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# Functional skills in mathematics

## Introduction

The term ‘functional’ should be considered in the broad sense of providing learners with the skills and abilities they need to take an active and responsible role in their communities, in their everyday life, workplace and in educational settings. Functional mathematics requires learners to be able to use mathematics in ways that make them effective and involved as citizens, able to operate confidently in life and to work in a wide range of contexts.

## Functional skills in the mathematics programme of study

The revised mathematics programme of study for key stage 4 embeds the level 2 functional skills standards in mathematics. As well as overlaps in the language used there are deliberate structural similarities (summarised in Links with functional skills). Functional skills are a subset of the key processes set out in the programme of study. All teaching needs to contribute to the development of the key processes. The key processes of representing, analysing, interpreting, evaluating, communicating and reflecting, comprise the skills necessary to be functional in mathematics.

The range and content set out in the programme of study goes beyond that which is likely to be required in the assessment of functional skills at level 2.

The key stage 3 programme of study lays the groundwork for pupils to apply their mathematics to real contexts in key stage 4. In addition, it requires that pupils be introduced to a range of real-life uses of mathematics, including its role in the modern workplace.

### Level 2 functional skill standard: representing – making sense of situations and representing them

• Recognise that a situation has aspects that can be represented using mathematics

• Make an initial model of a situation using suitable forms of representation

• Decide on the methods, operations and tools, including ICT, to use in a situation

• Select the mathematical information to use.

### Key stage 4 programme of study key processes: representing

• Identify the mathematical aspects of a situation or problem Simp

• Simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models

• Compare and evaluate representations of a situation before making a choice. Select mathematical information, methods and tools to use

• Select mathematical information, methods and tools to use.

### Level 2 functional skill standard: analysing – processing and using the mathematics

• Use appropriate mathematical procedures

• Examine patterns and relationships

• Change values and assumptions or adjust relationships to see the effects on answers in the model

• Find results and solutions.

### Key stage 4 programme of study key processes: analysing Use appropriate mathematical procedures

• Identify and classify patterns. Make and justify conjectures and generalisations, considering special cases and counter-examples

• Explore the effects of varying values and look for invariance and covariance

• Work logically towards results and solutions, recognising the impact of constraints and assumptions.

### Level 2 functional skill standard: interpreting – interpreting and communicating the results of the analysis Interpret results and solutions

• Interpret results and solutions

• Draw conclusions in the light of the situation

• Consider the appropriateness and accuracy of the results and conclusions.

### Key stage 4 programme of study key processes: interpreting and evaluating

• Form convincing arguments based on findings and make general statements

• Relate findings to the original question or conjecture, and indicate reliability

• Consider the assumptions made and the appropriateness and accuracy of results and conclusions.

### Level 2 functional skill standard: interpreting – interpreting and communicating the results of the analysis

• Choose appropriate language and forms of presentation to communicate results and conclusions

• Draw conclusions in the light of the situation

• Consider the appropriateness and accuracy of the results and conclusions.

### Key stage 4 programme of study key processes: communicating and reflecting

• Use a range of forms to communicate Engage in mathematical discussion of results

• Relate findings to the original question or conjecture, and indicate reliability

• Consider the assumptions made and the appropriateness and accuracy of results and conclusions.

## Planning for functional skills

The key concept of competence emphasises the need for students to be able to adapt and apply their understanding in a widening range of contexts within the classroom and beyond. This is also at the heart of functional skills. In this way functional skills are much more than a set of technical competencies in mathematics; students have to use mathematics to tackle tasks and problems. All teaching needs to be designed in a way that contributes to the development of functional skills.

When planning opportunities for students to develop and understand functional skills you should consider whether you have:

• provided opportunities for different skills you are focusing on in representing, analysing and interpreting to be developed in combination

• ensured that students understand that they are learning skills that they will use and apply in a variety of contexts

• given students the chance to select the skills and tools (including ICT) they need for a particular task

• provided opportunities for students to apply these skills for real purposes and contexts beyond the classroom.

For example, a year 10 project asked students to recommend to school managers a method for electing representatives for the school council. Students explored methods used in politics, including ‘first past the post’ and different methods of proportional representation. They collected data about different voting methods and carried out simulations, which enabled them to produce a clear recommendation with justification.

This project has the potential to be developed in conjunction with ICT, English and citizenship colleagues as it addresses wider curricular issues and also offers opportunities to develop functional skills in ICT and English as well as mathematics.