How well are learners progressing and achieving in numeracy? 1

Introduction
This guidance supplements other national advice and support materials available to help schools and establishments implement Curriculum for Excellence. The guidance brings together key messages from a range of available resources in such a way as to help staff in schools and establishments ensure learners are progressing and achieving in numeracy.
It can be the case that learners are achieving very well in mathematics but are not yet developing and applying numeracy skills well enough across learning. This is a key challenge for us to address as establishments continue to implement Curriculum for Excellence.
Numeracy, alongside literacy and health and wellbeing, sits at the heart of
Curriculum for Excellence, as the knowledge, skills and attributes which equip children and young people for learning, life and work. They are the responsibility of all teachers.
The relationship between mathematics and numeracy
Numeracy development progresses as part of mathematics and underpins much of what is taught in this area. Numeracy across learning provides essential analytical, problem-solving and decision-making skills across the curriculum. Numeracy is not just a subset of mathematics, it represents important skills for learning, life and work.
Numeracy can help young people develop the financial awareness they need for independent living, effective money and time management and the ability to interpret and use numerical information appropriately in making decisions and judgements.
Within their curriculum framework, schools are likely to develop programmes and courses for mathematics. They might not necessarily have a separate programme for numeracy across learning. However, all staff need to be increasingly confident about the standards and expectations within the numeracy experiences and outcomes. This will enable them to ensure children and young people have appropriately challenging opportunities to develop and apply their skills in numeracy across the curriculum.
There are numeracy experiences and outcomes within two of the three main mathematics/numeracy organisers:

Number money and measurement

Information Handling
There are no numeracy experiences and outcomes within the third organiser; shape, position and movement.
How well are learners progressing and achieving in numeracy? 2

Most of the aspects of number, money and measurement and information handling include numeracy experiences and outcomes. These are:

estimation and rounding

number and number processes

fractions, decimal fractions and percentages

money

time

measurement

data and analysis

ideas of chance and uncertainty
What does progress in numeracy look like?
The following extract is taken from the Principles and Practice paper for numeracy:
As children and young people gradually progress and build up the concepts and skills contained in the experiences and outcomes for numeracy across learning, they will demonstrate their competence and confidence in applying them in a number of ways. For example:

Can they explain their thinking to show their understanding of number processes and concepts?

Are they developing securely the full range of the skills and attributes set out within the experiences and outcomes? As they apply these to problems, can they draw on skills and concepts learned previously?

As they tackle problems in unfamiliar contexts, can they confidently identify which skills and concepts are relevant to the problem? Can they then apply their skills accurately when working independently and with others, and can they then evaluate their solutions?

Are they developing their understanding of personal finance?

Can they evaluate data to make informed decisions?

Are they developing the capacity to engage with and complete tasks and assignments?

Are they successful in demonstrating learning across the experiences and outcomes?

Can they respond confidently and accurately to challenging contexts and make good use of their numeracy skills? Can they use higher-order skills effectively?
You can access the full Principles and Practice paper from: http://www.ltscotland.org.uk/learningteachingandassessment/learningacrossthecurric ulum/responsibilityofall/numeracy/principlesandpractice/index.asp
As numeracy is progressively developed across children’s learning, there should be opportunities for learners to experience breadth, depth and challenge.
Within curriculum areas, do learners know, understand and use aspects of:
How well are learners progressing and achieving in numeracy? 3

number and number processes to:

calculate accurately, where appropriate, using efficient mental strategies

estimate and check answers before and after completing a calculation

estimate and round appropriately

use calculators and other ICT resources appropriately and efficiently apply numeracy to:

identify and use an efficient strategy for the calculations they need to do

confidently measure and estimate measurements

work confidently with money and time

choose suitable units

find, select, sort, collate and link information from a variety of sources. information handling to:

organise information appropriately

present graphs, charts and diagrams to suit purpose and audience

read numbers accurately from a range of diagrams, tables, graphs and real life objects

make inferences, predictions, informed decisions and draw valid conclusions

use information for different purposes understanding, analysing and evaluating to:

work in groups or individually to solve problems

confidently judge the reasonableness of solutions, checking them out when necessary

explain their thinking and share their approaches and solutions

form and respond to questions

interpret and use information effectively
Creating text:

present information/data clearly and effectively
Appendix 1 gives the numeracy content from within the mathematics/ numeracy experiences and outcomes. Please note that there are no numeracy outcomes within the shape position and movement organiser.
This guide is intended to support staff when planning and observing learning across the curriculum and in assessing or moderating the level of challenge that learners are experiencing.
Further illustrations of numeracy skills within different curriculum areas can be found in appendix 2.
Problem solving skills are a tool for thinking across learning. Where children and young people continue to learn discrete problem solving skills, they should be supported to use and develop these skills across learning.
How well are learners progressing and achieving in numeracy? 4

Achieving a level
Schools are also expected to report on learners’ achievement of Curriculum for
Excellence levels. Periodically , staff will evaluate a range of evidence of learning, taking a holistic approach using their professional judgement about the sufficiency and quality of the evidence in demonstrating standards and expectations for achievement of a particular level as a whole or for the components:
Number, money and measurement
Information handling
This will require children and young people to have evidence across the breadth of learning; demonstrate evidence in relation a level of challenge with an appropriate emphasis on higher order skills; and have evidence of applying their skills in new and unfamiliar situations.
As numeracy is not a curriculum area in itself, staff may report achievement in mathematics/ numeracy holistically. We would expect to see specific references to achievement in numeracy if such an approach is taken, and for children and young people to be increasing aware of their own progress and achievement in numeracy as they progress through their broad general education.
Establishments should consider how well children and young people are achieving
Curriculum for Excellence levels in line with national expectations. This could include professional dialogue about:
How staff use a range of evidence from day-to-day learning as well as from specifically designed assessment tasks, activities and tests and examinations to arrive at their overall judgements about achievement of a level
How staff are taking account of significant aspects of learning that are prerequisites to ensure successful progression to the next level
How they are using benchmarking materials and moderation activities to support their judgements
How they are monitoring and tracking achievement of individuals and groups and using assessment data and trends in achievement over time to support improvement.
Appendix 4 provides a sample of activities staff may wish to engage in when selfevaluating how well learners progress and achieve in numeracy. The activities and support materials can also help staff with their approaches to moderating assessments of learners progress.
How well are learners progressing and achieving in numeracy? 5

APPENDIX 1 – Summary of numeracy content
NUMBER, MONEY and MEASURE
Estimation and rounding
Early : developing a sense of size and amount by observing, exploring, using and communicating with others about things in the world around me.
First: share ideas with others to develop ways of estimating the answer to a calculation or problem, work out the actual answer, then check my solution by comparing it with the estimate.
Second : use knowledge of rounding to routinely estimate the answer to a problem then, after calculating, decide if answer is reasonable, sharing solution
Number and number processes including addition, subtraction, multiplication, division and negative numbers
Fractions, decimal fractions and percentages including ratio and proportion
Money with others.
Third : round a number using an appropriate degree of accuracy, having taken into account the context of the problem.
Early : understanding that numbers represent quantities, and use them to count, create sequences and describe order. Use practical materials and ‘count on and back’ to understand addition and subtraction, recording ideas and solutions in different ways.
First : Investigate how whole numbers are constructed, can understand the importance of zero within the system and use knowledge to explain the link between a digit, its place and its value. Use addition, subtraction, multiplication and division when solving problems, making best use of mental strategies and written skills developed .
Second :have extended the range of whole numbers I work with and having explored how decimal fractions are constructed, can explain the link between a digit, its place and its value. Having determined which calculations are needed, solve problems involving whole numbers using a range of methods, sharing approaches and solutions with others. Explored contexts in which problems involving decimal fractions occur and can solve related problems using a variety of methods . Can show understanding of how the number line extends to include numbers less than zero and have investigated how these numbers occur and are used.
Third: use a variety of methods to solve number problems in familiar contexts, clearly communicating processes and solutions. Can continue to recall number facts quickly and use them accurately when making calculations. Can use my understanding of numbers less than zero to solve simple problems in context.
Early : can share out a group of items by making smaller groups and can split a whole object into smaller parts.
First : Having explored fractions by taking part in practical activities, can show understanding of: how a single item can be shared equally, the notation and vocabulary associated with fractions and where simple fractions lie on the number line. Through exploring how groups of items can be shared equally, can find a fraction of an amount by applying knowledge of division.
Second : have investigated the everyday contexts in which simple fractions, percentages or decimal fractions are used and can carry out the necessary calculations to solve related problems. Can show the equivalent forms of simple fractions, decimal fractions and percentages and can choose preferred form when solving a problem, explaining choice of method.
Third : can solve problems by carrying out calculations with a wide range of fractions, decimal fractions and percentages, using answers to make comparisons and informed choices for real-life situations. Can show how quantities that are related can be increased or decreased proportionally and apply this to solve problems in everyday contexts.
Early : developing awareness of how money is used and can recognise and use a range of coins.
First : Use money to pay for items and can work out how much change should be received.
H ave investigated how different combinations of coins and notes can be used to pay for goods or be given in change.
Second : Manage money, compare costs from different retailers, and determine what I can afford to buy.
Understand the costs, benefits and risks of using bank cards to purchase goods or obtain cash and realise that budgeting is important.
Can use the terms profit and loss in buying and selling activities and can make simple calculations for this .

Time
Measure- ment
Third : When considering how to spend money, source, compare and contrast different contracts and services, discuss their advantages and disadvantages, and explain which offer best value . Budget effectively, making use of technology and other methods, to manage money and plan for future expenses .
Early : Aware of how routines and events in my world link with times and seasons, have explored ways to record and display these using clocks, calendars and other methods.
First : Tell the time using 12 hour clocks, realising link with 24 hour notation, explain how it impacts on daily routine and ensure that I am organised and ready for events throughout my day. Use a calendar to plan and be organised for key events for myself and my class throughout the year . Have begun to develop a sense of how long tasks take by measuring the time taken to complete a range of activities using a variety of timers.
Second : Use and interpret electronic and paper-based timetables and schedules to plan events and activities, and make time calculations as part of my planning.
Carry out practical tasks and investigations involving timed events and can explain which unit of time would be most appropriate to use.
Using simple time periods, give a good estimate of how long a journey should take, based on knowledge of the link between time, speed and distance.
Third : Using simple time periods, work out how long a journey will take, the speed travelled at or distance covered, using knowledge of the link between time, speed and distance.
Early : have experimented with everyday items as units of measure to investigate and compare sizes and amounts in my environment, sharing findings with others.
First : can estimate how long or heavy an object is, or what amount it holds, using everyday things as a guide, then measure or weigh it using appropriate instruments and units. Can estimate the area of a shape by counting squares or other methods.
Second : use knowledge of the sizes of familiar objects or places to assist when making an estimate of measure.
Use the common units of measure, convert between related units of the metric system and carry out calculations when solving problems.
Explain how different methods can be used to find the perimeter and area of a simple 2D shape or volume of a simple 3D object.
Third : solve practical problems by applying knowledge of measure, choosing the appropriate units and degree of accuracy for the task and using a formula to calculate area or volume when required.
INFORMATION HANDLING
Data and analysis
Early: collect objects and ask questions to gather information, organising and displaying findings in different ways. Match objects, and sort using own and others’ criteria, sharing ideas with others. Use the signs and charts around for information, helping me plan and make choices and decisions in my daily life.
First : explored a variety of ways in which data is presented and can ask and answer questions about the information it contains.
Have used a range of ways to collect information and can sort it in a logical, organised and imaginative way using own and others’ criteria.
Ideas of chance and uncertainty
Second : having discussed the variety of ways and range of media used to present data, can interpret and draw conclusions from the information displayed, recognising that the presentation may be misleading. Have carried out investigations and surveys, devising and using a variety of methods to gather information and have worked with others to collate, organise and communicate the results in an appropriate way.
Third : can work collaboratively, making appropriate use of technology, to source information presented in a range of ways, interpret what it conveys and discuss whether I believe the information to be robust, vague or misleading.
First : can use appropriate vocabulary to describe the likelihood of events occurring, using the knowledge and experiences of myself and others to guide me.
Second : Conduct simple experiments involving chance and communicate predictions and findings using the vocabulary of probability.
Third : can find the probability of a simple event happening and explain why the consequences of the event, as well as its probability, should be considered when making choices.

APPENDIX 2
What might numeracy across learning look like?
The table below indicates opportunities for children to apply and develop their numeracy skills in some different curriculum areas. This is an extract from our
Journey to Excellence ‘Learning together’ resource on developing literacy and numeracy across learning. Subject national specialists can given further advice on opportunities for literacy, numeracy and health and wellbeing within their areas of curricular expertise. The opportunities below are generic and not related to the standards/ expectations within particular levels. They are intended to support colleagues when evaluating learning in action, across the curriculum.
Languages
What knowledge, skills and techniques at word, sentence and at text level can we develop to support children and young people to: lve word problems;
Expressive Arts
How do we link:
scale factor in mathematics; mathematical sequences; and young people’s skills in organisation, logical thought and problem solving; and and speed?
Sciences
How do we use science to: ople’s understanding of numbers in context; sense of an answer, check the reasonableness of the answer and use mental methods to calculate an answer; proaches to written calculations; solution of equations compatible to approaches in mathematics; and and resilience to solving unfamiliar problems?

Technologies
How do we use technologies to: arners’ numeracy skills through the use of effective software packages; aspects of measurement including estimation; ort a common vocabulary in space, shape and measure; contexts; suitability of measuring equipment for a given purpose;
Religious and moral education
How do we use religious and moral education to: n and young people to gather, interpret and communicate information, making use of multiple sources of information; discussions and justify their conclusions; pment of children and young people’s problem solving skills through setting challenges that are real, relevant and purposeful; and charts, tables and graphs.
Health and Wellbeing
How do we use health and wellbeing to: performance data; e to become better informed citizens by interpreting and analysing data e.g. exploring citizens rights, exploring safe daily drinking levels for men and women.
Social Studies
How do we use social studies to :
Identify and collect data, analyse and represent data, interpret results in relation to a social studies topic;
Support children and young people’s understanding of measurement;
Support the development of children and young people problem solving skills through enquiry based approaches e.g. testing the hypothesis that the quality of the environment improves as the distance from built up areas increases;
Use graphs and charts e.g. investigating the range and type of diseases prevalent during particular period of time, examining affects on different ages.

APPENDIX 3 – Quality marked examples of children and young people applying and developing numeracy skills across learning can be found on the
National Assessment Resource www.narscoltand.org.uk
Social Studies
Second & Third Level : Shawbost School Eilean Siar (Western Isles)
Second Level : Keills Primary School Argyll and Bute
Languages
Second Level: Wallacehall Primary School Dumfries and Galloway
Third Level : Dunbar Grammar East Lothian
Expressive Arts
First Level : Whitelees Primary School North Lanarkshire
Second Level: Evie and Firth Primary Schools Orkney Islands
Sciences
Early: St Andrew’s School Aberdeenshire
Early & Third Level : Kersland School Renfrewshire
Third Level: St M atthew’s Academy North Ayrshire
Fourth Level: High School of Glasgow (independent school)
Technologies
First Level : Armadale Primary School West Lothian
Third Level: Crieff High School Perth and Kinross
Health and Wellbeing
Early Level: Polbeth Nursery West Lothian
Second Level : Marybank Primary School Highland
Third Level: Peebles High School Scottish Borders

Appendix 4 - reflective questions and activities to support self-evaluation and improvement
Evaluating how well your learners are progressing and achieving in numeracy
The following activities can help staff to moderate judgements about the achievement of a level or support selfevaluation of learner’s progress and achievement.
Working with learners
One possible activity to support self-evaluation and improvement activities is to sample learners who have been recorded as having achieved a level. Learners are not secure at a level unless they can apply their skills across learning. When talking with learners about their coursework, we might look for examples of where they have applied numeracy skills in other areas of learning.
We do not wish to ask learners stock or ‘test’ questions, but rather talk to them about their learning and their awareness of their own numeracy skills. The question stems below can be applied to any numeracy content to help us to evaluate if children and young people are secure at a particular level. The question stems relate to higherorder thinking skills which are linked to security within a level.
As part of this activity, we might talk to learners and review their numeracy work, asking questions in relation to specific content:
• Can you think of an example…
• Can you explain….
• Where/when have you used…..
• Can you apply….
• Here is a new example, can you work this one out…
Depending on the age and stage of the learners, we can challenge them to demonstrate particular numeracy skills or knowledge or ask them to ‘ show you know
’. Part of the discussions may include asking children and young people to calculate mentally and explain their thinking.
Appendix 1 includes the numeracy content from the experiences and outcomes in a useful 2 page compact format. This can be useful when working with learners, planning and observing learning in action. This should not be used as a checklist but is intended to support staff in understanding and interpreting the standards of numeracy within different levels.
Observing learning in action
Within an establishment, staff may be asked to indicate on timetables or through discussion where we are likely to see children and young people developing and applying their numeracy skills in different curriculum areas or contexts for learning.
The key challenge when observing learning in action is to evaluate the level of challenge for learners. Sometimes we see links being made to numeracy which are not appropriately challenging either in terms of the Curriculum for Excellence level or

in relation to higher order thinking skills such as analysis and evaluation. Staff sometimes helpfully ask children and young people at the end of lessons if they have used any numeracy skills. In the most effective practice, learners not only use their numeracy skills but develop these further through another aspect of learning. Some o f the ‘quality marked’ examples on the National Assessment Resource illustrate this. Appendix 3 gives examples from the National Assessment Resource of children and young people applying and developing numeracy skills across different curriculum areas.
All teachers, regardless of the subject being taught, are responsible for supporting, developing and extending learners’ numeracy skills and for ensuring that what a child has learned in earlier years is built upon, practised and refreshed regularly throughout their time at school.
When observing learning in action we may also sample young people’s written jotters and coursework in numeracy. This can be useful to evaluate how well children and young people present written calculations and how accurate these are. Written work or work on display can also be used as part of the dialogue about progress and achievement with children and young people. Observing learning in action may also provide the opportunity to evaluate children’s skills in mental agility, including the accuracy of calculations, the range of strategies used and how well children can explain the strategies they use.
Appendix 2 gives some useful illustrations of what numeracy might look like in different curriculum areas.
Questions to consider how well staff support learners to progress and achieve in numeracy.
• How confident are we in using the numeracy experiences and outcomes?
• How well do we discuss the standards and expectations within the numeracy experiences and outcomes to help develop a shared understanding?
• To what extent do we provide a broad range of experiences to develop learners’ skills in numeracy across learning?
• How well do we provide opportunities for learners to develop and apply their skills in mental calculation?
• To what extent do we put in place strategies and approaches to intervene and provide personal support to enable all learners to make the best possible progress in numeracy?
Questions to consider how staff are using information and data
• To what extent do we use range of evidence from day-to-day learning as well as from specifically designed assessment tasks, activities and tests and

examinations to arrive at their overall judgements about achievement of a level?
• How good are we at taking account of significant aspects of learning that are pre-requisites to ensure successful progression to the next level?
• To what extent do we use benchmarking materials and moderation activities to support our judgements?
• How do we monitor and track achievement and progress of individuals and groups using assessment data and trends in achievement over time to support improvement?
• To what extent do we record information relating to learners’ progress in numeracy; strengths and areas for improvement?