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Masters in Educational Practice: Numeracy learning pack

2

Understanding numeracy

2.6

Numeracy, literacy and language

 

Introduction

The acquisition, teaching, and learning of language and numeracy have often been treated as two separate areas of inquiry and practice (Gal, 2000). However, in everyday life, we experience numeracy, literacy and language as integrated rather than separate discrete subjects.

Indeed, it is difficult to think of a situation involving numeracy that does not also include aspects of literacy and language’ (Woolley, 2013, p.76).

Even when situations do not require numerical calculations, they may involve expressing an opinion based on interpreting statistical information, or decision tasks involving ideas of chance and uncertainty. Other tasks will involve numbers or quantitative statements embedded in text, e.g. forms, schedules, manuals, technical and financial documents, statistics in the media. The integration of these skill areas underlies the design of various large-scale surveys of numeracy and mathematical skills such as the International Adult Literacy Survey (IALS) and the design of some quantitative literacy tasks in the Trends in International Mathematics and Science Study (TIMSS) and PISA surveys.

Language of numeracy

Numeracy has its own language that uses ‘very specialised vocabulary’ (Newmarch and Part, 2007, p.19). For example:

Language of numeracy
Number Shape Data Using number
capacity centre column calculate
centimetres circle chart convert
compund cuboid cumulative consecutive

Source: adapted from Henderson (1998, p.109)

Some words can also have particular meanings in a numeracy context which are different from the way they are used in other everyday situations, e.g. difference, sum, average, similar, bar, table, prime.

Activity 2.14

1. Think about an ‘out of school’ scenario where numeracy activities take place (e.g. shopping).

List the words related to numeracy tasks within this situation.

What other words or phrases would be useful to know to carry out these tasks?  

For example:  discount, best buy, total, money, payment, credit, cash, budget, enough, add, subtract, multiply, divide, table: buy one get one free, half price, 1/3 off, voucher, supermarket, value, free, nutritional information on packaging, calories, signs on aisles, etc. (Woolley, 2013, p.77).

2. Think of a scenario where learners in your subject need to use numeracy within a task or activity.

What sort of numeracy language is used (e.g. in discussions, texts, diagrams, assessments)?

Which cause problems for your learners?

How do you help learners know how and when to use these?

What other context-specific words/phrases/diagrams are associated with these tasks in your own subject?

Being able to understand and use the wealth of language associated with formal and informal numeracy in and ‘out of school’ needs both linguistic and cultural knowledge relating to specific contexts. It is important not to assume that learners already have this explicit and implicit knowledge.

Language and conceptual understanding

Barton (2008, p.142) argues that ‘mathematics and language develop together’ so that numerical concepts are both explored and understood through written and spoken language.

The acquisition of language can affect the learning of numeracy either in terms of implications for a learner’s general developmental or due to the structure of the language. Counting in Welsh, for instance, supports the understanding of place value due to the constructs within the language. Professor Gareth Roberts explains in the following video clip.

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This advantage of language could be put to good effect where cross-curricular links support the learning and teaching of numeracy skills.

Activity 2.15

Read the second article ‘Linguistic influences on numeracy’ by Ann Dowker and Delyth Lloyd in the 2005 issue of Education Transactions (external link) which examines how the way numbers and arithmetical relationships are expressed in a language can influence children's arithmetical development.

  1. What are the six linguistic characteristics that Dowker and Lloyd argure are significant in mathematics and numeracy learning?
  2. What advantages and disadvantages might Welsh speaking learners experience in Welsh-medium and English-medium mathematics and numeracy settings?

Speaking and listening

Woolley (2013) suggests that many learners, not just English for Speakers of Other Languages (ESOL) learners or those with low literacy levels need opportunities to develop their language when learning numeracy. Learning to use and move between specialist mathematics ‘register’ and the way we talk about numbers in everyday life can be a challenge for everyone.

Research by Mercer and Sams (2006) suggests that the teacher is an important model and guide for learners’ use of language for reasoning. They found that providing children with guidance and practice in how to use language for reasoning enabled them to use language more effectively as a tool for working on maths problems together. They also observed that improving the quality of children’s use of language for reasoning together improved their individual learning and understanding of mathematics.

Woolley (2013) suggests that when learners speak to each other or the whole class about their understanding of a numerical concept there are a number of benefits.

  • Speakers can clarify and evaluate their understanding.
  • Learners begin to identify themselves as someone who ‘can do’ numeracy.
  • Other learners can compare spoken explanations with their own concepts.
  • Teachers can formatively assess understanding of concepts.
  • Classroom ethos promotes clear explanations that make sense, rather than expectation of immediate ‘right answers’.
  • Ownership and explanations of numerical concepts is shared between learners and teacher.

Activity 2.16

What activities could you set up to encourage learners to do more ‘numeracy talk’ within your own subject area?

 

Language of summative assessment

Most summative assessments which involve numeracy (explicitly or implicitly) rely almost entirely on reading and writing. This presents an additional barrier for many learners, especially, but not only those with lower levels of literacy or whose first language is not English. Wroe (2008) observes that:

One of the biggest difficulties my learners have is deciphering the language of the questions. Most of them are more than capable of ‘doing’ the maths but find they spend a lot of time trying to work out what is required.

According to Gal (2000, p.22), making sense of verbal or text-based problems that require learners to interpret quantitative data involves:

  • reading, writing, language comprehension and other literacy skills, and
  • ‘solid familiarity with the content of the task, conceptual understanding, and a critical stance, rather than only computational prowess’.

Woolley (2013) argues that the focus on ‘process skills’ such as representing, analysing and interpreting within functional mathematics and key/essential skills approaches place even higher demands on learners in terms of literacy and language. The ‘Developing numerical reasoning’ strand of the numeracy component of the National Literacy and Numeracy Framework (LNF) makes similar demands on learners as they are required to:

  • identify processes and connections 
  • represent and communicate 
  • review.

Challenges

The PISA framework also requires ‘real-world’ problem-solving or ‘mathematisation’ – ‘making assumptions about which features of the problem are important, generalising and formalising’. The problem can then be solved before a reverse process is used to make sense of the solution ‘in terms of the real situation’ (OECD, 2009). However, learners may need additional specific support to move from the language of everyday numeracy to formal mathematics register and back again. Some issues to consider are:

  • learners may be too unfamiliar with both the context and language of the problem to identify which information to value or ignore
  • learners may be unable to transfer their mathematical skills and numerical reasoning
  • learners may assume they won’t be able to complete a question because they don’t know enough about the context
  • ESOL learners can be stumped by not knowing a particular word, e.g. runway*
  • questions may assume shared cultural knowledge (Baynham and Whitfield, 2004; Cooper and Dunne, 2000 )
  • ‘real-life’ assessment problems may actually be quite unrealistic (Oughton, 2009)
  • learners may be unable to decipher ‘specialised command verbs, e.g. justify, calculate, illustrate, estimate.

*Abedi and Lord (2001) also reported that the discrepancy between performance on verbal and numeric format problems strongly suggested that factors other than mathematical skill contribute to success in solving word problems. Their research was based on a comparison between English as an Additional Language (EAL) learners and proficient English speakers concluding that unfamiliar or infrequent vocabulary and passive voice constructions affect comprehension for certain groups of learners.

Activity 2.17

Look at an example of a ‘real-life’ problem involving numeracy (from your own subject area, or a question from a past numeracy paper or TIMMS or PISA survey).

  1. What language and literacy barriers might this present to your learners?
  2. What shared cultural knowledge is assumed?
  3. What strategies might help overcome these barriers?

References

Abedi, J., and Lord, C. (2001) ‘Language Factor in Mathematics Tests’. In Applied Measurement in Education. 14(3), pp.219–234.

Baynham, M. and Whitfield, S. (2004) ‘Bilingual Students Learning in ESOL and Numeracy Classes: a contrastive study of classroom diversity’. In English for Speakers of Other Languages (ESOL) – case studies of provision, learners' needs and resources. NRDC, pp.70–91. (online) (accessed 30 September 2013)

Cooper, D. and Dunne, M. (2000) Assessing children’s mathematical knowledge. Buckingham, Open University Press.

Els De Geest (2007) Many Right Answers Listening in mathematics through speaking and listening. London, Basic Skills Agency. (online) Available from accessed 30 September 2013).

Dowker, A. and Lloyd, D. (2005). ‘Linguistic influences on numeracy’. Education Transactions B, pp.20–35. (online) (accessed 30 September 2013).

Gal, I. (2000) ‘The numeracy challenge’. In Gal, I. (Ed.), Adult Numeracy Development: Theory, research and practice (pp.9–31). Cresskill, NJ: Hampton Press.

Henderson, A. (1998) Maths for the Dyslexic: A Practical Guide. London, David Fulton Publishers.

Mercer, N. and Sams, C. (2006) ‘Teaching children how to use language to solve maths problems’ in Language and Education, 20(6), pp. 507–528. (online) (accessed 30 September 2013).

Newmarch, B. and Part, T. (2007) Number. London, NRDC. (online) (accessed 30 September 2013).

Organisation for Economic Cooperation and Development (2009) PISA 2009 Assessment Framework Key competencies in reading, mathematics and science. Paris: OECD. (online) (accessed 29 September 2013).

Oughton, H. (2009) ‘A willing suspension of disbelief?: ‘Contexts’ and recontextualisation in adult numeracy classrooms’. In Adults Learning Mathematics International Journal, 4(1) pp.16–31. (online) (accessed 30 September 2013).

Woolley, R. (2013) ‘Language and mathematics’. In Griffiths, G. and Stone, R. (Eds.) Teaching Adult Numeracy Principles and Practice. London, OUP Mc Graw Hill Education.

Wroe, G. (2008) ‘Is the Level 3 Numeracy test valid?’. In Numeracy Briefing, 14, pp.10–13.

Useful links

In Many Right Answers (external source) Els De Geest (2007) looks at how speaking and listening can be used as an effective tool to engage learners and develop their understanding and use of mathematics and numerical reasoning in collaborative problem solving. Six secondary mathematics teachers use practitioner enquiry to design, implement and reflect on a number of classroom ‘experiments’ using speaking and listening. Many of the concepts, ideas and discussions are likely to apply equally to primary teachers and post-16 practitioners.

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