel really pleased, you feel great, as if you were on top of the world. You've got that right and everyone else is finding it difficult. Naturally you want to venture on to harder things." Karen got a B in 'O' level mathematics. She is studying

English, German and French at 'A' level, and did not enjoy mathematics lessons, principally because of the teacher's attitude.

Karen: "I used to be successful at maths, that's what I don't understand. When I was about 11 or 12 1 got 93 per cent in the exam. I did quite well in the third year here. Then in the fourth year - I don't know - I think it was partly the teacher. She sort of assumed we sort of knew it and could grasp it quite easily and didn't explain. She always got cross if I asked. She thought I was just playing dim, whereas in fact I was just dim. Certainly she used to get very impatient with me."

"There's something feminine about a girl being bad at maths, if you talk in terms of stereotype roles. Males are supposed to be logical and good at sciences - in a way, if they're not it makes them seem a bit effeminate. It's all right for a girl to be a bit wet and not good at maths."

Changes It is difficult and perhaps inappropriate to generalise from the comments of the students in my sample. Many of them, because they wrote or talked at length, came across as very strong individuals. Perhaps the tone of criticism implicit in some of the comments quoted is there because for many of them the opportunity to write about their experiences of mathematics provided a cathartic release for suppressed resentment. However I did find elements in common in their responses which perhaps support suggestions that have already been made elsewhere for changes in direction for mathematics teaching.

The lack of enthusiasm for the subject of some boys, even those studying it at 'A' level, often seems related to its apparent irrelevance. "We believe it should be a fundamental principle that no topic should be included (in a course for 11-16

year olds) unless it can be developed sufficiently for it to be applied in ways which the pupils can understand".3

It would be helpful for teachers to be more aware of the relative lack of confidence of girls, although its origin may be beyond their control. "Whatever their level of attainment pupils should not be allowed to experience repeated failure."3 For girls, as Karen said, it is easier to switch off when faced with failure, and to move to subjects where personal endeavour seems more often to be rewarded.

More methods which involve investigation and dis- cussion would enable students to feel the subject is less rigidly "right" or "wrong" in its approach. The Cockcroft report also encourages this. It suggests that pupils should be encouraged to ask questions of the kind "what would happen if... ?" "There should be willingness on the part of the teacher to follow some false trails and not to say at the outset that the trail leads nowhere."3

To some extent, because of career expectations of boys, we have, as mathematics teachers, a "captive audience" for 'A' and 'O' level mathematics. Possibly an attempt to attract more girls to the subject could result in improved attitudes to mathematics from students of both sexes.

References 1. Beldon, T. (1982) "Girls and Their Mathematics", Mathematics Teach-

ing, 101. 2. Buerck, D. (1982) "An experience with some able women who avoid

Mathematics." For the Learning of Mathematics Vol. 3, no. 2. 3. Cockcroft, W. H. (1982) Mathematics Counts, HMSO. 4. DES, (1982), Mathematics in the Sixth Form, HMSO. 5. Dickins, G. and Wood, M. (1983) "A View of Mathematics from the

Fifth Form", Mathematics in School, Vol. 12, no. 2. 6. Eddowes, M. (1983) Humble Pi: The Mathematics Education of Girls,

Longman. 7. Russell, S. (1983) Factors Influencing the Choice of Advanced Level

Mathematics by Boys and Girls, from Centre for Studies in Science and Mathematics Education, University of Leeds.

ASSESSING LOWER-ATTAINERS

As part of the post-Cockcroft programme of research sponsored by the DES, the NFER is undertaking a national review of current practices in secondary schools in assessing lower-attainers in mathematics.

The research team wishes to contact those who have been involved in devel- oping, or are using any forms of assessment of these pupils. Anyone having relevant information is asked to get in touch with

Moira Lavery-Callaghan at the NFER Upton Park Slough, Berks SL1 2DO

34 Mathematics in School, January 1984



a captive audience?

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