“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 bestdifferentiating 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 Successhighlighted 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 periodonly 7% of the age group were studying this course (Matthews and Pepper 2005). Some of the declinefollowed the introduction of Curriculum 2000which 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 beingon 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 Treasury2006), 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 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 beenshown 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 aresearch 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 thesethree 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).
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 high-attaining 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). Theyare 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,Bartholomew2000).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 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 studentswho had considered and not considered taking mathematics were found and the reasons given for this decision were classified into separate 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 consideringand intending to study mathematics at AS-level.
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.
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 A-level 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).