This paper explores the behaviour, attitudes and beliefs of primary school pupils towards mathematics in the classroom and the impact that this may have on their mathematical ability. The study focused on year 3 pupils from a local school, some of whom took part in focus groups towards the end of the project. The children completed short worksheets, which were used to stimulate a guided discussion on what aspects of mathematics the children liked and disliked. The aim of this project was to isolate possible causes of negative attitudes towards mathematics and to discuss what their implications might be. Keywords: Primary, Attitudes, Purpose, Anxiety, Confidence, Language, Reflection

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Introduction

Mathematicians have long held a high level of respect amongst their academic peers. Yet the subject of mathematics, although revered, remains a source of anxiety and trepidation for a large number of people. Widespread negativity towards mathematics appears in many forms, from misrepresentation in the media to the social stigma that seems to surround those who are mathematically gifted. Children often set mathematics aside as a cause for concern, despite their limited exposure to it (Hoyles 1982). It is a subject unlike most others, since it requires a considerable amount of perseverance from the individual in order to succeed.

A negative attitude towards mathematics could considerably reduce a person’s willingness to persist with a problem. Without the ability to persevere, mathematical development is likely to be difficult. The purpose of this project is to determine the possible root causes of these negative attitudes towards mathematics.

The study focused on Year 3 pupils from a local school, some of whom took part in focus groups. Three focus groups were carried out, each consisting

of four children with similar abilities. Children were selected based on observations from previous visits. Subjects were chosen if they displayed strong feelings for or against mathematics, or if they were at the extremes of the ability range. The focus groups lasted for approximately 30 minutes and were broken into two parts. Firstly, the children were given 10 minutes to attempt four questions tailored to their ability range. The questions involved symmetry, arithmetic, a word problem and a problem solving exercise.

The remaining time was used to discuss what the children felt about mathematics, using the worksheet as a focal point. It is hoped that this project will provide significant insights into why many children have a pessimistic outlook on mathematics and indicate where future research is needed. Mathematics and its apparent lack of purpose

Children may find the nature of mathematics difficult to cope with as its wider reaching implications can be hard to see. Experiments are carried out for the physical sciences,

From Informal Proceedings 29-1 (BSRLM) available at bsrlm.org.uk © the author – 7

Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 29(1) March 2009

pictures are drawn in art class and language skills are used in everyday interactions with other people. However, mathematics has a very formal written sense about it, where activities remain intangible to the child. From the remarks I witnessed in the focus groups, it seems that children find it difficult to make a connection between the work they do on paper and its practical applications. The following transcript is taken from the high-ability focus group: Charlie:

You need to be good with numeracy, say when you’re say, shopping for something – You need to work out how much you’re paying. You don’t have to be a genius at it, but you have to be quite good at it.

f you’re a shopkeeper, and someone gave you like about £20, and something was like £15 and they didn’t know much how much to give them back. And if you didn’t know, you should learn more in your maths.

It was rather surprising to see pupils across the entire ability range unable to make connections between mathematics and its many practical uses. Counting money was the only association that they were able to make, even though it had not been covered in recent work. It is interesting that the high achievers, although mathematically gifted, could not establish any more real world applications than the low achievers. However, the low achievers present more of a concern, as motivation to improve their mathematical understanding cannot be aided by their innate ability. Certainly, the children cannot be expected to make these connections without assistance from a teacher.

In fact, some believe that the most effective teachers are connectionists (Askew et al. 1997), although perhaps there is currently insufficient emphasis on the practical uses of mathematics in the curriculum. Human nature does not favour futile endeavours; if a difficult task appears to have no purpose, then few will continue to follow it through. If low achievers are unable to see the wider benefits of having strong mathematical skills, then they may lack motivation, which is vital in a difficult subject such as mathematics.

Understanding the purpose of mathematics should not only help to improve motivation, but could help in the actual formulation of concepts. In 1991, Harel and Tall discussed the importance of what they called ‘the necessity principle’:

From Informal Proceedings 29-1 (BSRLM) available at bsrlm.org.uk © the author – 8

Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 29(1) March 2009

This principle states that the subject matter has to be presented in such a way that learners can see its necessity. For if students do not see the rationale for an idea (e.g., a definition of an operation, or a symbolization for a concept), the idea would seem to them as being evoked arbitrarily; it does not become a concept of the students. (Harel and Tall, 1991 41)

They believed that a notion is more likely to be abstracted successfully if the learner can acknowledge the necessity of the concept. In the context of this project, the learner needs to be aware of the purpose behind their work. For young learners, understanding the practical uses of mathematics could be sufficient to both motivate them and allow the necessity principle to be satisfied.

Further research is required on this issue, as its scope may be greater than previously thought. As with all the findings in this project, the data was collected from a small sample group, and so it may be difficult to generalise to a larger population. However, based on the remarkable similarities between responses in this particular classroom and the general attitude towards mathematics in our society, I would suggest that the apparent lack of purpose in mathematics is a sentiment felt by many.

Self-belief and mathematical ability

Nothing was more evident during the focus groups than the lack of self-belief shown by many of the children. Low and middle achievers quickly resigned themselves to failure, without truly attempting all of the questions on their worksheet. There was a consistent association of mathematics with ‘cleverness’, as many of the children felt not only that numeracy was harder than literacy, but that to be clever you had to be good at numeracy. In effect the children were implying that someone who excels in literacy will not be perceived as being clever unless they can display a similar exemplary ability in numeracy. As a result, children who perceived themselves to be weak felt that they would be incapable of solving harder mathematical problems. A girl from the middle-ability group remarked: Faye:

I’m just going to do a simple answer, which is probably wrong.

While some would say that any answer is better than no answer, Faye’s decision to give up and guess occurred before she had given any real consideration to the question. This example was typical of her low confidence in mathematics; an attitude which I believe greatly misrepresents her ability.

Many of the children showed signs of anxiety whilst attempting the worksheets, shuffling awkwardly in their seats, glancing at their peers with worried expressions and making negative comments about the difficulty of the current task. Previous research into anxiety and mathematics (Hoyles, 1982) indicates that a connection may lie between an individual’s perceived ability and their level of success. The absolute nature of mathematics, where there is normally only one right answer, could add considerably to a negative attitude towards mathematics.

Overall, girls expressed much lower confidence than boys, even among the high achievers. They frequently attributed success and failure to external factors, such as luck and the perceived difficulty of a question. In comparison, most boys recognised that success was due to their own ability, and that failure was caused by either a lack of effort or understanding on their part. Whilst this distinction was not absolute it did apply to the vast majority of pupils that took part in the focus groups.

The difference in attitudes towards mathematics between genders has been researched in depth by many, notably Stipek and Gralinski (1991). Although girls and boys are roughly equal in the league tables at GCSE level, there is a remarkable difference in A-level and University uptake. It is quite possible that primary school experiences are alienating girls from the subject, to the detriment of their long term mathematical development. The reason for this is currently unclear and warrants further

From Informal Proceedings 29-1 (BSRLM) available at bsrlm.org.uk © the author – 9

Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 29(1) March 2009

Undoubtedly, the teacher faces an uphill struggle trying to balance a diverse range of abilities and attitudes, an ever changing curriculum and strict time constraints. However, there are several outcomes of this project that should be considered by the education community. For example, it may be worth exploring how the children perceive mathematics and its uses outside of school. By improving the understanding of the uses of mathematics, pupils will hopefully see the benefits of developing strong mathematical skills for more than just academic purposes. Likewise, low self-belief is an issue that all teachers can attempt to address.

We need to dispel the notion that mathematics is a subject limited to geniuses and that children of all abilities can be successful in the subject. The structure of the lesson and the time constraints of the school day should also be up for revision, as

the current lesson format may not be the most efficient. The school curriculum is often subject to repetition, some of which may be avoidable with a subtle shift in lesson structure.

Conclusion

It is clear that children’s attitudes towards mathematics can be influenced by a wide variety of factors. This project has gone some way to identifying what a few of these factors might be, but there is still plenty of scope for future research. In particular, children’s views on practical uses of mathematics and the difference in attitudes between genders require further study. Additionally, the importance of reflection in primary education needs to be discussed in much greater detail.

References

Beth, E. and J. Piaget. 1966. Mathematical Epistemology and Psychology, Dordrecht: Riedel. Hoyles, C. 1982. The Pupil’s View of Mathematics Learning. Educational Studies in Mathematics 13 (4): 349-372.

Dubinsky, E. 1991 Reflective Abstraction in Advanced Mathematical Thinking. In Advanced Mathematical Thinking, ed. D. Tall, 95-102. Dordrecht: Kluwer Academic Publishers. Harel, G., and D. Tall. 1991. The general, the abstract and the generic in advanced mathematical thinking. For the Learning of Mathematics 11 (1): 38-42. Stipek, D. and H. Gralinski. 1991. Gender Differences in Children’s Achievement-Related Beliefs and Emotional Responses to Success and Failure in Mathematics. Journal of Educational Psychology 83 (3): 361-371.

Askew, M., M. Brown, V. Rhodes, D. Johnson, and D. William. 1997. Effective Teachers of Numeracy: Final Report. London: Kings College.

From Informal Proceedings 29-1 (BSRLM) available at bsrlm.org.uk © the author – 12