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MEP learning pack

Masters in Educational Practice: Numeracy learning pack


Learning and teaching numeracy


Assessing numeracy

The National Numeracy Tests and the National Literacy and Numeracy Framework (LNF)

Numeracy, when delivered as part of the LNF, will be assessed nationally and externally by annual numeracy tests. These tests for all learners in Years 2 to 9 are intended to generate comparable data which will enable individual teachers, schools and local authorities to measure aspects of learner progress and focus their attention on improving performance. As the tests do not assess learners of reception or year 1 age, assessment here is wholly teacher-led and, therefore, not governed by the same statutory requirements (Hill Report).

From May 2013, learners will undertake a test of procedural knowledge, followed by the introduction of a numerical reasoning test in May 2014. These results will enable schools to plan numeracy delivery and intervention for forthcoming years. For example, to improve the identification of learners who are falling behind and to provide more able learners with greater challenge.

From September 2014 schools will be required to report individual learners’ attainment in numeracy across the curriculum to parents and carers but there will be no national data collection in relation to assessments made against the LNF. Beyond the LNF, at Key Stage 4 the new GCSE in Numeracy will be introduced in 2015.

Previous research suggests that learners’ abilities to reason are at least as important as their knowledge of mathematical procedures with Nunes et al. identifying ‘reasoning’ as having a greater impact on learners’ achievements  than ‘arithmetic’ within Key Stages 2 and 3.

Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics.

Mathematical reasoning and knowledge of arithmetic (as assessed in year 4) make independent contributions to children’s achievement in mathematics in KS2 and 3. While both are important, mathematical reasoning is more important than knowledge of arithmetic for achievement in KS2 and 3. (Nunes et al. 2009, p.1).

The new numerical reasoning tests will support teachers to assess how well their learners are progressing in identifying the mathematical skills needed to solve a problem and applying these in context.

Assessment for planning and learning

The LNF is primarily a curriculum planning tool. However, it is also an assessment tool that informs teacher assessment.

Assessment against the LNF should be formative, used by schools and individual teachers to support learner progress, classroom and curriculum planning. Teachers should use ongoing, formative, classroom assessment to monitor progress, discuss next steps needed for improvement with learners and set tasks that will give learners opportunities to make progress in their literacy and numeracy skills (Welsh Government, 2013, p.7).

There is recognition that teachers’ understanding of progression across the LNF will develop over time. As this develops, the appropriate identification of next steps in learning should improve, and in time, learners should be able to make decisions about their own next steps in learning, initially supported by the teacher. These next steps specific to individual learners should inform a teacher’s curriculum planning.

Activity 3.26

Watch this short video of a Key Stage 2 teacher reflecting upon the use of the LNF in her school.

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What challenges does she identify for learners in terms of their recognition of their next steps in learning?

What strategies might you employ to support learners’ understanding of their own progress and their ability to identify their own next steps?

Following the launch of Curriculum 2008, many schools across Wales took part in the ‘Developing thinking and assessment for learning’ programme funded by the Welsh Assembly Government. Estyn identified that the programme had had a positive impact in terms of developing teachers’ confidence in the use of developing thinking and assessment for learning strategies in many of the schools involved and in increasing student engagement in the learning process. However, the report also concluded that there was still too much variation in practice within and across schools (2011, p.13), with practice in secondary schools less well developed than in the primary schools visited.

Activity 3.27

  • How might a shared whole-school approach to using the LNF as a formative assessment tool be achieved? Which assessment for learning strategies already in place might support learner self- and peer-assessment?
  • How might teachers use the outcomes of the assessments to inform short-, medium- and long-term planning for progression of skills within and across subjects, year groups and key stages?
  • How might the outcomes of assessment be used at the point of transition from one phase/key stage to another?
  • What whole-school systems might be needed to support the ‘consistent and rigorous’ assessment of numeracy skills across the curriculum (Welsh Government, 2013, p.8)?
  • How might you map learners’ competency in numeracy skills across the LNF’s continuum of development? When will you decide that a learner has sufficiently demonstrated an outcome in order to judge the skill ‘acquired’?

In a study for the Teacher Training Agency, Askew et al (1997) concluded that the most effective teachers of numeracy used systematic assessment and recording methods to monitor learners’ progress which, in turn, informed planning and teaching. However, the less effective teachers either used ‘little assessment’ or assessment as a means of checking that methods taught had been learned (p.5)

Within the study, Askew et al., explore teachers’ belief systems in relation to numeracy learning and teaching. They present three ‘orientations’ which were important in characterising the approaches teachers took towards the teaching of numeracy:

  • connectionist: a belief that being numerate involves being both efficient and effective (p.31)
  • transmission: a belief in the importance of a collection of procedures or routines (p.32)
  • discovery: a belief that all methods of calculation are equally acceptable (p.34).

Activity 3.28

Read pp.29–36 of Effective teachers of numeracy (external link) which describes these ‘orientations’ in more detail.

Reflect upon your learning from Topic 2, ‘Understanding numeracy’, and the main distinctions between connectionist, transmission and discovery orientations towards teaching numeracy.

With which orientation do you most align yourself? Has your practice changed or shifted? If so, why?

Now read pp.73–76 of Askew et al’s study of ‘Effective teachers of numeracy’ (1997) and consider these ‘orientations’ in relation to the assessment practices described.

Do you consider any of these practices to have relevance to how you might use the LNF as an assessment tool? Do they support the effective use of the LNF as a continuum of development?  


Askew, M., Rhodes, V., Brown, M, Wiliam, D., and Johnson, D. (1997) Effective Teachers of Numeracy: Report of a study carried out for the Teacher Training Agency. London: School of Education, King’s College.

Estyn (2011) The ‘Developing thinking and assessment for learning’ programme. Cardiff: Estyn.

Nunes, T., Bryant, P., Sylva K., and Barros, R. (2009) Development of Maths Capabilities and Confidence in Primary School. University of Oxford: Department of Education.

Welsh Government (2013) Curriculum planning guidance. Cardiff: Welsh Government.

Useful links

View the Learning Wales workshop materials on ‘Tracking, monitoring and recording progress’ which support implementation of the LNF.

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