What is functional mathematics?

The generic definition of functional skills is that will:

‘provide an individual with the essential knowledge, skills and understanding that will enable them to operate confidently, effectively and independently in life and at work. Individuals of whatever age who possess these skills will be able to participate and progress in education, training and employment as well as develop and secure the broader range of aptitudes, attitudes and behaviours that will enable them to make a positive contribution to the communities in which they live and work.’

The vision described is of learners:

• developing the practical applied skills needed for success in work, learning and life

• tackling the skills gap, improving productivity, enterprise and competitiveness

• becoming more confident in their studies in further and higher education

• becoming more confident in interaction with people in their lives.

Functional mathematics will contribute to this agenda. Learners who are functional in mathematics are able to use and apply the mathematics they know to address problems that arise in their life and work.

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.

The aim of the mathematics standards is to encourage people to demonstrate their mathematical skills in a range of contexts and for various purposes. They are essentially concerned with developing and recognizing the ability of learners to apply and transfer skills in ways that are appropriate to their situation.

It is important to recognize that all mathematics can be used in these ways, and that teachers cannot know what mathematics their learners will use as they move through their lives. This means that we cannot identify a curriculum core that every learner will use. Instead, and much more powerfully, learners should be taught to use and apply the mathematics that they know and have learned, and to recognize when they need to develop additional skills. It is essential to think of learners becoming functional in their mathematics, rather than thinking there is a vital body of mathematical material, known as functional mathematics. 

For teachers, helping learners to become functional in mathematics means helping them to:

• recognize situations in which mathematics can be used

• make sense of these situations

• describe the situations using mathematics

• analyse the mathematics, obtaining results and solutions

• interpret the mathematical outcomes in terms of the situation

• communicate results and conclusions.

This will mean that learners should experience sessions that have a significantly new emphasis and focus on problems of sufficient scope to permit these processes to flourish. Learners need to demonstrate the ability to

use and apply straightforward mathematical skills in complex contexts. This is different from much mathematics teaching in which learners often use challenging mathematics in very simple contexts, or entirely out of context.

The problems that learners meet in sessions with this new emphasis may sometimes be complicated and extensive. If this is the case, the problems will need to be solvable using mathematics that the learners have already encountered some time before. It is important that learners are not told, at the time a problem is set, which of the mathematical tools they have at their disposal will actually be needed.

Selecting the right tools is a core aspect of becoming functional in mathematics. The problems should also be plainly relevant to learners, appealing to them by being motivating, interesting and realistic. Mathematics teaching should reveal how mathematics is used in life, enabling learners to gain experience of the breadth of applications of the subject. It is important for specialist mathematics teachers to liaise with colleagues to identify and maximize the opportunities to embed functional mathematics in other curriculum areas.

Part of the push towards relevance and motivation depends on making the use of technology integral to teaching and learning mathematics. When encouraging learners to become functional in mathematics, technology should be given an important role that reflects its significance in life and in the workplace as well

as its potential to enhance and motivate mathematics learning. Indeed, it is good practice to give learners opportunities to use all three functional skills when tackling problems, as is often the case in real life.

The implications for teaching and learning of the features of functional mathematics described above are significant. They will need to be introduced gradually and thoughtfully but they do not threaten aspects of existing good practice. ‘Teaching and learning functional mathematics’ sets out some of the ways in which making adjustments to help learners become more functional in mathematics is supported by existing practices including:

• learning through application

• learner-centred approaches

• active learning and a problem-centred approach

• partnership learning

• assessment for learning.