# What do ‘levels’ mean in assessing adults’ numeracy skills?

Levels provide a comparative measure of adults’ skills. Across the regions of the UK, this measure is yet to be standardised. In England, the Adult Literacy, Language and Numeracy sector uses a five-level system to categorise adult skills. Starting at the bottom, these are Entry Level 1 to 3, Level 1 and Level 2. Wales has taken a similar approach to measuring basic adult skill levels. Scotland and Northern Ireland have, on the other hand, chosen to use international levels as the basis of measuring adult skills (for more details see the description below).

The chart below presents the measures of adult skills together with school and vocational levels used by different parts of the UK:

From this, it can be seen that, for example, adults at Entry Level 3 have the skills equivalent to the standard expected of children in the last two years of primary school, i.e. aged 9-11.

For the National Standards for adult numeracy the skills and understanding expected at each level are described thus:

Understanding information given by numbers and symbols in simple graphical, numerical and written materials. For example, recognising and selecting coins, or ordering and comparing numbers up to 10. Adults below Entry Level 1 may not be able to select floor numbers in lifts.Entry Level 1: Entry Level 2: Understanding information given by numbers, symbols, simple diagrams and charts in graphical, numerical and written material. For example, calculating costs and change, or adding and subtracting two-digit whole numbers. Adults below Entry Level 2 may not be able to use a cash point to withdraw cash.Entry Level 3: Understanding information given by numbers, symbols, diagrams and charts for different purposes and graphical, numerical and written material in different ways. For example, dividing two digits by one digit and interpreting remainders, or comparing weights using standard units. Adults with skills below Entry Level 3 may not be able to understand price labels on pre-packaged food or pay household bills.Level 1: Understanding straightforward mathematical information used for different purposes and being able to independently select relevant information from given graphical, numerical and written material. For example, doing simple percentages or converting units of measure. Adults with skills below Level 1 may not be able to check the pay and deductions on a wage slip.Level 2: Understanding mathematical information used for different purposes and can independently select and compare relevant information from a variety of graphical, numerical and written material. Adults with skills below Level 2 may not be able to compare products and services for the best buy, or work out a household budget. |

#### UK-wide measures of numeracy levels

In 1996, IALS (The International Adult Literacy Skills Survey) conducted a ground breaking measure of “adult literacies” which looked at numeric, document reading and prose-reading abilities.

That survey featured all regions in the UK and is so far the only report which included Scotland, Northern Ireland, England and Wales in a comparative data set of “adult literacies”. The levels used to rate competencies only roughly matched the UKs vocational and school-level curriculum. The measures, ranging from Below Level 1 to Level 5 have kept their names across a number of international surveys. However, what they measure has changed.

The Adult Literacy and Life Skills Survey (ALL) and the OECD’s measure of adult competencies i.e. large international surveys since the end of the 90s, have measured numeracy in its larger definition. This definition is in line with our definition of numeracy. We have provided the latest rough and exact equivalencies in the tables on this page.

Both Wales and England have implemented strategies for improving adult literacy and numeracy. Hence they have also measured their performance by each conducting two surveys which measure numeracy in a contemporary fashion. England conducted the Skills for Life survey (2003/2011) and Wales ran the National Survey of Adult Skills (2004/2010). Those surveys use levels exactly equivalent to learning curriculums for adults and young people within the two regions.

Scotland continues to only measure numeric ability of its adult population in its narrow definition - derived from the IALS report. It did not participate in the OECD Survey of Adult Skills (PIAAC).

Northern Ireland on the other hand did, although that was the first time they had conducted a wide-ranging survey of adult skills since the 1996 IALS report.

Independently of these reports, the British Cohort Study intermittently includes measures of numeric abilities and is conducted across all four parts of the UK. Although a number of reports which talk about numeracy emphasise the need to measure levels of numeracy throughout a person’s life-time, the study is not geared towards providing an accurate snap-shot of the levels of numeracy across the UK.

#### International measures of numeracy levels

The OECD uses international measures of numeracy levels which only roughly correspond to levels in the UK curriculums. In the table above we have provided more exact correspondence between UK measures and international ones. Level 2 in the English and Welsh National standards, which we define as the minimum, starts roughly half-way through International Level 3.

For the PIAAC Survey of Adult Skills Levels the skills and understanding expected at each level are described thus:

Below Level 1: Tasks at this level require the respondents to carry out simple processes such as counting, sorting, performing basic arithmetic operations with whole numbers or money, or recognising common spatial representations in concrete, familiar contexts where the mathematical content is explicit with little or no text or distractors.Level 1: Tasks at this level require the respondent to carry out basic mathematical processes in common, concrete contexts where the mathematical content is explicit with little text and minimal distractors. Tasks usually require one-step or simple processes involving counting, sorting, performing basic arithmetic operations, understanding simple percentages such as 50%, and locating and identifying elements of simple or common graphical or spatial representations.Level 2: Tasks at this level require the respondent to identify and act on mathematical information and ideas embedded in a range of common contexts where the mathematical content is fairly explicit or visual with relatively few distractors. Tasks tend to require the application of two or more steps or processes involving calculation with whole numbers and common decimals, percentages and fractions; simple measurement and spatial representation; estimation; and interpretation of relatively simple data and statistics in texts, tables and graphs.Level 3: Tasks at this level require the respondent to understand mathematical information that may be less explicit, embedded in contexts that are not always familiar and represented in more complex ways. Tasks require several steps and may involve the choice of problem-solving strategies and relevant processes. Tasks tend to require the application of number sense and spatial sense; recognising and working with mathematical relationships, patterns, and proportions expressed in verbal or numerical form; and interpretation and basic analysis of data and statistics in texts, tables and graphs.Level 4: Tasks at this level require the respondent to understand a broad range of mathematical information that may be complex, abstract or embedded in unfamiliar contexts. These tasks involve undertaking multiple steps and choosing relevant problem-solving strategies and processes. Tasks tend to require analysis and more complex reasoning about quantities and data; statistics and chance; spatial relationships; and change, proportions and formulas. Tasks at this level may also require understanding arguments or communicating well-reasoned explanations for answers or choices.Level 5: Tasks at this level require the respondent to understand complex representations and abstract and formal mathematical and statistical ideas, possibly embedded in complex texts. Respondents may have to integrate multiple types of mathematical information where considerable translation or interpretation is required; draw inferences; develop or work with mathematical arguments or models; and justify, evaluate and critically reflect upon solutions or choices. |

#### Some caveats

Adult skills levels are only nominally – not directly - equivalent to school and academic levels. Comparing the skills of adults and children is complex and comparisons are by necessity crude, given children’s and adults’ different experiences and understanding of the world. Such comparisons are a shorthand descriptor (in the absence of anything better) and should be used with caution. We tend to say ‘roughly equivalent’ to reflect this.

Levels of numeracy and literacy are commonly compared asymmetrically. For example, the Skills for Life survey highlights the proportion of adults at Entry Level 3 or above in numeracy, but the proportion at Level 1 or above in literacy – the assumption being that Entry Level 3 numeracy is as acceptable as Level 1 literacy. This assumption is long-standing and one that we challenge.

Back to resources##### Other resources that may be of interest

- ‘Count me in’ Improving Numeracy in England. A Guide for Charities and Funders (2010) New Philanthropy Capital
- Post-16 Mathematics: A strategy for improving provision and participation (2012)
- Predicting Long-Term Growth in Students’ Mathematics Achievement: The Unique Contributions of Motivation and Cognitive Strategies (2012)
- Towards universal participation in post-16 mathematics: lessons from high-performing countries (2013)
- CBI Education and skills survey 2012 - “Learning to grow: what employers need from education and skills”
- ’Making Mathematics Count’ – 2004 – Report by Professor Adrian Smith into Post-14 Mathematics Education
- College Mathematics Project - 2012
- The Institute for Learning (IfL) Final Report to the Commission on Adult Vocational Teaching and Learning
- In the Balance: The STEM human capital crunch - March 2013
- Why maths really matters at work