The ‘affective’ component of numeracy includes the beliefs, attitudes and emotions that contribute to an individual’s ability and willingness to engage, use and persevere in mathematical thinking and learning, or in activities involving numeracy (Ginsburg et al, 2006).
A number of numeracy frameworks internationally recognise the impact of ‘affective’ factors on the acquisition and application of numeracy and use terminology such as:
- ‘enabling beliefs and attitudes’ (ALL, UK)
- ‘confidence’ (Australian Adult Numeracy Assessment)
- ‘emotional dimension’ (Scotland Curriculum Framework)
- ‘habits of mind’ (Adult Basic Education Framework for Mathematics, Massachusetts, US).
Recent advances in neuroscience suggest a strong link between emotional states and capacity to learn.
Practitioners will also have developed beliefs, attitudes and emotions related to mathematics and numeracy as a result of their own classroom experiences as learners, their cultural environments and/or messages from family members, work colleagues, media and society in general.
As practitioners, we have various ‘beliefs’ or ‘sets of ideas’ related to using mathematics and numeracy which may influence our expectations or how we understand new experiences. These include beliefs about:
- our own ability or capacity to learn maths (fixed at birth versus learning to learn)
- the nature of maths – i.e. absolutist, instrumentalist, fallibilist views; numeracy as social practices; critical numeracy (refer to Glossary)
- the usefulness or relevance of mathematics in our personal and professional everyday lives
- the problem-solving process itself (obvious to those who can – obscure to those who can’t; ‘know that’ versus ‘know how’; implicit versus explicit knowledge)
- the process of learning mathematics (memorising versus experiencing; teacher tells versus learner constructs: passive/active learning)
These may impact on practitioners’ views of what numeracy is and how it should be learned and taught.
- What is the history of your own relationship with mathematics and numeracy? You could capture this in a number of ways, for example:
- a chart or graph, e.g. plot confidence levels in mathematics against milestones or life experiences
- pictorial or diagrammatic form, e.g. flowchart, concept map or cartoon strip
- a blog or letter
- a recording (audio and/or visual)
- a collage.
- Is mathematics something that has been ‘done to you’ or is it a subject you’ve engaged with in a positive or fulfilling way? How has this been affected by context or life changes or other people? What numeracy practices do you engage in at home, at work, in class? How does your personal history with maths and numeracy impact on you now in your personal and professional life?
- Try this task with colleagues or peers and compare your results.
Attitudes include feelings and preferences about particular content or teaching practices. Common negative attitudes relate to a dislike of word problems, anxiety about algebra and discomfort in asking questions of a teacher (Ginsberg et al, 2006).
- How would you describe your own attitude to mathematics or numeracy?
- What sort of feelings do you experience when doing mathematics or numeracy?
- Do you have any personal preferences or dislikes about certain topics or learning activities or teaching approaches?
- Are these different to the sorts of learning activities or teaching approaches you use with other subjects? Why? Why not?
During his research on adults’ mathematical thinking and emotions, Evans (2000, p.179) found that:
Every single student expressed some emotion related to the doing of mathematics, or the use of numbers. Not only was anxiety expressed by many, as expected, but also confidence, pleasure, and sometimes dislike or anger.
Intense and short-lived emotions such as panic, joy or frustration are to be expected when we engage in numeracy activity that challenges us. Feelings of frustration during a mathematical activity might provide the impetus and resolve to re-engage with a problem until it is solved. Alternatively, we might panic and perform some calculation (however meaningless) just to have something to put down on paper, or simply stop work after the first unproductive attempt (Goldin, 2006). Many adults, (including teachers) link repeated negative emotional reactions to self-perceptions of incompetence, maths anxiety and feelings of lack of control (Tobias, 1978).
Implications for practice
Practitioners need to reflect on how their own affective responses may influence their understanding, confidence and engagement with mathematics and numeracy. If we are to support our learners, Ginsburg et al (2006) suggest practitioners need to develop positive attitudes, beliefs and emotions towards numeracy including:
- productive engagement in numeracy activity
- the expectation that mathematics and numeracy will make sense
- a commitment to problem-solving approaches
- persistence and perseverance when encountering false starts or other frustrations.
Think about an occasion where you have taught (or might teach) some numeracy as part of a lesson. Reflect on the following questions.
- Was your approach more learner-centred or teacher-centred? Was knowledge presented or discovered? Were tasks directed or open-ended? Did learners work individually or collaboratively?
- Did you approach teaching numeracy in the same way as you would your ‘normal’ subject specialism? Why/why not?
- Does your approach relate to your own views and experiences of what mathematics/numeracy is?
- What other factors do you think played a part in your choice of approach? Why?
The interrogative teacher
As well as reflecting in a balanced but critical way on their own mathematical identities, values and beliefs, Stone (2013) argues that practitioners also need to be able to critically interrogate the values and beliefs in their external environments too – at institutional and national level.
Successful and meaningful implementation of the National Numeracy Programme in Wales across subjects and phases will require practitioners to challenge views of mathematics, numeracy and its pedagogy as knowledge held only by ‘experts’. In turn, the idea of mathematical knowledge as absolute and unchangeable is also unhelpful as practitioners will have to work together and become empowered to identify and develop:
- purposeful numeracy practices within their own subject areas
- appropriate and effective learning and teaching approaches
- appropriate tools, procedures, texts and terminologies for their particular learners and specific learning contexts.
Absolutism – the belief that mathematics pre-exists human beings and is ‘discovered’ usually by ‘great mathematical persons’ (Lerman, 1990). It is unchanging, context free and universal, passed down through generations of teachers and learners.
Instrumentalism – the belief that mathematics is a process, a tool for solving problems rather than a single defined body of knowledge (Ernest, 1989; Skemp, 1989)
Fallibilism – the belief that mathematics is invented, a social construction like the rest of human knowledge (Ernest, 1989). Rather than being neutral and value-free, it has a social, historical and cultural context like other subjects.
Social practices – a view of numeracy or mathematics as practices we all carry out regularly in our own lives (Papen, 2005; Miller and Baker, 2001; Street et al, 2005). ‘School’ mathematics, university mathematics, numeracy for plumbers or nurses, ‘street’ maths are all examples of different ‘numeracy practices’.
Critical numeracy – a view that mathematical knowledge can empower individuals to participate fully in society as critically aware ‘users of numeracy’ and active citizens (Kerka, 1995; Benn, 1997; Gutstein, 2006)
More on ‘maths histories’ can be found in:
Coben, D. and Thumpston, G. (1995) Researching Mathematics Life Histories: A Case Study, in Coben, D. (comp.) Mathematics with a Human Face: Proceedings of ALM-2, the Second International Conference of Adults Learning Maths – A Research Forum 7–9 July 1995. London: Goldsmiths College, University of London in association with Adults Learning Maths – A Research Forum
Tomlin, A. (1999) A ‘democratic classroom’, but who speaks loudest/Research with basic mathematics students. In Coben, D. and van Groenestijn, M (Eds.) mathematics as part of Lifelong learning. Proceedings of the Fifth Internatiponal Conference of Adults learning Maths – A research Forum. London: Goldsmiths College, University of London in association with ALM. (online) (accessed 20 Sept 2013)
More on beliefs about the nature of mathematics and on how mathematics and numeracy are taught and learned can be found in:
Swan, M. (2006) Collaborative Learning in Mathematics: A Challenge to our Beliefs and practices. London: NRDC/NIACE.
Stone, R. (2010) ‘I, robot’. Free will and the role of the maths teacher – who decides how we teach? In Griffiths, G. and Kaye, D. (Eds) Numeracy Works for Life. Proceedings of the 16th International conference of Adults Learning Mathematics – A Research Forum. London: ALM and LLU+/London South Bank University. (online) (accessed 20 September 2013).
More on maths anxiety, negative attitudes and beliefs in pre-service teachers can be found in:
Beswick, K. (2008/2009) Influencing Teachers’ Beliefs About Teaching Mathematics for Numeracy to Students with Mathematics Learning Difficulties, in Mathematics Teacher Education and Development 2007/2008, 9, pp.3–20. (online) (accessed 28 September 2013)
Hawera, N. (2004). Addressing the Needs of Mathematically Anxious Preservice Primary Teachers. In Putt, I., Faragher, R. and McLean, M. (Ed.), Mathematics Education for the Third Millennium,Towards 2010.Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia Inc., held at Jupiter’s Hotel, Townsville, Australia, 27–30 June 2004 (pp. 287–294). Sydney: MERGA, Inc. (online) (accessed 20 September 2013).
Klinger, C. M. (2006) Challenging negative attitudes, low self-efficacy beliefs, and math-anxiety in pre-tertiary adult learners. In Horne, M. and Marr, B. (Eds.), Connecting voices in adult mathematics and numeracy: practitioners, researchers and learners. Proceedings of the Adults Learning Mathematics (ALM) 12th Annual International Conference, Melbourne, July, 2005 (pp. 164-171). Melbourne: Adults Learning Mathematics – A Research Forum & ACU National. (online) (accessed 20 September 2013).
Klinger, C. M. (2009) Passing it on: linking adult innumeracy to mathematics attitudes, low self efficacy beliefs, and math-anxiety in student primary teachers. In Safford-Ramus, K. (Ed.), A declaration of numeracy: empowering adults through mathematics education. Proceedings of the 15th International Conference of Adults Learning Mathematics, Philadelphia, USA, June 30 – July 3, 2008 (pp. 123–132). Lancaster, PA: Adults Learning Mathematics – A Research Forum. (online) (accessed 20 September 2013).
Peker, M. (2009) Pre-Service Teachers’ Teaching Anxiety about Mathematics and Their Learning Styles, in Eurasia Journal of Mathematics, Science & Technology Education, 5(4), pp335–345. (online) (accessed 20 September 2013).
Perry, B., Way, J., Southwell, White, A. and Pattison, J. (2005) Mathematical beliefs and achievement of pre-service primary teachers. In Clarkson, P., Downton, A., Gronn, D., Horne, M., McDonough, A. Pierce, R. et al. (Ed.), Building connections: Research, theory and practice. Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia. 2, pp. 625–632. Sydney: MERGA. (online) (accessed 20 September 2013).
Stables, A., Martin, S. and Arnhold, G. (2004) Student teachers' concepts of literacy and numeracy. Research Papers in Education, 19 (3), 345–364.
Taplin, M. (1998) Preservice teachers’ problem-solving processes. Mathematics Education Research Journal, 10 (3), 59–76. (online) (accessed 20 September 2013).
Uusimaki, L., and Nason, R. (2004) Causes underlying pre-service teachers' negative beliefs and anxieties about mathematics. In Høines, M. J. and Fuglestad, A. B. (Ed.), Proceedings of the 28thConference of the International Group for the Psychology of Mathematics Education. 4, pp. 369–376. Bergen: Bergen University College, ISSN 0771-100X. (online) (accessed 20 September 2013).
Benn, R. (1997) Adults Count Too: Mathematics for Empowerment. Leicester: NIACE
Dweck, C. S. (1999) Self Theories: Their Role in Motivation, Personality, and Development . Hove: Psychology Press, Taylor and Francis Group
Ernest, P. (1989) The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics Teaching: The state of the Art. London: Falmer
Evans, J. (2000) Adults’ mathematical thinking and emotions: A study of numerate practices. New York: Routledge Falmer
Ginsburg, L., Manly, M. and Schmitt, M.J. (2006) The Components of Numeracy. Cambridge MA: NCSALL [online] (accessed 20 Sept 2013)
Goldin, G. A. (2006) Aspects of affect and mathematical modeling processes. In Lesh, R., Kaput, J. and Hamilton, E. (Eds.), Foundations for the future in mathematics education curriculum. Mahwah, NJ: Lawrence Erlbaum Associates
Gutstein, E. (2006) Reading and Writing the World with mathematics: Towards a pedagogy for Social Justice. New York: Routledge
Kerka, S. (1995) Not Just a Number: Critical Numeracy for Adults. ERIC Digest No. 163 (online) (accessed 20 September 2013)
Lerman, S. (1990) Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal, 16(1) pp.53–61
Miller, K. and Baker, D. (2001) Mathematics and science as social practices: investigating primary student teacher responses to critical epistemology. Ways of Knowing Journal, 1(1) University of Brighton.
Papen, U. (2005) Adult Literacy as Social Practice. London: Routledge
Parsons, S. and Bynner, J. (2006) Does Numeracy Matter More? London: NRDC. (online) (accessed 29 September 2013)
Skemp, R. (1989) Prologue: relational understanding and instrumental understanding. In Skemp, R., Mathematics and Primary Education. London: Routledge. (online) (accessed 28 September 2013).
Stone, R. (2013) Attitudes, Beliefs and Teaching. In Griffiths, G. and Stone, R. (Eds.) Teaching Adult Numeracy: Principles and Practice. Berkshire: OUP/McGraw Hill
Street, B., Baker, D. amd Tomlin, A. (2005) Navigating Numeracies: Home/School Numeracy Practices. Dordrecht: Kluwer Academic Publishers
Swain, J., Baker, E., Holder, D., Newmarch, B. and Coben, D. (2005) ‘Beyond the Daily Application’: Making Numeracy Teaching Meaningful to Adult learners. London, NRDC. (online) (accessed 28 September 2013)
Tobias, S. (1978). Overcoming Math Anxiety. San Francisco: Houghton Mifflin.
TED talk on Maths Anxiety (external link)
Overcoming Maths anxiety (external link)