“I would rather die”: attitudes of 16-year-olds towards their future participation in
mathematics
Margaret Browna, Peter Browna, and Tamara Bibbyb
Department of Education and Professional Studies, King’s College Londona; Institute of
Education, University of Londonb
Improving the numbers of students in England continuing with specialist mathematics
after it ceases to be compulsory at age 16 is part of government policy. To investigate
students’ reasons for their expected future participation or non-participation in
mathematics, both open and closed questionnaire responses were analysed from
almost 2000 students in 17 schools in England and Wales. The analysis supports
findings from previous studies in demonstrating that perceived difficulty and lack of
confidence are the major reasons for students not continuing with mathematics, and
that disaffection and perceived lack of relevance are also important factors. The study
shows a clear relation between these factors and both predicted GCSE grades and
gender. School participation rates varied, even after correcting for differences in
predicted grade distribution, with the degree of enjoyment best differentiating schools
with high and low participation rates. Building on these results, ways of improving
participation rates are discussed.
Policy background
The Roberts (2002) report SET for Success highlighted a serious shortage in the UK
economy of people qualified in science, technology, engineering and mathematics
(STEM), with the rising demand outstripping a declining supply. For example entries for
General Certificate of Education Advanced (A-level) mathematics examinations at age
18, where mathematics is studied normally as one of only 3 or 4 specialist subjects, fell
by 28% between 1982 and 2003. By the end of this period only 7% of the age group were
studying this course (Matthews and Pepper 2005). Some of the decline followed the
introduction of Curriculum 2000 which split the A-level course into modules at
Advanced Supplementary (AS-level), usually taken at age 17, after which some students
continue no further, and A2-level, usually taken at age 18. Despite signs of upturn in
2005 and 2006, the number of mathematics A-level students still remains below the 2001
figure.
The attention paid by Roberts to the key role of mathematics, despite the subject
being on the edge of his brief, was soon followed up by the Smith Report Making
Mathematics Count (2004). Smith stressed the national need for more young people to
study mathematics for longer, and suggested that this could be achieved by wider
recognition of the importance of mathematics, improved teacher supply and professional
development for teachers, and changes in the curriculum and qualifications pathways so
as to provide appropriate progression for all students.
The response to the Roberts and Smith reports was a government paper issued as part
of the Budget papers, Science and innovation investment framework 2004-2014: next
steps (Her Majesty’s Treasury 2006), which expressed concern about the harmful effect
of these trends on the future skills within the workforce, and set targets for increasing the
A-level passes in mathematics, physics and chemistry; the target for mathematics is a
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21% increase. This is being accompanied by additional investment in STEM education,
managed by a new committee structure.
The long-term trend of falling participation also affects other developed countries
(Holton et al. 2001), although most countries expect all students to continue with some
study of mathematics until they leave school.
Students’ choice of subjects has been shown to be significantly influenced by their
attitudes to the subjects and performance in them (Dick and Rallis 1991, Johnston 1994).
This paper seeks to make a contribution to the discussion on students’ attitudes towards
mathematics at age 16 and their reasons for deciding not to continue studying it for
external examinations at AS-level (age 17) or A2-level (age 18).
Research background
Osborne et al. (1997), in a research review of participation in STEM subjects, report that
the main reasons why mathematics is not selected is because it is perceived to be ‘hard’,
‘boring’ and ‘useless’. Relevant literature is thus summarised below under separate
headings which broadly address these three characteristics, leading onto a consideration
of gender effects.
Difficulty, self-efficacy and identity
Several studies report that A-level mathematics is perceived to be more difficult
than other subjects (DFE 1994, Ofsted 1994, Landau 1994, Sharp et al. 1996).
Matthews and Pepper (2005), in the interim report of a recent QCA-funded
research project on participation in AS- and A-level mathematics, suggested that
the major cause of poor take-up is that students do not feel that they are good
enough to continue, reflecting a perception of ‘elitism’ which is also reported by
Nardi and Steward (2003). Matthews and Pepper demonstrate that A-level
mathematics students do indeed form ‘a clever core’, with higher mean overall
grades in General Certificate in Secondary Education (GCSE) examinations at age
16 compared than other major subjects. They also report considerable differences
between schools in the proportion of students that continued with mathematics,
partially reflecting the differences in the range of pupils that were encouraged to
participate by the schools – some schools only accepted students with A* or A
grades or from ‘the top set’, whereas others welcomed students with B and C
grades,.
The same study notes that the perception of mathematics as ‘difficult’ was primarily
created by information gathered from older students, from teachers (some of whom had
talked about a ‘big jump’ in difficulty between GCSE and AS-level), and from observing
the school’s past A-level results. In addition to social comparison with peers, Kyriacou
and Goulding (2006) showed that in key influences in identity formation in relation to
mathematics included views about mathematics held by the student’s family and friends,
interests/ strengths in related fields, and social expectations and roles. Mendick (2006)
also construes choice in terms of socially grounded processes of identity construction.
Some students were reported by Matthews and Pepper (2005) as having low
confidence in the subject even when they had achieved a high grade in GCSE
mathematics. This is part of a larger problem with of students’ low ‘self-efficacy’ in
mathematics, which has been highlighted by other researchers (e.g. Hannula 2002,
Pietsch et al. 2003, Kyriacou and Goulding 2006).
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Disaffection
The idea of affective assessment, as set out by Williams and Ivey (2001), suggests
that once a student adopts a certain stance towards a subject this then becomes the
basis for future action, which in turn can then reinforce the stance taken, forming
either a positive or negative loop. Thus, a student that decides mathematics does
not interest them may disengage from the subject and make less effort, which will
lead to lower achievement and satisfaction. Students can then attribute apparently
permanent characteristics either to themselves (‘I am not interested in maths’) or
to the subject (‘maths is boring’). Girls are especially likely to form a fatalistic
view of their lack of ability in mathematics as innate (Dweck 1986, 2000).
Negative attitudes have been described in detail at Key Stage 3 (age 11-14) by Nardi
and Steward (2003) who found that mathematics was perceived as tedious, with too much
individual work and rote learning, elitist, and de-personalised (T.I.R.E.D.). This was
attributed to the concentration on ‘teaching to the test’ and not enough emphasis on
engaging and inspiring students. They identify a “mystification through reduction”(p.357)
effect in which teachers, in an attempt to make mathematics simpler, reduce mathematics
to a list of rules and thereby fail to enhance a proper understanding of the underlying
concepts. Teaching methods were also criticised in other participation studies (Quilter
and Harper 1988, Landau 1994, Matthews and Pepper 2005).
Nardi and Steward also report lack of affective dimension as a perceived
characteristic (e.g. in mathematics there are “no positive or negative emotions, you just
have to do it. It’s like a null period.”) (p. 361). With an age 16 group, Matthews and
Pepper (2005) note that the perception that mathematics is ‘dull’ is expressed by highattaining as well as low attaining students.
Utility
Tebbutt (1993) found that sixth-formers believed mathematics A-level to be less useful
for their careers than other science subjects, as well as more traditional, narrow, and less
interesting. Quilter and Harper (1988) found that one of the two most important reasons
for students failing to continue with mathematics was it’s irrelevance to the ‘real world’.
Matthews and Pepper (2005) similarly report that many pupils could not see how
mathematics A-level would be useful in later life.
Gender effects
There has been a persistent gender gap in terms of mathematics participation in England,
with males making up 62% of the 2004 A-level entry. This gap exists despite the now
very similar achievement of boys and girls in mathematics GCSE examinations at age 16.
Boys hold higher academic self-concepts than girls in relation to mathematics
(Kyriacou and Goulding 2006, Elwood and Comber 1996, Woodrow 1996), which leads
them to be more likely to specialise (Armstrong 1985). They are often over-represented
in top sets with some indication that boys enjoy the masculine atmosphere of competition
that tends to exist in these sets (Landau 1994, Boaler 1997, Bartholomew 2000). Female
students tend to suffer more from low confidence and mathematics related anxiety, and to
hold a more negative overall view (Hannula 2002).
Boys tend to continue with mathematics more for utility reasons, such as for their
career or the usefulness of mathematics, while girls more often cited reasons to do with
comfort, such as enjoying the subject and coping well with it (Matthews and Pepper
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2005, Williamson 2004). Mendick (2006) explained the gender differences in
participation as due to mathematics being identified with characteristics of masculinity.
Methods
The data for the research was taken from a Qualifications and Curriculum Authority
(QCA) study evaluating the 2005 pilot and trial of new two-tier GCSE maths
examinations (Stobart, Bibby and Goldstein 2005). The study involved an eight-page
questionnaire given to students in the period after they had taken their GCSE
examinations, but before they had received the results.
This research is based on answers given by the students to a small part of the
questionnaire, which was not analysed as part of the main study. The relevant questions
concerned:
1) Gender and predicted grade at GCSE
2) The attitude words students associated most with mathematics. They could either ring
one or more of the ten descriptive words that had been provided in the questionnaire
(enjoy, like, hate, excited, bored, frightened, anxious, worried, difficult, easy) or
insert their own word(s).
3) Whether students were continuing their studies at AS-level, and if so which subjects
they were intending to take.
4) Whether they had considered continuing with mathematics.
5) The reasons for them considering or not considering continuing with mathematics.
This was an open question so students could provide any reason(s) they wished.
The sample consisted of 1997 students from 17 schools (although for the attitude words
the sample is only the 427 students from 5 schools who had the amended version).
The choice of schools was dictated by the awarding bodies involved in the QCA
study. Although these are therefore not a representative sample, they did cover a
geographical spread across England and Wales and a wide size range (106 – 410 pupils in
the cohort). There was one single sex school (boys’) and two faith schools. (The boys’
school is excluded from analysis of gender differences.)
The percentage of pupils in the 14 English schools achieving five or more A*-Cs
ranged between 30 – 85% with a mean of 65%, compares to a national English average of
57%, indicating that the sample of schools is significantly above average in terms of
overall attainment. This bias was also evident when the distribution of predicted grades in
mathematics was compared with national GCSE results. (Comparable data was not
available for the three Welsh schools.)
Predicted GCSE grades were used in preference to the awarded grades, since they
would have been available to students while they were choosing AS-level subjects. We
do not have any analysis of the accuracy of the predicted grades.
We undertook the analysis in the following stages:
1) For attitude, we found the proportion of students that had ringed or written in each
descriptive word/ phrase. Some of these words/ phrases were then grouped together
on a semantic basis (e.g.‘worried’ and ‘anxious’).
2) Choices of subjects for AS-level were considered only in terms of whether or not
students included mathematics..
3) Proportions of students who had considered and not considered taking mathematics
were found and the reasons given for this decision were classified into separate
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groups, again on semantic grounds. The proportion providing each reason was
calculated.
4) All results were re-analysed by gender, by school and by predicted grade.
In seeking schools where a high proportion of students were intending to take AS-level
mathematics we realised that the effect of the attainment of the students within each
school had to be removed. For attitude words, this was done in the following manner:
1) We compared the proportions that ringed each attitude word in each grade in each
school to the proportion in the same grade across all schools.
2) We then calculated an overall school index for each attitude by taking an average of
these deviations across the grade groups, weighted for the proportion of students that
were predicted at each grade within each school.
3) We also further combined some of the attitude words, partly on the basis of
similarities in behaviour across schools and partially on a consideration of semantics.
When combining the words, different weightings were assigned depending on the
strength and direction of the attitude that they indicated, e.g. on the ‘like’ scale, ‘like’
was awarded +1, ‘dislike’ if supplied was awarded -1, and ‘hate’, -2 . For each
school, we therefore had four final indices that indicated how positive or negative
student attitudes were towards mathematics using the constructs ‘like’, ‘enjoy’,
‘anxious’ and ‘easy’; having removed the effect of the predicted attainment of
students in mathematics within each school. The same process was then repeated for
the proportions of students considering and intending to study mathematics at ASlevel.
4) We then correlated indices across schools (using the Pearson’s Product Moment
Coefficient) to see how significant an impact attitudes appeared to have on the
proportion of students continuing with mathematics.
5) We also further examined the schools with the three highest and two lowest indices
for students intending to continue with mathematics to investigate possible
connections or explanations for their results. The reasons that the students had given
for considering or ruling out mathematics as an AS-level subject were examined, as
were the school’s Ofsted inspection reports.
Results
The results will be reported in three sections: section 1 on the results by predicted grade;
section 2 on the results by gender; and section 3 on the results by school.
Section 1: Results by Predicted Grade Attainment
(Figure 1)
The proportions of predicted A* and A grade students intending to continue with
mathematics (less than 70% of A* and less than 60% of A grade students) shown in
Figure 1 is disappointing. However, the dramatic fall in participation rate comes between
the predicted grade A and grade B levels, with fewer than 20% of students in the latter
group intending to continue with mathematics. Although we do not have comparable data
for other subjects, this seems low for a core subject that is important in many individual
degree subjects and careers.
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Figure 2 illustrates the reasons why students are not considering mathematics, by
predicted grade.
(Figure 2)
Difficulty
From Figure 2, the main reason that students predicted A or B grades gave for not
continuing with mathematics was the perceived difficulty of the subject. Many responses
suggested that this might be more to do with future expectations than with experiences so
far. It must be of concern that almost half the students predicted to get a grade A were not
continuing because they felt it was too hard. In some cases this reflected past experience:
“…it is too damn hard...” (male, School 3, predicted grade A).
For other students, even those predicted to get A and A* grades, it was more a case
of lack of confidence about the future. This was particularly prevalent amongst girls and
will be discussed in the next section under gender differences.
There was certainly a perception that only students with A and A* would be able to
cope: “I get the impression that to do and cope with AS level you need to be an A or A*
student” (male, school 4, predicted grade B); “I would love to have done maths for Alevel but I don’t feel I have achieved a high enough grade to cope with the hard work it
takes to do maths for an A-level” (female, School 5, predicted grade B).
It was clear from the student responses that there were a number of different
influences on this perception of difficulty. Several mentioned the existence of a
significant gap in difficulty between GCSE and AS-level: “I have heard that it is a huge
step up from GCSE” (male, School 4, predicted grade A). Meanwhile, many students’
perceptions had been informed by those who had already taken AS-level or were
currently on the course, including older siblings: “Everyone who I have spoken to who is
on the course says it is way too hard and is not worth it” (male, School 6, predicted grade
B); “My sister found A2 maths very hard and her frustration with it persuaded me not to
study it” (male, School 13, predicted grade A).
Teachers often added to the perception of difficulty, indicating that they also
consider mathematics to be a particularly difficult AS/A-level: “I did consider doing
maths at six form but was informed by one of the teachers there that if I did not get an A
in my GCSE then there was no point taking it at A level ” (male, school 6, predicted
grade B); “I have been told by teachers it is too difficult for me” (male, School 4,
predicted grade B).
Those students that had only taken intermediate level clearly felt that they would
struggle, even where they had achieved a grade B: “I feel that because I only did
intermediate level at GCSE I would not be confident enough to continue at AS or A2
level” (female, school 6, predicted grade B).
A small number of students stated that the quality of teaching provided was
responsible for their difficulties: “… in the last 2 years I have had too many maths
teachers - about six - which all have different methods which confused me a little and put
me off maths” (male, School 10, predicted grade C); “…from year 10-11 I had the worst
teacher imaginable he had no idea of teaching methods, could not control the class and
although I tried I learnt almost nothing” (female, School 4, predicted grade B).
Some students seemed to believe that there are fixed ‘boundaries’ reached in
mathematics, beyond which learning becomes extremely difficult and frustrating. In the
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questionnaire, just over 5% of all students either circled both ‘difficult’ and ‘easy’ or
alternatively wrote in a response which indicated ambivalence: “easy when I can do it,
difficult when I cannot” (male, school 8, predicted grade B). Bearing in mind that such
responses seem initially inconsistent, this is a relatively large proportion of students.
Moreover, there were a number of students who pointed towards this ‘fixed boundary’
effect within their reasons for not continuing with mathematics: “Always feel as if there
have been boundaries…not sure I am at the correct level to attempt AS” (male, School 6,
predicted grade B); “I cannot do some of it at GCSE, so the thought of learning more
seems very daunting to me” (male, School 3, predicted grade B); “I struggle with some
parts of maths, and so do not think I am good enough to do it at A level” (female, School
6, predicted grade A). These students do not seem to realise that with further study, some
of the mathematics that currently puzzles them is likely to become better understood,
even though new areas may still open up which present difficulties.
Disaffection
Figure 2 shows that, for students predicted to get grades A, B or C, the second and third
most prevalent reasons for not continuing with Mathematics are lack of enjoyment and a
belief that the subject is boring. In the attitudes section of the questionnaire, the word
boring was selected most commonly as a description for mathematics (37% of students).
‘Boring’ suggests lack of interest and a feeling of dullness: “Throughout school life, I
have not been interested in maths. I may be reasonably good at it, but feel the lack of
interest would not survive the subject” (male, School 4, predicted grade A); “Though it
may be more interesting than at GCSE, my GCSE maths experience has put me off it for
life.” (male, school 13, predicted grade A); “I decided to pursue subjects I was more
interested in” (male, School 3, predicted grade A*).
Some students were more explicit about the reasons for being bored, for example the
lack of opportunity for creativity: “I enjoy subjects where I can express myself like
English.” (female, School 13, predicted grade B).
Unlike the findings of Nardi and Steward (2003), in which there was a lack of
emotional response to mathematics lessons, the disaffection was sometimes charged with
emotion: “I enjoy it when I get it right, but I didn’t choose it because I hate it when I get
it wrong and get frustrated.” (female, School 4, predicted grade A); “because it SUCKS
and I wouldn’t want to spend any more of my time looking at algebra and other crap”
(male, school 13, predicted grade B); “I hate mathematics and I would rather die.” (male,
School 13, predicted grade D).
As with the perception of difficulty, a small number of students connected not
enjoying/ liking mathematics to the teaching they had received: “I despise the way it is
taught” (male, School 3, predicted grade A).
Utility
A smaller number of students said the reason for ruling out mathematics was that the
subject was not useful or relevant either for their future degree/ career (8%) or more
generally in life (3%). Career/ university concerns were most prevalent among predicted
A* students. “I don’t think it will take me to where I want to be in life” (male, School 1,
predicted grade A*).
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A significant number of predicted A* students said they had not considered
mathematics because they preferred other subjects: “…[I] dropped it in favour of
economics as a more real-world related course.” (male, school 13, predicted grade A*).
Some students rejected mathematics as they felt that the content was irrelevant for
real life: “…the amount of insignificant maths work that I will NEVER use is quite big”
(male, School 3, predicted grade A); “who needs to know trigonometry in everyday life?”
(female, School 13, predicted grade B).
Positive reasons for continuing with mathematics
Although not the main focus for this paper, it is worth noting that the reasons given by
those students intending to continue with their study of mathematics were the reverse of
the reasons for giving up, although not in the same order. ‘Enjoyment’/’liking’ was the
most cited reason at grades A-C, with similar frequencies of about 35% across all
predicted grades; at A* it was also cited at about 35% but was marginally less frequent
than the feeling that students were ‘good at mathematics’. The selection of ‘enjoyment’
was particularly prevalent amongst girls, where it reached almost 50%, as compared with
under 30% for boys. While being good at mathematics and, to a much lesser extent,
appreciating its importance, were key at higher grades, students from lower grades, and
especially boys, were more likely to have as a factor its relation to their expected careers.
Section 2: Results by Gender
Figure 3 shows the participation levels of students grouped by gender.
(Figure 3)
As indicated by national data, a lower proportion of female students both considered and
intended to continue with mathematics. Figure 4 shows the reasons why male and female
students did not consider continuing with mathematics.
(Figure 4)
Figure 4 shows that the major difference between the genders is that, despite having
similar attainment to male students, a far higher proportion of female students rule out
mathematics because they perceive it to be too difficult. In some cases, this lack of
confidence was linked to a concern that they did not have a proper understanding of the
subject, even where they were predicted to get high grades: “I feel it would be too
difficult at a higher level” (female, School 13, predicted grade A*); “I don’t feel
confident enough to do so even if I’m at an A grade” (female, School 4, predicted grade
A); “because I don’t feel maths is a natural skill – I have to learn it ‘by rote’ rather than
completely understanding it” (female, School 18, predicted grade A*).
These results are further supported by the data from the attitude survey shown in
Figure 5.
(Figure 5)
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The results on the enjoyment of mathematics are relatively similar between male and
female students. The significant differences come in attitudes surrounding confidence in
the subject, where a higher proportion of female students both perceive mathematics to be
difficult and associate it with anxiety. One female student stated she had not considered
continuing mathematics: “…because I have no confidence I will get stressed and it will
get on top of me and I’m a bit rubbish at it” (female, School 4, predicted grade B). This
and several other female responses in this section seem to attribute lack of understanding
to fixed and limited ability, echoing the theories and findings of Dweck (1986, 2000),
noted earlier.
Section 3: Results by School
When analysing the results in school groups, we wanted to find how significant an impact
the school attended had on students’ attitudes towards and participation in mathematics.
Comparing students that were predicted at the same grade across schools, there was a
relatively wide variation in the proportion of students intending to continue with
mathematics suggesting that the school attended had a highly significant impact.
Figure 6 shows the mean proportion of students intending to continue mathematics in
each predicted grade group, together with the proportions in each predicted grade group
from the schools with the two highest and two lowest indices of intended student
participation. For School 1 the results for predicted A and A* grades should be treated
with some caution as they refer to a small number of students.
(Figure 6)
When we went on to investigate the reasons behind these variations it became clear that
students’ attitudes to mathematics within a school had an important impact on
participation. The correlations between the indices for students’ attitudes within a school,
broken down into the four attitude headings described in the methods section, and the
indices for their intended and considered participation, are shown in Table 1. (These
indices had now removed the effects of student attainment). In addition, the correlations
with overall predicted attainment at mathematics (taken from data in this project) are also
given.
(Table 1)
Strong and significant (p<0.05) positive correlations were found between the extent to
which students both ‘liked’ and ‘enjoyed’ mathematics in a school and student
participation in mathematics. A weak and non-significant positive correlation was found
between students’ perception of the ease of mathematics in a school and mathematics
participation (i.e. the more difficult students found mathematics the lower the
participation). Lastly, mathematics participation appeared to be largely unrelated to both
anxiety and predicted attainment in mathematics within the schools, once the factor of
distribution of predicted grade had been removed from the participation figures.
At the school level as with individual students’ rationale for continuing with
mathematics, enjoyment and liking have the strongest effect. However at the school level
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the perception of ‘difficulty’ does not have a strong contribution, although this was the
major reason for rejecting participation at the individual level.
We went on to investigate the two schools with lowest participation (Schools 6 and
12) and the three schools with highest participation (Schools 1, 8 and 11). (For clarity the
results of School 8 are not shown on Figure 6.) These schools were selected on the basis
that their participation levels were noticeably different than would have been predicted
using their attainment levels. It might be expected that these differences in participation
could be explained partially through overall student attainment (i.e. those schools with
higher GCSE grades overall might not value students with grade B’s). However, this was
not the conclusion that could be drawn from our results. In fact it was the schools with
lowest attainment (judged in terms of percentage of students gaining 5A*-C grades at
GCSE) that also had the lowest participation index in our study, as well as the lowest
absolute participation rate.
In the two schools with lowest participation indices, students were particularly
negative about the difficulty and boring nature of mathematics.
In the three high participation schools, the factors that seemed to particularly
influence students’ choice were not consistent, with the importance of mathematics
qualifications, the enjoyment from learning mathematics and career concerns respectively
the most prevalent reasons. But from the attitude survey, it was clear that students in all
three schools were consistent in finding mathematics significantly more enjoyable (and
less boring) than the average. This lends further support to the high correlation found
between enjoyment and participation at the school level that was found earlier.
We also checked the reports by Ofsted inspectors on the mathematics teaching in all
five schools; in only three cases out of the five did the judgements of the quality of
teaching support our findings.
Discussion
At the start of this article, it was noted that there was general agreement in education and
government that we need more students studying mathematics. As a result of the
Curriculum 2000 changes, students have been given a greater range of subject options to
choose from, with mathematics losing out to ‘newer’ subjects. We therefore need to make
mathematics a more attractive option.
The results from this study support the recommendation of Matthews and Pepper
(2005) that the messages and guidance given to students should be differentiated both by
grade and gender, since different factors are more salient in different groups. In particular
the data suggest three partially overlapping groups from which there is most potential to
recruit additional students:
a) students with grade B at GCSE who think mathematics is too difficult;
b) girls at all levels who lack confidence in their own ability;
c) students with high GCSE grades who are either not very interested in mathematics
or do not appreciate its importance.
Difficulty, self-efficacy and identity
The results of this study suggest that the main factor deterring students is the perceived
difficulty of the subject, which is in line with previous literature referred to in the
research review. There are a number of sources informing this perception, with older
students and teachers being two of the most important. Although the recent rise in the
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numbers suggests that changes made after Curriculum 2000 have helped to reduce the
level of difficulty of AS mathematics in particular, the general impression is still that
students need at least a B grade in GCSE and preferably an A or A* to cope with the step
up in difficulty. Therefore, solutions to the problems of participation clearly need to
address the attitudes of teachers and older students as well as those of 16 year-old
students.
Decreasing the difficulty of mathematics AS-level is a possible solution. However,
this is unattractive, as it would mean that more able students are not sufficiently
challenged and it might reduce the status of mathematics, which is still one of its
attractions.
Another option is to introduce alternative easier qualifications to run alongside the
current AS-level, such as the Use of Mathematics AS and others currently being trialled
as part of the Pathways projects of the Qualifications and Curriculum Authority(QCA).
These would be aimed especially at those students currently achieving at the lower end of
B, and also C at GCSE, most of whom do not consider AS-level mathematics due to its
difficulty. Such alternatives would consolidate and expand on student’s knowledge from
GCSE without trying to cover the full range of mathematics currently in the AS-level
course. There are drawbacks with this option; in particular the possibility that students
that are currently taking the full AS-level would settle for the easier option, and also the
creation of a new status division between different curricula which may constitute a
barrier in widening participation. However, if implemented effectively these problems
could be largely overcome.
There are a range of other measures that might help make AS-level mathematics less
daunting. For example running bridging courses that are designed to consolidate students’
GCSE knowledge and prepare them for the step up to AS-level is cited by Ofsted (2006)
as an example of good practice.
The results of this report show that some students, especially girls, predicted A or
even A* grades at GCSE are still doubtful of their ability. Part of the solution might be
provided by greater encouragement and support from teachers where there is considerable
potential for greater recruitment. In particular, teachers need to assure students that just
because they have struggled with some of the very hardest elements within GCSE topics,
this does not mean that will fail at AS-level. The common idea that there are fixed
‘boundaries’ to mathematical knowledge beyond which a person cannot progress has to
be confronted.
Teaching methods can also have a vital impact on pupil understanding, confidence
and self-efficacy in mathematics. Because of league table and performance management
targets, teaching strategies are currently focused on training students in procedural skills
that are necessary to pass examinations (Ofsted 2006, Smith 2004). Teaching styles that
promote a better understanding of mathematics and its relevance to students’ lives need to
be encouraged. An improved understanding of the concepts underlying procedures will
help students to form a better identification with the subject. In their reports, Kyriacou
and Goulding (2006), Ofsted (2006)and the QCA (Matthews and Pepper 2005)
specifically mention the effective use of formative assessment, oral work and greater
class discussion, peer support and collaboration, investigative work, and the effective use
of ICT. However achieving such changes may require considerable professional
development as well as changing the nature of GCSE assessment and releasing the
pressure on teachers from targets, league tables and performance management.
11
Disaffection
Too many students decide not to continue with mathematics because of a sense of
disaffection. As noted earlier, Nardi and Steward (2003) list common attributes of
disaffection as being tedium, elitism, isolation, rote learning and depersonalisation. This
is supported by our own findings, which included ‘boring’ as the most commonly used
description for mathematics. We also identified among a minority of students with
stronger emotional negative feelings than Nardi and Steward found in a younger age
range; Bibby (2002) describes similarly emotional responses to school mathematics
among primary teachers.
The results of this report suggest that changing the attitude of some students towards
mathematics at a school level is important for improving participation. The high
correlations found between students’ enjoyment/liking of mathematics in a school and
that school’s participation index suggest that schools and others need to acknowledge that
developing a positive attitude towards mathematics is a key aspect of students’ learning,
alongside attainment. At the heart of the problem, once again, often seems to lie
procedural teaching methods. Boaler’s work provides evidence to support the positive
effect that more varied and open teaching methods can have on pupil’s perception of
mathematics (Boaler 1997, Ofsted 2006).
Utility
It was clear that many students appreciated the importance and usefulness of
mathematics; however for students predicted an A*, the strongest reason for not
continuing with mathematics was that they felt they would not need it either for their
degree or their career. This need to raise information and awareness supports the work in
this area of the HEFCE-funded ‘More Maths Grads’ initiative, as well as in other areas
like the improvement of teaching methods.
The future
It seems likely, given the recent commitment to all students being required to engage in
education until the age of 18, that eventually England will catch up with other countries
and make mathematics compulsory for all students. In this case a suite of Pathways will
be needed. Although this would solve the problem of participation in the broadest sense,
in order to persuade more students to opt into more specialist mathematics courses such
as AS and A-level, most of the concerns in this report would still need to be addressed to
assure students’ engagement, commitment and success.
The design of the study and collection of data formed part of an evaluation of a two-tier
GCSE funded by the Qualifications and Curriculum Authority. The extraction and
analysis of this data set was funded jointly by the Department of Education and
Professional Studies at King’s College London and the Institute of Education, University
of London.
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15
Captions to figures and tables in order of appearance
Figure 1. Students who considered/ intended continuing with mathematics, by grade
Figure 2. Student reasons for not continuing with mathematics, by predicted grade
Figure 3. Students who considered/ intended continuing with mathematics, by gender
Figure 4. Student reasons for not continuing with mathematics, by gender
Figure 5. Student attitudes to mathematics, by gender
Figure 6. Mathematics participation across different schools
Table 1. Correlations between school attitude and participation within mathematics
16
Figure 1
100.0
Proportion (%)
80.0
60.0
Considered continuing
w ith mathematics
40.0
Intended to continue w ith
mathematics
20.0
0.0
A*
A
B
C
Predicted grade
17
Figure 2
Proportion of
students giving
reason (%)
Too difficult
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
Do not enjoy/ like it
Boring
Not needed for future
degree/ career
Not useful in life
A*
A
B
C
Prefer other courses
Predicted Grade
18
Figure 3
Proportion of students
(%)
35.0
30.0
25.0
20.0
Considered
continuing
15.0
Intending to
continue
10.0
5.0
0.0
Male
Female
Gender
19
Figure 4
Too difficult
Does not enjoy/like it
Proportion of
studnets
mentioning
reason (%)
70
60
Boring
50
40
Not needed for future
degree/ career
30
20
Not continuing education
10
0
Male
Female
Gender
Not useful in life
Prefer other subjects
20
Figure 5
Proportion of
students giving
description (%)
45
Bored
40
35
Like
30
25
Difficult
20
Anxious
15
10
Hate
5
0
Male
Female
Gender
21
Enjoy
Easy
Proportion of students intending to
continue with mathematics (%)
Figure 6
100
80
School 11
School 1
60
Mean
40
School 6
School 12
20
0
A*
A
B
Predicted grade
22
C
Table 1
School index for student attitude towards
mathematics
Like
Enjoy
Anxious
Easy
Correlation with
student intended
participation
Correlation with
student
considered
participation
School attainment
indices
Predicted
attainment in maths
0.59
0.65
-0.04
0.10
-0.07
0.57
0.67
0.09
0.22
0.04
23