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MEP learning pack

Masters in Educational Practice: Numeracy learning pack

3

Learning and teaching numeracy

3.1

Effective learning and teaching practices

Background

In 2011, Estyn produced a report on Numeracy for 14 to 19-year-olds (external link). Recommendations to improve numeracy provision in schools, colleges and work-based learning providers included:

  • ensure that numeracy is planned and delivered in relevant and practical contexts across the curriculum
  • on shared courses, ensure that learners’ prior numeracy skills are identified and the information transferred to the receiving provider
  • train staff to understand how to develop learners’ numeracy skills
  • provide support and resources in Welsh for Welsh-language learners
  • enter learners at an appropriately challenging level for essential skills qualifications and include evidence from subjects other than mathematics in
    portfolios of work.

In 2013, Estyn produced a baseline study into Numeracy in Key stages 2 and 3 (external link). The report observes that provision for numeracy is highly effective when practitioners offer ‘well-planned and imaginative opportunities’ for learners to apply and develop their skills across the curriculum (2013, p.4). However, the study also acknowledges that there is a particular training need in schools in Wales in order to develop teachers’ competency and confidence in teaching numeracy.

The Learning Wales website (external link) also highlights findings from international evidence-based research. These indicate that ‘what matters most’ is quality teachers and teaching supported by strategic professional development. Best practice is seen when teachers have a well developed knowledge of numeracy and its pedagogical principles and this underpins their teaching. Teachers can also achieve best practice through systematically employing a range of teaching methods, materials and learning tasks matched to the numeracy needs of the specific learners they are teaching.

 

Effective numeracy learning and teaching in the Foundation Phase

Pre-school practice and schematic learning

It is very important that pre-school practice has a focus on schematic learning that will provide a natural link into opportunities for numeracy to be developed and challenged.

Schemas are observed when a child participates in physical and creative activities. The language used will often indicate the type of schema that the child is exploring. The young brain makes thousands of links between cells every hour. The strongest links are those where the child is given an opportunity to repeat an activity over and over to establish a level of understanding. These opportunities are provided for through continuous provision. Children can return to the same activity and repeat their actions over and over until the brain establishes a neural pathway that supports a level of understanding.

The key in early years in developing numeracy is to be able to identify the type of play that is taking place so that appropriate questions are asked. Without understanding the context of learning in the child’s mind, we often ask the wrong type of questions and then misunderstand the level of comprehension when the child does not answer as we think he or she should. For example, a child that is developing trajectory schema (i.e. shows interest in straight lines, up and down, across and oblique) will often line up everything they play with. Their drawing and painting may also consist of lots of lines; they may follow the same route every time they go on a tricycle; they build long tracks and roads. They may well be playing with farm animals and line them up by mixing all the animals. Without realising that the focus is to create a line (early measurement), the practitioner may be tempted to intervene and suggest grouping the farm animals or even count them. This prevents the flow of dialogue and the child can present themselves as not understanding what the adult has asked for or suggested. When children are engaged in schematic play they will often display high levels of concentration and engagement in the activity.
Common schematic play that practitioners need to be aware of in order to develop numeracy is:

  • trajectory (straight lines, up and down, across and oblique)
  • connecting (measuring, length, quantity, fitting together, securing, properties of materials)
  • rotation (learning about speed, angles, forces, centrifugal forces, clockwise and anti-clockwise)
  • containing (size, volume, capacity)
  • enveloping/enclosing (area, perimeter, around and surround, length, estimation equivalence)
  • transporting (conservation of amount and number, capacity spatial awareness, direction, friction, forces).

(Athey, 2007)

Further reading

Carruthers, E. and Worthington, M. (2006). Children’s Mathematics (2nd Edition):  Making Marks, Making Meaning. London: SAGE publications.

The role of the adult

The role of the adult is crucial in developing numeracy through understanding how children learn best, hence the ratio that has been recommended for effective learning in the pedagogical approach in the Foundation Phase in Wales. If the role of the adult is to always work with individuals and groups of learners in a focused task session, key opportunities will be missed to engage in shared sustained thinking that will promote future independent thinking and learning (Welsh Assembly Government, 2008).

Through schematic play children make sense of the world around them and they then apply this understanding to activities that can be provided by the adult. What is very important to remember when teaching young children is that schema cannot be planned. The organisation of the environment is crucial in allowing the child an opportunity to demonstrate schema and for the adult to recognise this way of learning and enhance it by providing opportunities for further exploration and consolidation.

Activity 3.01

Read the following scenario.

It is observed that a child is continuously taking things inside and out. When playing in the home corner the child puts everything into the washing machine and then takes it all out repeating this action over and over. In the water tray the child continuously fills and empties containers (containing schema).

  • How would you further embed this learning process?
  • Could you provide an opportunity in the outdoor learning environment?
  • What early mathematical language might the adult introduce the learner to?

Now read about how Rogerstone Primary School used children’s schematic interests to deliver numeracy elements from the National Literacy and Numeracy Framework (LNF).

Effective teachers of numeracy in the early years

In 1999–2001 the ‘Early Numeracy Research Project’ carried out in Victoria, Australia, aimed to gain insights into effective numeracy practice in the first three years of schooling – ages 5 to 8.

The case studies revealed that effective teachers of numeracy in the early year:

  • Focus on important mathematical ideas and make this focus clear to the children.
  • Provide open-ended tasks which encourage the use of different strategies and allow for different outcomes.
  • Choose tasks that engage and involve children.
  • Use a range of materials and contexts to explore the same concept.
  • Grasp opportunities to develop knowledge, understanding and skills as they arise.
  • Make connections to prior learning and experiences.
  • Engage and focus children’s mathematical thinking through an introductory, whole-class/group activity.
  • Use a variety of individual and group teaching approaches.
  • Use a range of question types to probe and challenge children’s thinking and reasoning.
  • Avoid ‘telling’ children. 
  • Encourage children to explain their mathematical ideas and thinking, and evaluate others’ ideas.
  • Listen attentively to individual children.
  • Provide experiences which progressively build on children’s mathematical ideas and strategies.
  • Have high, but realistic expectations of all children.
  • Promote and value effort, persistence and concentration.
  • Draw out key mathematical ideas both during and at the end of learning and teaching activities.
  • Use a variety of assessment methods, including observation. 
  • Reflect on learning outcomes.
  • Modify planning as a result of assessment.
  • Believe that numeracy can and should be enjoyable.
  • Are confident in their own subject and pedagogical content knowledge.
  • Demonstrate pride and pleasure in individuals’ success.

Activity 3.02

1. Do you consider these themes only to be relevant to early years teaching and/or numeracy teaching? All? Some?

Identify an aspect that you feel that you could develop in your own practice. Reflect upon this and how you might go about this in your professional journal.

2. Doig, McCrae and Rowe (2003, pp.22–23) identify the following effective numeracy practices in the early years.

  • The involvement of parents/carers.
  • An early assessment of what children know and can do.
  • A clear focus on concepts and thinking.
  • An emphasis on valuing the strategies children use. 
  • Encouraging children to share their strategies and solutions.

They also suggest that ‘sharing ideas by parents and teachers about what and how [numeracy] should be taught could reduce the gap between the home and school culture’ (2003, p.23).

Consider this statement in the light of your own teaching context.  How much engagement is there with parents or carers about the teaching of numeracy (i) at a whole-school level (ii) with individual teachers?

Do you agree that parents and carers should be involved in discussions about how numeracy should be taught? What might need to happen for such conversations to take place?

Ofsted’s survey into successful mathematics practice (2011, p.6) identifies that in order to develop a secure foundation in use and understanding of the four number operations that the following elements are crucial.

  • Practical, active learning experiences within the early years.
  • The development of mathematical language and mental mathematics.

Within the ‘Mathematical Development’ guidance (Welsh Assembly Government, 2008, pp.6–7) for the delivery of the Foundation Phase in Wales, it states the importance of activities which promote problem-solving and encourage children to use the language of mathematics. Recounting the steps taken to solve a problem will support the embedding of the mathematical process and lay the groundwork for progression to recording mathematics.  

Activity 3.03

View the exemplification materials for Year 3, Christening. This focuses upon the ‘estimate and check’ element of the ‘Using number skills’ strand of the LNF. Which ‘developing reasoning skills’ does Daniel also demonstrate?

Consider your own Foundation Phase setting. What learning experiences or contexts for learning do you provide which promote problem-solving and children’s articulation of the steps they have taken to solve a problem? How else might you support skill progression so that learners are able to meet the Year 3 expectations of the LNF?

Further reading

Bruce, T (2001). Learning through play: Babies, Toddlers and the Foundation Years.  London: Hodder and Stoughton.

Doig, McCrae and Rowe (2003) provide useful suggestions for the development of numeracy at home, pre-school numeracy and numeracy in the early years of school in ‘A good start to numeracy’ (external link).

Glossary

Schemas – patterns of repeated behaviour which children use to explore and express their developing ideas and thoughts through play and exploration. Clusters of schemas later develop into concepts (Athey, 2003).

Useful links

Schematic Play (external link): A leaflet for parents and carers produced by Salford Local Authority.

Learning to count: Alexandra Nursery School, OFSTED 2013 (external link): This inspection report shows how a nursery devised a structured teaching programme to develop children’s understanding of words and phrases. There is a strong emphasis on counting and developing the concept of number through song, alongside adult-led sessions and a wide range of linked experiences indoors and out.

Taking problem solving, reasoning and numeracy into the great outdoors: Farley Nursery School, OFSTED 2012 (external link): This inspection report highlights how children at Farley Nursery School spend much of their day exploring outside where imaginative activities are planned to develop their problem-solving, reasoning and numeracy skills. Using the outdoor space gives children excellent opportunities to explore concepts such as distance and height, which are more limited indoors.

Effective numeracy learning and teaching in Key Stage 2

Within its study of Year 5 classroom practice in ‘excellent’ schools, drawn from a large-scale research study that has followed the progress of over 3,000 children since 1997, Siraj-Blatchford et al (2011) identified that there are significant differences in the strategies used by teachers in excellent, good and poor schools.

In excellent schools, Year 5 teachers:

  • have organisational skills
  • establish a positive classroom climate
  • personalise their teaching
  • use dialogic teaching and learning
  • make more frequent and better use of the plenary.

The study which drew on 125 primary schools identified few differences in the extent to which ‘dialogic’ teaching occurred in the three ‘groups’ of schools (i.e. ‘excellent’, ‘good’ and ‘poor’). However, in numeracy, teachers in excellent schools received the highest ratings on using dialogic learning and teaching. This was as a result of their use of analysis in mathematics and the depth of their learners’ knowledge and understanding. They also rated more highly on mathematics discussion and communication, and on sharing maths ‘authority’ (Alexander 2011 cited in Siraj-Blatchford et al, 2011) – meaning that the learners, and not just the teacher, can be the leaders and experts on mathematical questions and concepts.

Activity 3.04

Reflect upon your own numeracy teaching, considering specific examples.

  • Do you routinely use ‘dialogic teaching’? Is this a genuine, ‘two-way’ process?
  • Does this occur in ‘maths’ lessons and in lessons across the curriculum which develop numeracy skills?
  • Do you share maths ‘authority’ (Alexander 2011) with your learners? If so, how? 
  • How do you use the ‘plenary’ in numeracy teaching? Does this ‘deepen’ learning (i.e. provide opportunities for further discussion; the exploration of issues in more depth; extension and application of learning to other contexts) or does it focus upon the ‘checking’ of answers?

Activity 3.05

Read the following case study of a primary school in Caerphilly local authority

Primary school – Using an ‘app’ to develop effective numeracy learning practices

Teachers in this school use mobile technology to enhance the learning and teaching across the range of subjects. An ‘app’ which consists of a digital whiteboard tool with sound and screen recording functions provides learners with the opportunity to capture their mathematical thinking and methods, recording these in a variety of ways.

Learners work as individuals, in pairs or small groups to create their own still pictures or videos (records of learning) using the onscreen tools on their tablet devices. These can then be controlled by the teacher’s own tablet device, allowing all learners to view the same screen. This supports ‘dialogic’ teaching (Alexander 2010) with learners engaging in discussions about problem-solving strategies, methods used and skills developed, both during activities and in the final plenary. Such work is also often saved to a secure location and revisited at a later date. This supports formative assessment practices and helps to build a profile of individual learners’ numeracy skill development.

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Which skills in the ‘Developing numerical reasoning’ strand of the LNF could be developed through such an approach? How does this practice relate to Siraj-Blatchford et al’s (2011) study?

Further reading

Read Alexander’s Dialogic Teaching Essentials (2010) (external link) which is adapted from Towards Dialogic Teaching: rethinking classroom talk (2008)

Alexander, R.J. (2008) Towards Dialogic Teaching: rethinking classroom talk (4th edition)

Read the full report on Effective Primary Pedagogical Strategies in English and Mathematics in Key Stage 2 (external link) by Siraj-Blatchford et al (2011) for the Department of Children, Skills and Families.

Glossary

Dialogic teaching (external link) – ‘Dialogic teaching is an approach to teaching which in a highly disciplined fashion harnesses the power of talk to stimulate and extend pupils’ thinking and advance their learning and understanding’ (Alexander, 2013).

Useful links

Playing with numeracy: Inch View Primary and Tulloch Primary (external link): This case study describes a project involving two primary schools in Perth and Kinross. Learners had to design and make a new numeracy board game as well as plan, monitor and evaluate their own learning. Audio recordings of learners, class teachers and numeracy support staff are included.

The Allotment Project: St Joseph’s Primary School (external link): This case study with video clips shows how a Year 6 teacher made concrete links for children between numeracy skills and the outdoor environment.

Effective numeracy learning and teaching in Key Stages 3 and 4

Learners develop their numeracy skills when they can see the relevance of what they are doing which is why it is important that the context for the numeracy skill is appropriate and realistic, as discussed in Topic 2, ‘Understanding numeracy’. The skills they learn in maths lessons should be recognisable and transferable to other areas of the curriculum and all teachers should be confident in their own numeracy skills to support this approach.

The Scottish Government’s Numeracy Across Learning: Principle and Practice (external link) states that:

‘A rich and supportive learning environment will support a skilful mix of a variety of approaches, including:

  • active learning and planned, purposeful play
  • development of problem-solving capabilities
  • developing mental agility
  • frequently asking children to explain their thinking
  • use of relevant contexts and experiences, familiar to children and young people
  • using technology in appropriate and effective ways
  • building on the principles of Assessment is for Learning, including understanding the purpose and relevance of the activities
  • both collaborative and independent learning
  • making frequent links across the curriculum, so that concepts and skills are developed further by being applied in different, relevant contexts
  • promoting an interest and enthusiasm for numeracy.’ (p.2)

Activity 3.06

Identify aspects of your own subject that require numeracy. How can you highlight this to the learners in a way that supports and develops their numeracy skills?

Useful links

Whole-school dedication + innovation = better numeracy skills: Ysgol Gyfun Gymraeg Bro Myrddin, ESTYN 2011 (external link): This inspection report highlights how a secondary mathematics department led a school numeracy training day to assess provision for numeracy in all subject areas. They made plans to cover missing provision and focused on transfer of skills from one subject to another. Numeracy is now embedded in all subjects and standards in numeracy-based sections of mathematics GCSE have improved.

In the Doghouse', a numeracy across learning project: Deans Community High School (external link): This case study relates to a collaborative, interdisciplinary project undertaken within the mathematics and craft design and technology (CDT) departments in Deans Community High School, Livingston, Scotland.

Co-operative learning activities: an active approach to teaching numeracy: Our Lady’s High School (external link): This case study focuses on the use of cooperative learning to promote an active approach to teaching numeracy. Video clips of five activities used with a range of learners are shown.

Effective numeracy learning and teaching post-16

Many young people in further education come with poor experiences of school mathematics and a lack of confidence and enthusiasm to improve even when mathematical skills and numerical reasoning are key components of their chosen academic or vocational subjects.

In Tackling the challenge of low numeracy skills in young people and adults (external link) OFSTED (2011) evaluated numeracy programmes for post-16-year-olds in 59 providers in England. These included colleges, independent training providers, local authority providers of adult and community learning, prisons and Probation Trusts.

The report identified common features of effective numeracy learning and teaching such as:

  • developing learners’ ability to tackle numeracy-related problems by setting them in purposeful contexts:

Tasks should be accessible, extendable, encourage decision-making, promote discussion, encourage creativity, and encourage ‘what if’ and ‘what if not’ questions (Ahmed, 1987). Learners often find it difficult to generalise and transfer their learning to other topics and contexts. Effective teachers make connections and build bridges between ideas (Askew et al, 1997)

  • showing learners how to build on their previous knowledge and skills to develop their understanding:

This means developing formative assessment techniques and adapting our teaching to accommodate individual learning needs.

  • providing opportunities for learners to work out the most appropriate approaches to problems individually and with other learners:

Activities are more effective when they encourage critical, constructive discussion, rather than argumentation or uncritical acceptance (Mercer, 2000).  Shared goals and group accountability are important (Askey and Wiliam, 2005)

  • encouraging learners to tackle their misconceptions by analysing incorrect answers:

Learning activities should expose current thinking, create ‘tensions’ by confronting learners with inconsistencies, and allow opportunities for resolution through discussion (Askew and Wiliam, 1995)

  • developing learners’ conceptual understanding of numeracy through activities which helped them reach the stage where they could explain why a specific method worked:

Often learners are more concerned with what they have ‘done’ than with what they have learned. It is better to aim for depth than for superficial ‘coverage’ (Swain et al 2007)

  • enabling learners to apply mathematical techniques in their training, at work or in their personal lives.

Learners from these successful sessions said that they could see how numeracy related to their careers or everyday lives and were motivated to put in the effort needed to become more adept at tasks they had previously preferred to avoid.

In contrast, learning in the weaker sessions:

  • lacked variety
  • was broken up into the acquisition of disparate mathematical skills, often involving repetitive exercises
  • often involved memorising arbitrary rules and replicating steps in a method, often without understanding
  • did not encourage learners to make connections between what they had learnt and to draw on their existing knowledge and understanding in solving realistic problems (i.e. related concepts often remain unconnected such as division, fractions and ratio; percentages, decimals, fractions and probability; decimals, measures and scales).
    (Ofsted, 2011)

Activity 3.07

Look at pages 19 and 20 of the Mathematics Matters Final Report (2011) (external link).The principles for effective teaching listed here build on extensive research and discussions within the mathematics education community.

  1. Compare these principles with ideas for effective numeracy teaching identified by Ofsted (2011) (external link) and Estyn (2011) (external link)
  2. Which principles do you agree with? Why?
  3. How do you/might you use them within your own learning and teaching to support numeracy learning?
  4. Which principles would you find harder to implement? Why? 
  5. Are there any other principles you would add?
  6. Are there any principles, commonly held by teachers that are positively unhelpful for supporting numeracy learning? If so, then what are they? 
  7. Identify any continuous professional development (CPD) you would like as a result of this activity.

Case studies in post-16 settings

For most learners, successful achievement of Essential Skills Wales Application of Number (external link) is also required to gain an overall qualification. In many subject areas however, there may be no single naturally occurring or realistic real-world project or even small number of projects likely to evidence all the specified skills and competences within the standards. According to Hall (2013), teachers can end up adopting a ‘bottom-up’ model of teaching where mathematical topics are tackled discretely out of context and where the vocational applications of numeracy are often limited and unconvincing to students.

Hall (2013) describes a number of practitioner research projects being carried out at a further education college in Wales. The case studies demonstrate how teachers on vocational courses can develop more ‘top down’ strategies that allow learners to experience realistic numeracy problems and in the process to further develop their mathematical skills. Students progress from tasks set by the teacher, through increasing student involvement in the solution of real world problems, to totally independent project work in engineering, construction, computing, and environmental science courses.

Special subject: construction students who had been studying heat losses from buildings investigated the topic further through a quantitative project looking at the effects of double glazing of windows, cavity insulation of walls, and insulation of the roof space.

Investigation report: students training in outdoor pursuits have found that the time calculations for expeditions in the mountainous area of North Wales using Naismith’s Rule are very inaccurate. Using actual times and relating these to the nature of the terrain, they are attempting to develop a more accurate journey time formula.

Paper discussion: computing students were asked to model an epidemic of a non-fatal illness such as influenza. They were provided with resources from books, journal articles and the Internet which allowed them to teach themselves the necessary quantitative techniques for solving the problem.

Mini scientific research: engineering students investigated the motion of a car passing over a speed hump, in response to the springs and shock absorbers of the car suspension system.

In addition to student motivation, Hall (2013, p.10) observes that improvements have occurred in:

  • use of specialised mathematical vocabulary
  • the combined use of numerical and algebraic methods in problem solving
  • abstract reasoning
  • a deeper level of understanding of the mathematics used in problem solving.

Activity 3.08

How might you adopt a ‘top-down’ approach to help learners experience realistic numeracy problems in your own subject area? What mathematical skills or competences might they develop?

Further examples of good practice

Teaching and Learning Measures (external link): This is an online resource that provides teaching materials related to the subject of 'measures'. It also provides samples of the data that came out of this 20 month research project which aimed to 'establish the features of successful learning and teaching of measurement', with a focus on entry levels of the curriculum.

Liverpool Community College Case study – measuring for a purpose (external link): A number of video clips feature learners developing essential skills through planning a production, including designing and building a stage set as part of their BTEC National Award in Performing Arts (QIA Teaching and Learning Programme).

Effective numeracy support that makes a difference: New College Durham, Ofsted, 2013 (external link): Many students joining New College Durham have weak numeracy skills and an ingrained fear of mathematics. This example shows how the college has developed a flexible system of support that has proved to be highly successful in building students’ confidence and raising their levels of numeracy.

It all adds up: Ysgol Gyfun Gŵyr, Ofsted, 2012 (external link): Staff developed numeracy-based activities that were relevant to the experiences of learners in the sixth form. They held weekly tutorials for learners to research buying a car resulting in learners improving their skills in the application of number.

Activity 3.09

Look at some of the video clips on Maths in Work (external link) and Workplace Maths (external link).

How might you use some of these ideas to support and develop numeracy within your own learning and teaching?

The use of calculators

Learners need to be familiar with certain technologies available to them as this is an ever-increasing technological society. However, it is not good practice for learners to rely solely on such technology to the point where their skills diminish and they become complacent. It is important that learners develop sound numeracy skills initially and then use calculators to enhance their learning.

The most common shortcomings in learners’ numeracy skills identified in the report on Improving numeracy in key stages 2 and key stage 3 (Estyn, 2010), included too many learners (in Key Stage 3) who: 

  • cannot estimate the results of written or mental calculations or reflect on whether their answers are reasonable; and 
  • use calculators for simple calculations, where a mental or written method would be more appropriate. (p.9)

This shortcoming is recognised and within the LNF there is the expectation that from Year 3 upwards learners should be able to:  

. . . choose an appropriate mental or written strategy and know when it is appropriate to use a calculator. (Developing numerical reasoning strand)

In the introduction to the National Numeracy Strategy, it is suggested that this 'powerful and efficient tool' be used to make use of real data across the curriculum and it states how it can 'offer a unique way of learning about numbers and the number system, place value, properties of numbers and fractions and decimals'. The question remains of how best to do this and hence 'enable more ambitious exploration of numbers to be undertaken' (National Numeracy Strategy Framework, Department of Education and Employment, 1999, p.8).

The Center for Implementing Technology in Education (CITEd, 2007) reported that the use of calculators can benefit all learners when they engage in higher-order thinking such as solving problems, exploring patterns, conducting investigations, and working with real-world data. The use of calculators can also give greater access to those with learning disabilities who might otherwise be unable to participate in these engaging activities. Thompson and Sproule (2000) created a decision-making flowchart on whether or not to allow the use of a calculator.

Calculator decision-making flow chart (Thompson and Sproule, 2005)
Calculator decision-making flow chart (Thompson and Sproule, 2005)
Calculator decision-making flow chart (Thompson and Sproule, 2005)

Returning to the point that learners need to develop sound numeracy skills before using calculators, this is essential, as statutory tests require them not to use a calculator, e.g. end of Key Stage 2 tests, the National Numeracy Tests, GCSE Mathematics.

References

Alexander, R. (2008) Towards Dialogic Teaching: rethinking classroom talk (4th edition). York: Dialogos.

Athey, C. (2007) Extending thought in young children: A parent-teacher partnership (2nd edition). London: Sage Publications.

Center for Implementing Technology in Education (CITEd) (2007) Getting the Answer: Calculators Help Learning Disabled Students Get the Concepts. (accessed 3 October 2013).

Doig, B., McCrae, B and Rowe, K. (2003) A good start to numeracy: Effective numeracy strategies from research and practice in early childhood. Canberra: Commonwealth Department of Education, Science and Training. (accessed 3 October 2013).

Department for Education and Employment (1999). National Numeracy Strategy Framework. Suffolk: DfEE publications.

Estyn (2011) Numeracy for 14 to 19 year olds. Cardiff, Estyn. (online) (accessed 29 September 2013).

Estyn (2012) Numeracy in key stages 2 and 3: a baseline study. Cardiff, Estyn. (online) (accessed 29 September 2013).

Hall, G. (2013) Integrating Real-World Numeracy Applications and Modelling into Vocational Courses. In The Korean Society of Mathematical Education Proceedings of the 2013 International Conf. on Math. Edu.on Creativity & Giftedness. (online) (accessed 29 September 2013).

NCETm (2011) Mathematics Matters Final Report. NCETm (online) (accessed 29 September 2013).

OFSTED (2011) Tackling the challenge of low numeracy skills in young people and adults. Manchester, Ofsted (online) (accessed 29 September 2013).

Siraj-Blatchford, I., Shepherd, D.L, Taggart, B., Sammons, P. and Sylva, K. (2011) Effective Primary Pedagogical Strategies in English and Mathematics
in Key Stage 2: A study of Year 5 classroom practice drawn from the EPPSE 3-16 longitudinal study
. London: Department for Children, Schools and Families. (accessed 27 September 2013)
.

Thompson, T., and Sproule, S. (2005). Calculators for students with special needs. Teaching Children Mathematics, 11(7), 391–395.

Welsh Assembly Government (2008). Learning and Teaching Pedagogy. Cardiff: Welsh Assembly Government.

Welsh Government (2010) Essential Skills Wales Application of Number. Cardiff, Welsh Government. (online) (accessed 29 September 2013).

 

Useful links

An article by Clare Green, Calculating the Difference (external link), which discusses the use of calculators in the English primary classroom.

This Numeracy booklet (2006) summarises key messages and themes from NRDC research and development work in numeracy in post-16 compulsory education.

This Embedded teaching and learning booklet (2006) summarises the key messages from NRDC research and development activity that explores the potential benefits of embedding numeracy (as well as literacy and language and in vocational programmes).

Coben, D., Newmarch, B. and Rhodes, V. (2007) ‘Bestimation’: Using basic calculators in the numeracy classroom. NRDC, London. (online) (accessed 25 September 2013).

This report looks at how the imaginative use of calculators can enhance teaching and learning in adult numeracy classes. It suggests a range of activities to develop estimation and problem-solving skills, providing learners with opportunities for self-directed and self-paced learning.

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. NRDC, London. (online) (accessed 25 September 2013).

This report investigates approaches to the teaching of numeracy, aiming to identify the extent of learners' progress, and to establish correlations between this progress and the strategies and practices used by teachers.

Cara, O., Casey, H., Eldred, J, Grief, S., Hodge, R., Ivanic, R., and Jupp, T. (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. NRDC, London. (online) Available from http://nrdc.org.uk/publications_details.asp?ID=73#  (accessed 25 Sept 2013).

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 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.

The Education Scotland Sharing Practice website (external link) provides a number of case studies of how some schools in Scotland are developing numeracy across the curriculum. A range of video clips and support materials are included.

Activity 3.10

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