The third goal of mathematics education listed above is the promotion of interest in the practice and study of mathematics. Whether mathematics is conceptualised as an absolute body of discovered truth or as an evolving, culturally developed system of logic and reasoning, an argument can be made that mathematics is a field of human intellectual endeavour which should be valued in its own right, as well as for its applications and effectiveness (for instance Hardy 2005). It follows from this position that mathematics education should be conducted in a manner which cultivates a general interest in mathematics and encourages learners to continue with its study, thus ensuring the continuance of the field. The evaluation of this goal requires an examination of both reported attitudes towards mathematics and levels of participation.
It is problematic to summarise the extant research concerning learners’ attitudes towards mathematics; opinions are neither uniform nor static, and research often explores affective variables as they relate to specific aspects of teaching and learning, or measures affect within specific subgroups of learners. Nevertheless, there is a growing body of evidence which clearly holds that learners do not see mathematics as interesting. In one survey of 2000 secondary school children (BBC News 2004) mathematics was determined to be the second most boring school subject, and
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mathematics teachers were labelled the ‘most evil’; more recently Jin, Muriel and Sibieta (2011) found that mathematics was the least favourite subject of pupils aged 14. Negative opinions have also been expressed by adults; for instance, the three most frequently expressed attitudes in Lim and Ernest’s (2000) research into public images of mathematics were that mathematics was difficult, that mathematics was boring, and that mathematics caused anxiety.
Such pejorative perspectives would appear to be inflated by aspects of current practice in mathematics education. Research such as Nardi and Steward (2003) associates poor attitudes to the subject with dominant pedagogic elements of the mathematics classroom, notably the practice of rote-learning and a depersonalised presentation of the curriculum. Picker and Berry (2000) offer that pupils’ attitudes to mathematics are further steered by their lack of appreciation of the purpose of mathematics; in their research into lower secondary pupils’ images of mathematicians they report that “as far as pupils of this age are concerned, mathematicians are essentially invisible” (p.73). Although it is proper to note once more that many pupils do engage positively with the subject, and that research often points towards instances of good practice, it is fair to say that for many pupils their experiences are failing to encourage interest in the study of mathematics, and may even be doing the opposite.
A similar mixed picture emerges from the data surrounding the issue of participation in the study of mathematics. Whilst recent years have seen some increase in the number of candidates studying post-compulsory mathematics in the form of the mathematics A- level, there is evidence of a gradual decline in uptake since the late 1980s (Matthews and Pepper 2007). Similarly, although mathematics was commendably the second most popular A-level in 2010 (The Telegraph 2010), this figure should be understood as
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partly consequent of the economic return associated with the qualification (Dolton and Vignoles 2002), and it should be stressed that there are still concerns that not enough students are choosing to study mathematics. Further to this, participation also seems to be linked inequitably to gender and other social characteristics (Noyes 2009).
As was the case with attitudes towards mathematics, there is an increasing awareness that the issues surrounding participation are compounded by aspects of current practice in the mathematics classroom. Research into the uptake of A-level mathematics, such as Brown, Brown and Bibby (2008) demonstrates that many potential candidates move away from the study of mathematics in a very definite, vehement way, citing as reasons that it is too difficult, boring, and that they do not enjoy the subject. These concerns persist into A-level; Noyes and Sealey (2012) observe in their research that the rate of attrition is higher in A-level mathematics than in almost every other subject. They go on to demonstrate that attrition rates vary substantially between schools, suggesting that the quality of teaching can be very influential in steering learners’ decisions.
In contrast to many of these findings, there has been great success in recent years with the provision of A-level further mathematics in more schools, and in 2010 further mathematics was the fastest growing A-level (The Telegraph 2010). This success could be used to argue that mathematics education is successfully equipping an elite core of pupils to go on and study mathematics at university, and in this sense mathematics education is meeting the third goal. However, this achievement is partially diluted by further problems which emerge at university level. Alongside further instances of standard attrition, a significant number of undergraduates studying mathematics are becoming disaffected in higher education and are choosing to leave mathematics behind after graduating (Wiliam 2005; Burton 2004).
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In summary, although recent years have seen some significant improvements, and a core of students are studying mathematics successfully to a high level, there are a number of substantial ways in which the current mathematics education system is failing to meet this third goal. There would appear to be an extensive negative attitude towards mathematics amongst both learners and the general population, and rates of participation in post-compulsory study remain questionable and inconsistent despite concerted levels of intervention and political attention.