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Masters in Educational Practice: Numeracy learning pack

2

Understanding numeracy

2.5

Learner beliefs, attitudes and emotions

Almost 40 years ago, White (1974) suggested that to be ‘illiterate’ is shameful but to be ‘unnumbered’ carries less stigma, since numeracy is regarded as a ‘special gift’. Whether this is still the case or not is explored in more detail in Topic 1.5 but there is certainly considerable evidence to support the idea that learners’ attitudes, beliefs and feelings about mathematics and numeracy, and their confidence (or lack of) in their own mathematical abilities have a significant effect on their learning (Coben, 2003; Ernest, 2011). These can effect:

  • achievement in mathematics and related subjects
  • persistence in problem-solving
  • choices to opt out of studying mathematics (especially but not only girls and women)
  • anxiety about mathematics in school and in adult life.

Beliefs

Research studies suggest that school children construct powerful images of mathematics for themselves on the basis of their learning experiences. They tend to see mathematics as:

  • algorithmic and mechanical or
  • open ended, intuitive and experience-based.

Learners’ classroom experiences also tend to be decisive in developing their views of mathematics with many primary and secondary learners tending to regard mathematics and numeracy as exclusively school-based and isolated from other areas of study. The impact of mass media or other popular images on younger learners is harder to discern (Ernest, 2011).

Attitudes

Learner attitudes to mathematics and numeracy can be entrenched and enduring. According to Bishop and Nickson (1983, p.20):

As a result of the kind of mathematical experience they will have had at primary level and, more particularly, their achievement or lack of it with respect to the subject, attitudes to it are likely to be entrenched by the time they enter secondary school.

There are several large-scale international surveys which explore learners’ attitudes to school mathematics.

  1. Liking/disliking mathematics.
  2. Confidence/lack of confidence in one’s own mathematical ability.
  3. Anxiety towards mathematics. 
  4. The importance, utility or usefulness of mathematics.

Successive Trends in International Mathematics and Science Study (TIMSS) assessments, for example, have shown a strong positive relationship within countries between student attitudes toward mathematics and their mathematics achievement. These also show a tendency for attitude scores (especially on enjoyment and confidence) to decline as learners move from primary to secondary school.

In the TIMSS 2011 international comparison of samples of students from 63 countries, 85 per cent of 14 and 15-year-olds thought that learning mathematics would help them in their daily life and that they needed to do well in mathematics to get the job they want. Internationally, nearly one-half of students that valued mathematics had the highest average achievement, followed by those that somewhat valued the subject. Those that did not value mathematics (15 per cent) had the lowest average achievement.

However, compared to 10 and 11-year-olds surveyed at the same time, 14 and 15-year-olds had less positive attitudes towards learning mathematics. Nearly one-third did not like learning mathematics and only 14 per cent expressed confidence in their mathematics ability, with most learners divided between somewhat confident (45 per cent) and not confident (41 per cent). The learners lacking confidence had the lowest achievement.

Research (Singh, 1993; Tobias, 1993; Evans, 2000) into factors influencing older learners’ experiences of mathematics and numeracy has found that:

  • abstraction and lack of relevance are common reasons given by learners’ for their dislike of and failure in mathematics
  • fear of failure in tests and teaching approaches contribute to learner anxiety
  • teachers play a key role in motivating or disaffecting learners
  • women are more likely to develop negative attitudes to mathematics as a result of wider societal factors, and the content and way mathematics is often taught
  • learners can develop a very Eurocentric view of mathematics in school, that ignores developments of key ideas and contributions from other cultures.

Welsh context

In Estyn’s latest report (June 2013, p.25), Numeracy in key stages 2 and 3: a baseline study, most primary learners in the surveyed schools in Wales were positive about numeracy and thought that good numeracy skills:

  • are as important as good literacy skills
  • help get on well in secondary school and are useful in finding a well-paid job.

However, a majority of these learners struggled to give examples of how numeracy was relevant to their everyday lives and although most thought they needed to improve their numeracy skills, only a very few could explain how they would do this.

Within the same report, many secondary school learners thought that both numeracy and literacy skills were important and that good numeracy skills would help them to progress further in education or employment. Around half of learners could relate numeracy to their everyday lives, but only a minority regarded numeracy as relevant to their schoolwork. A few said that it was often difficult to apply their numeracy skills in other subjects because ‘although they use the skills in mathematics lessons their understanding of why they are doing it is unclear’. A very few secondary learners had negative attitudes to numeracy and did not think being numerate was a necessary life skill.

Activity 2.11

  1. Sort out the learner statements below according to the attitude categories above (and the extent to which each is positive or negative).
    • Maths is fascinating and fun
    • It makes me nervous even to think about doing a maths problem
    • I really like maths
    • I avoid maths because I’m not very good with numbers
    • I feel a sense of insecurity when attempting maths
    • I do not like maths; it scares me to have to study it
    • Maths tests make me very nervous
    • I enjoy most maths work
    • Given the choice I would have nothing to do with maths
    • I have always been confident about maths
    • I feel at ease in maths and I enjoy it
    • Having to work out maths problems makes me nervous
    • I enjoy solving maths puzzles
    • Maths is a subject which I find difficult
    • I am fairly confident about my mathematical ability
    • At times I am fearful of maths
    • I have never liked maths
    • I don’t feel sure of myself in maths
    • I am less confident about maths than about other subjects
    • I’m not very good at maths
    • I find maths very interesting
    • I’m afraid of maths
    • Anything to do with maths makes me anxious
    • Maths is a subject I find easy
    • I have never been confident in maths
    • I like maths more than most subjects
    • Maths homework has always worried me
  2. Investigate your own learners’ attitudes to mathematics and numeracy by adapting some of these statements.

Emotions

Ernest (2011) defines mathephobia as fear of or anxiety towards mathematics and associates it with an extreme lack of confidence and strong dislike of mathematics. Buxton (1981) noted that although only a few per cent of younger children suffer from maths anxiety, it is significant amongst adults. However, Relich (1996) found that traumatic experiences at primary school had a lifelong effect on some Australian primary teachers. While researching 14-year-old learners’ attitudes to mathematics, Hoyles (1982, p.368) found that ‘anxiety, feelings of inadequacy and feelings of shame were quite common features’ related to learners’ bad experiences of mathematics learning.

There is a great deal of research on maths anxiety in college students both in the UK and the USA, particularly as they need to study some form of mathematics or numeracy as a course requirement regardless of the academic or vocational pathway they have chosen. Research on some courses (Coben, et al, 2007) suggests that when numeracy is taught as part of the basic skills element of a full-time course or as part of a vocational course it can be difficult to motivate learners. However, other research (Casey et al, 2006) has found that embedding numeracy within vocational education appears to decrease anxiety and increase learner motivation and engagement – so long as the embedding is well executed.

Mathematical myths

Frank (1990, p.10) defines a mathematical myth as:

A belief about mathematics that is (potentially) harmful to the person holding that belief because belief in a maths myth can result in false impressions about how mathematics is done.

Myths commonly held by learners who are maths anxious or want to avoid mathematics (Paulos, 1992; Lim, 2002) include the following:

    1. Maths is a difficult subject.
    2. Some people have a maths mind and some don’t.
    3. Maths requires logic, not intuition.
    4. You must always know how you got the answer.
    5. There is a best way to do a maths problem.
    6. Maths requires a very good memory.
    7. Men are better at maths than women.
    8. Mathematicians do problems quickly in their heads.
    9. It’s always important to get the right answer quickly.
    10. Maths is not creative.
    11. It is bad to count on your fingers.
    12. There is a magic key to doing maths.
    13. Maths problems have only one correct answer.

Activity 2.12

Many of these myths are related to beliefs about the nature of mathematics and learning mathematics as discussed in Topic 2.5). Try to identify which of the statements above:

  • suggest gender differences in mathematical ability
  • imply maths is a logical, rigid and hierarchical subject
  • suggest a fixed way of getting right answers
  • indicate that memory and being able to working quickly are essential.

Gender differences

There is a great deal of research on gender differences in attitudes to mathematics and numeracy. These have been observed in children as young as seven years old (Vanayan et al., 1997; de Abreu and Kline, 2003). Even when no differences are observed on variables such as liking and enjoyment, more boys than girls report that they are good at mathematics and boys are likely to believe they are more competent than girls do. Boys also tend to attribute their success at mathematics to intrinsic factors like skill and ability and their failures to extrinsic factors like bad luck or lack of effort. Girls, on the other hand, put success at maths down to good luck and hard work and see their failures as a result of lack of skill and ability (Ernest, 2011).

Dowker et al. (2012) in their recent work with primary school children in England also found that:

The only significant gender difference was in self-rating, where boys rated themselves higher than girls did. There were no gender differences in actual performance or in other attitudes.

They concluded that self-rating, rather than mathematics anxiety, is the key factor in younger primary children’s attitudes to mathematics.

The results from another recent study (Devine et al, 2012) involving over 400 British secondary school students found that both maths anxiety and test anxiety had a negative impact on performance in mathematics. However, although girls showed higher levels of maths anxiety and test anxiety than boys, there were no gender differences in actual mathematics performance. The authors suggest that the girls in the study may have had the potential to perform better than boys in mathematics if their maths anxiety had been lessened.

In secondary school, more boys than girls also tend to perceive mathematics as useful and boys tend to exhibit more positive attitudes towards mathematics than girls do. This disparity tends to increase with age and fewer girls opt to study mathematics beyond GCSE and A level. Much of the research on girls and mathematics also identifies stereotypical perceptions of mathematics as a male domain, especially in Western English-speaking countries.

Implications for practice

Suggestions for generating positive beliefs about mathematics and numeracy, and reducing maths anxiety.

  • Develop ‘habits of mind’ to help learners see themselves as successful learners of mathematics and numeracy (Cuoco et al., 1996; Pearse and Walton, 2011).
  • Foster learner (and teacher) view of ability in maths and numeracy as changeable not fixed (Askew and Wiliam, 1995, p.28; Dweck, 2006 on ‘fixed’ versus ‘growth mindset’).
  • Create classroom climates where learners expect to face challenges, be stuck and make mistakes as vital parts of learning and improving their maths and numeracy.
  • Create environments where maths anxiety can be openly discussed (Tobias, 1993) and learners are encouraged to try to understand emotional blocks (Hoyles, 1982; Evans, 2000).
  • Value persistence in understanding ideas over the need for speed so that learners regard challenges as opportunities for learning (Brown et al. 2001; OFSTED, 2008).
  • Use pictorial journals, games, visualisation in problem solving, and story problems with younger learners.
  • Make use of historical and global context in the development and use of mathematics (Fauvel, 1991).
  • Use more real-life problem solving.
  • Emphasise understanding rather than procedures (Boaler and Greeno, 2000; Johnston-Wilder and Lee, 2010).
  • Ensure feedback on learners’ work is constructive and positive.
  • Adopt more active, connected and challenging teaching approaches (Swain and Swan, 2007).

Activity 2.13

  1. Identify ways in which you (could) actively promote positive beliefs about mathematics and numeracy in work with your own learners.
  2. Are there situations when mathematical myths go unchallenged in your classroom? If so, what could you do differently?

Further reading

Fauvel (1991) suggests making use of the historical and global context in the development and use of mathematics as this helps to:

  • increase motivation for learning
  • makes mathematics less frightening 
  • gives mathematics a ‘human face’
  • changes perceptions of what ‘maths’ is 
  • enable learners to see that they are not the only ones who have faced difficulties.

McLeod, D. B. (1994) provides a useful review of research on affect and mathematics learning in general in the JRME from 1970–1990s.

Pugalee (1998), Burns (1998) and Hatch (1998) found that use of pictorial journals, games, visualisation in problem solving, and story problems with younger learners reduced learner anxiety and had beneficial effect on young children’s numerical reasoning and problem solving.

References

de Abreu, G. and Kline, T. (2003) School Mathematics and Cultural Knowledge, in Pedagogy, Culture and Society, 11(1), pp. 11–30.

Askew, M. and Wiliam, D. (1995) Recent Research in Mathematics Education 5–16. London, HMSO.

Bishop, A. J. and Nickson, M. (1983) A Review of Research in Mathematical Education, Part B, NFER-Nelson, Windsor.

Boaler, J. and Greeno, J. (2000) Identity, agency and knowing in mathematics worlds. In Boaler, J. (Ed.), Multiple Perspectives on Mathematics Teaching and Learning (pp. 171–200) Westport, CT: Ablex Publishing.

Brown, M., Askew, M., Rhodes, V., Denvir, H., Ranson, E., and Wiliam, D. (2001) Magic bullets or chimeras? Searching for factors characterising effective teachers and effective teaching in numeracy. Paper presented at the British Educational Research Association (BERA) conference, University of Leeds. (online) (accessed 30 September 2013).

Burns, M. (1998). Math: Facing an American phobia. USA: Math Solutions Publications.

Buxton, L. (1981) Do you Panic about Maths? Coping with maths anxiety. London: Heinemann Educational.

Casey, H., Jupp, T., Grief, S., Ivanic, R. Lopez, D. Cara, O. Eldred, J. McNeil, B. (2006) “You wouldn’t expect a maths teacher to teach plastering …”
Embedding literacy, language and numeracy in post-16 vocational programmes – the impact on learning and achievement. London, NRDC
. (online) (accessed 30 September 2013).

Coben, D. (2003) Research Review Adult numeracy: review of research and literature. London, NRDC. (online) (accessed 30 September 2013).

Coben, D., Brown, M., Rhodes, V., Swain, J., Ananiadou, K., Brown, P., Ashton, J., Holder, D., Lowe, S., Magee, C., Nieduszynska, S., and Storey, V. (2007) Effective Teaching and Learning: Numeracy. London, NRDC. (online) (accessed 30 September 2013).

Cuoco, A., Goldenberg, P. and Mark, J. (1996) Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behaviour, 15, pp. 375–402. (online) (accessed 30 September 2013).

Devine, A., Fawcett, K., Szűcs* D., and Dowker A. (2012) Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety in Behavioral and Brain Functions, 8(33) doi:10.1186/1744-9081-8-33 (online) (accessed 19 September 2013) * Corresponding author: Dénes Szűcs ds377@cam.ac.uk

Dowker, A., Bennett, K. and Smith, L. (2012) Attitudes to Mathematics in Primary School Children, in Child Development Research, vol. 2012, Article ID 124939, 8 pages,. doi:10.1155/2012/124939 (online) (accessed 19 September 2013).

Dweck, C. (2006) Mindset: The New Psychology of Success. Random House: New York.

Ernest, P. (2011) The Philosophy of Learning Mathematics. Saarbrücken, Lambert Academic Publishing.

Estyn (June 2013) Numeracy in key stages 2 and 3: a baseline study. Cardiff, Estyn. (online) (accessed 30 September 2013).

Evans, J. (2000) Adults’ Mathematical Thinking and Emotions: A study of numerate practices. London: Routledge/Falmer, Taylor & Francis Group.

Fauvel, J. (1991) Using History in Mathematics Education in For the Learning of Mathematics, 11(2) Special Issue on History in Mathematics Education. pp.3–6. FLM Publishing Association.
Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? Arithmetic Teacher, 37(5), pp.10–12.

Hatch, G. (1998). Replace your mental arithmetic test with a game. Mathematics in School, 27(1), pp.32–34.

Hoyles, C. (1982) The pupil’s view of mathematics learning. Educational Studies in Mathematics, 13, October, pp.349–372.

Johnston-Wilder, S. and Lee, C. (2010) Developing Mathematical Resilience. Milton Keynes, Open University. (online) (accessed 30 September 2013).

Lim, C. S. (2002) Public images of mathematics. Philosophy of Mathematics Education Journal, 15. (online) (accessed 30 September 2013).

OFSTED (2008) Mathematics: Understanding the Score. London, OFSTED. (online) (accessed 13 Sept 2013).

Paulos, J. A. (1992) Beyond Numeracy. Pennsylvania, Vintage Books.

Pearse, M. and Walton, K.M. (2011) Teaching numeracy – 9 Critical Habits to Ignite Mathematical Thinking. California, Corwin, Sage.
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Pugalee, D. (1998). Promoting mathematical learning through writing. Mathematics in School,  pp.20–22.

Relich, J. (1996) Gender, self-concept and teachers of mathematics: Effects on attitudes to teaching and learning. Educational Studies in Mathematics, 30(2), pp. 179–195.

Singh, E. (1993) The political dimension of adult numeracy: Conclusions of a survey into attitudes to mathematics. In C. Julie, D. Angelis & Z. Davis (Eds.) Political Dimensions of Mathematics Education 2: Curriculum Reconstruction for Society in Transition (pp. 335–341). Cape Town: Miller Maskew Longman (Pty) Ltd.

Swan, M. and Swain, J. (2007) Maths4Life Thinking Through Mathematics Research Report . London, NRDC. (online) (accessed 30 September 2013).

TIMSS (2011) International Results in Mathematics Executive Summary. Boston, TIMSS and PIRLS. (online) (accessed 30 September 2013).

Tobias, S. (1993) Overcoming Maths Anxiety. WW Norton and Company.

Vanayan, M., White, N., Yuen, P. and Teper, M. (1997). Beliefs and attitudes toward mathematics among third- and fifth-grade students: A descriptive study. School science & mathematics 97 (7), pp. 345–351.

White, D. (1974, 30 May) Unnumbered problems. New Society.

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