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Masters in Educational Practice: Numeracy learning pack

3

Learning and teaching numeracy

3.4

Planning for learning

The National Literacy and Numeracy Framework (LNF) guidance identifies that ‘whole-school’ planning is necessary for effective implementation of numeracy learning and teaching and the LNF is designed with differentiation and progression in mind (Welsh Government, 2013). These two features are important for individual schools but also for clusters of schools, so that transition across phases is a smooth and coherent process.

Skills development

The teaching of numeracy skills falls into two categories: procedural and reasoning, as reflected in the National Numeracy Tests. The procedural aspect would generally be considered the domain of the mathematics department (in a secondary school) and that of practitioners delivering mathematics lessons in primary schools. However, as part of a whole-school planning approach, the methods and timing of the skills need to be consistent and supported across the curriculum. For example, the numeracy skills needed in science in Year 8 must be consistent with the procedural mathematics skills in Year 8. The reasoning aspect can be contextualised and embedded across the curriculum, but learners need to be aware that the skills are transferable.  

Estyn emphasises the importance of coherent whole-school action planning and consistency in approach in order to develop learners’ capabilities in numeracy:

Too often, there is no agreed, whole-school approach to building pupils’ numeracy skills or to performing basic calculations. This leads to a lack of consistency in using numeracy skills across classes and departments that confuses pupils (2013, p.4).

The methods used in cluster primary schools, if consistent, can lead to continued use in the teaching at secondary schools. This approach also supports teacher assessment standardisation and moderation processes and effective transition from Key Stage 2 to Key Stage 3. At present, Estyn identifies that very few primary schools pass on information about learners’ standards in numeracy to secondary schools, although they generally transfer information about standards in mathematics (2013, p.4).

Progression of skills in the LNF

Within the National Literacy Programme (NLP) and National Numeracy Programme (NNP), progression is identified from early precursor skills, which are described in detail in the Routes for Learning routemap (Welsh Assembly Government, 2006), and into the LNF’s Routes to literacy and Routes to numeracy. The columns in the LNF show how learners’ skills are refined and augmented as they progress towards the expected standards for Reception. Progression is then described through the Foundation Phase into Key Stage 2 and Key Stage 3.

Within the LNF some skill elements do not emerge until a later stage. In such cases, the relevant cells in the LNF are empty to show this. Skills development, as described by the LNF, should be viewed as a continuum and not as a series of discrete skills to be learned and demonstrated each year from the age of 5 to 14. Progression is cumulative and each element/aspect assumes that the elements/aspects in previous years’ expectations have been achieved and consolidated.

Progression through the stages is demonstrated by an ability to develop and demonstrate increasing competence in literacy and numeracy skills. The expectations are essentially concerned with developing and recognising a learner’s ability to select and apply literacy and numeracy skills in ways that are appropriate to each context.

Within the context of the NLP and NNP, progression is defined as:

. . . increasing the breadth and depth of learning at each stage of development as well as providing greater challenge for learners.

(Welsh Government, 2013)

Consolidation involves practising a skill in a variety of contexts – showing increasing capability of applying the skill to more unfamiliar situations and requiring less support and direction.

The LNF describes the fundamental skills of literacy and numeracy which should be developed across the curriculum and sets out broad expectations for progression in these skills with its yearly expectations. However, it is important to recognise that ‘progress’ will not necessarily be ‘linear’ and individual learners will progress with different skills at different rates. The LNF offers opportunities for learners to practise, consolidate and extend learning in these transferable skills.

Progression within the LNF may therefore occur:

  • within individual outcome statements
  • through links between elements (or aspects) within an individual strand
  • through links between elements (or aspects) across strands.

At all points, progression will require careful planning and monitoring of next steps.  

Activity 3.21

Consider the following statements provided within the Workshop 3: Curriculum planning for progression materials on the LNF.

Statements provided within the Workshop 3: Curriculum planning for progression materials on the LNF.
Learners demonstrate the use of the skill with increasing independence. Learners recognise the skill. Learners can follow instructions to perform the skill.
Learners can replicate the skill in a similar context. Learners can link and transfer the skill to other contexts. Learners demonstrate the use of the skill with more confidence.
Learners demonstrate the skill in less time. Learners can use the skill to take forward their learning. Learners can apply the skill in a variety of contexts.
Learners identify the appropriate skill for the task.


Now take one of the following year group expectations from the LNF and consider how you would design learning opportunities for a learner to ‘progress’ in this numeracy skill.  What opportunities for ‘consolidation’ would you provide?

Next steps and differentiation

‘Next steps’ can be considered as a series of small improvements which a learner can make in order to ‘close the gap’ towards successive expectations in skills development described by the LNF. Within its ‘Curriculum planning guidance’ (2013) for the LNF, the Welsh Government states:

In planning effective learning opportunities, it is vital that next steps are considered not in terms of what learners can/can’t do reliably and consistently but in terms of what they need to do next in order to make progress. Thus ‘next steps’ describe improvements learners need to put into action in order to make progress. These are most effective in supporting progression when they provide clear direction for learners, specifically identify where and how improvements can be made, and are generated in collaboration with the learners themselves (p.9).

It is important to note that next steps to improvement will often be within or between statements in the year group expectations, rather than a direct jump from one statement to the corresponding one in the following year group. By increasing the complexity and demand or changing the context (from familiar to less familiar) and/or the level of independence required, the learner can make progress, consolidate and apply the skill across the curriculum. This is how ‘differentiation’ using the LNF should work.  

The LNF is designed so that the year group below and the year group above can be used as an indicator of skill level in comparison to the school year of the learner.  Expectations within the LNF reflect the need to have high expectations of learners and Year 6 statements are purposely aligned more closely to national curriculum Level 5 expectations than Level 4. Differentiated tasks can allow for the skills development across the year groupings. For example, more able learners being given tasks for their age-equivalent level, rather than the year group expectations. Age equivalence is identified and used as a measure of attainment in the standardised scores of the National Reading and Numeracy Tests. Extension expectations are provided for more able and talented learners who may be working above Year 9 expectations.  

Progression of numeracy skills within the Foundation Phase should be planned carefully based on the Foundation Phase: Framework for Cchildren’s Llearning for 3 to 7-year-olds in Wales (Welsh Assembly Government, 2008), stages of child development (Welsh Assembly Government, 2008) and the LNF. The LNF focuses on year group expectations, but using the cognitive stages of development in conjunction with the LNF will support the development of appropriate skill application for individual learners.

When setting challenging tasks to progress numeracy for learners across all age phases, these should aim to:

  • introduce
  • consolidate
  • apply and
  • progress specific numeracy skills.  

The LNF Curriculum planning guidance (Welsh Government 2013) emphasises that each learner will be at different points in each skill.  Therefore, the choice of task or learning opportunity is crucial to success.

Activity 3.22

Routes to numeracy and Foundation Phase

Within the Curriculum planning guidance, Welsh Government identifies that effective planning for progression will:

  • be coherent
  • be consistent
  • have a clear structure for skill development (2013, p.18).

Use the criteria provided on pp.18–19 of the Curriculum planning guidance to evaluate current planning practices for numeracy in your school. In particular, consider the following questions.

  • Are problem-solving tasks which allow learners to practise and demonstrate a number of numeracy elements within the same task provided?
  • Is differentiation (through questioning, structures, flowchart templates, etc.) appropriately planned for to support learners’ next steps as well as ensuring sufficient stretch and challenge for more able and talented learners?

Key Stage 2

1.  View the exemplification material, ‘Making honey cakes’ (Year 4).

Read this example of how numeracy can be developed through the context of the history curriculum. Consider how else a teacher might differentiate this task to meet the needs of all learners.  

  • Which numeracy skills might be further progressed? How?
  • Can you identify another opportunity within this history topic in which learners might consolidate or apply the skills progressed here?
  • How else might they progress these numeracy skills across the curriculum?

2.  Examine this example of medium-term planning by a Year 3 teacher. The teacher has mapped how skills from the LNF (‘Using data skills’ strand) will be progressed during the year:

  • Does this planning support the progressive development of learners’ numeracy skills across a range of contexts?  
    What additional information would need to be provided at the ‘short-term’ planning stage for the numeracy skills identified here?

Key Stage 3

Study the attached document which is an ‘early’ draft of curriculum planning for Year 8 from the Geography department of Llantwit Major School. Consider how these subject teachers are using the LNF as a planning tool.

Contextual learning

It is essential that learners progress through appropriate stages of development in order to apply numeracy skills that relate to everyday experiences. It is essential that the opportunities provided are within the learner’s experiences. Word problems and standardised test items are designed to approximate real situations, but when they are used in educational settings, they are generally structured so that they have only one correct answer (Ginsburg  2006).

Cognitive aspects of learning support the development of numeracy when addressed in situations that allow the learners to transfer skills and knowledge that relates directly to their school, home, work and community life.

(Welsh Government, 2012).

Continuous and enhanced provision within the Foundation Phase (for example: role play, construction, sand, water, malleable, outdoor, ICT, workshop, block play) allow for these opportunities to take place in a non-threatening environment and reinforce the experiences that each learner might have had. Role play areas that the learner has no knowledge or experience of, for example, will lead to inconsistency of skill development. This experience may not necessarily come from home, but can be provided by the school in the form of an external visit at the beginning of a topic – e.g. a Year 1 visit to a travel agent’s.

Learners are not always given the opportunity to transfer the skills they are developing in Mathematical Development sessions relating to money, addition, subtraction, multiplication and division. Through role play they can practically use and apply these taught skills and understand the purpose for the learning process. Learners will only transfer knowledge and understanding if planning for these opportunities occurs.

As a further example, construction provides opportunities for learners to practically create and manipulate three-dimensional objects and allow their thought process to become concrete. It is essential that opportunities are provided for child-initiated learning to take place. When learners are given the freedom to engage in constructive play that inspires without restriction, many opportunities are provided to apply and embed numeracy strategies. For example, constructing a bridge that can take the weight of a car; building towers using construction blocks and identifying which tower is the tallest; or building a hotel (after experience of a holiday) thinking about capacity, or the number of floors or windows.

Through block play learners are able to sort, match, compare, tessellate and count. By providing a stimulus, without being too prescriptive, the learner is able to develop numerical reasoning at an appropriate stage of development as well as ensure progression of identified skills – e.g. using measuring skills:

Nursery: Free play building towers that support small world play.
Reception: Using comparative language when building structures.
Year 1: Build structures with non-standard specifications that link to a topic or theme. Evaluate and modify the structure.
Year 2: Design and build a bridge that can hold a given weight. The design will incorporate specific measurements.

Without specifying the type of structure or bridge allows the children to think, reason and research. They can select appropriate equipment and resources as the activity is open- ended and use every day mathematical language to talk about their own ideas and choices. The practitioner can observe the targeted skills, as well as any other skills the children might have demonstrated as a result of the open-ended nature of the task.

Activity 3.23 (Foundation Phase)

  • Read the following case study of how numeracy is developed through enhanced and continuous provision in a Foundation Phase setting. Identify which skills from the numeracy elements of the LNF might be consolidated, progressed or extended through these opportunities.

Case study – Numeracy through role play (The local grocer’s shop), Milton Infants’ School

Using real money from an early age is crucial. By three years of age most children will have had experience of handling coins in their home environment (e.g. money for birthdays, a relative visiting and leaving money as a treat, festivals (EID/Christmas).

Children will have had an opportunity to visit a shop and spend money; therefore, by using real coins the child immediately knows what the money is for and that they can use it to purchase and exchange it for something else. They may not know the value of the coins, but this will not deter from the actual understanding of what money is used for. It should be noted that plastic money tends to have less impact as the child is not familiar with plastic money and doesn’t make the connection.

In one infants’ school, reception children visited a local grocer’s shop.  Before the visit they wrote a list of what they wanted to buy and experienced focused activities in their mathematical development sessions on weighing, measuring and sorting objects. During the visit to the grocer’s, they used their shopping lists to identify the items required and weighed them, deciding which were heavier and which were lighter. The children paid for their fruit and vegetables with coins and received change.

Following this hands-on experience, the children then worked in groups to develop an ‘architect plan’ of a grocer’s shop, identifying what would be needed for a role play area.  Together, the children, class teacher and learning assistants then created the role play area.

During their role play, children took vegetables from their ‘garden’ and sorted them into bags, according to their own criteria. They used the weighing scales to then decide who had the lightest bag and who had the heaviest. The children then decided that they needed ‘labels’ to tell the customer the cost of the items and so produced these for their grocer’s shop.

  • What further role play activities might be developed in order to progress childrens’ skills in the ‘Manage money’ element?  Review other examples of role play scenarios provided by Milton Infants’ School.

Activity 3.24 (Key Stage 2)

  • Examine these contextualised learning examples for Key Stage 2: Rationing in the Second World War and Utility Bills. Consider how these activities might also encourage learners to transfer skills and knowledge directly to a home life context.
  • View the following films which explore the approach to curriculum planning taken by Langstone Primary School. Consider how the school is ensuring that numeracy skills are being developed through contextualised learning opportunities.
Unable to play video as javascript is disabled on this browser. Please enable javascript to play video.

Activity 3.25 (Key Stage 3)

  • Examine this contextualised learning example for Key Stage 3: Health Risk? which provides a ‘scenario’ through which to develop literacy and numeracy skills.
  • Now identify a ‘real life’ context that relates directly to the learners’ community. How might learners’ numeracy skills be further developed through this context? Consider the range of ‘elements’ presented in the LNF.

Planning next steps in learning

Within its Curriculum planning guidance, the Welsh Government emphasises that all tasks need to be matched carefully to a learner’s individual next steps and be appropriate in terms of subject content and the literacy and numeracy skills focus.

If the task is inappropriate in terms of context and/or demand progress will be lost.’ (2013, p.27)

While the LNF is designed as a curriculum planning tool, it is also intended to support formative assessment, helping teachers and learners to identify next steps and therefore, plan the most appropriate teaching and learning context and tasks for learners to make progress.  

The next subtopic explores the assessment of numeracy.

References

Ginsburg, L. Manly, M., Schmitt, M. 2006. The Components of Numeracy, NCSALL Occasional Paper. Harvard Graduate School of Education.

Welsh Assembly Government. 2008. Foundation Phase Framework for Children’s Learning for 3 to 7-year-olds in Wales. Cardiff: Welsh Assembly Government.

Welsh Government. 2013. Curriculum Planning Guidance. Cardiff: Welsh Government. (accessed 30 September 2013).

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