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National Curriculum

Developing personal, learning and thinking skills in mathematics


What are we trying to achieve?

The new secondary curriculum focuses on developing the skills and qualities that learners need to succeed in school and the broader community. The development of personal, learning and thinking skills (PLTS) is essential to meeting the three national curriculum aims of becoming successful learners, confident individuals and responsible citizens.

The individual subjects, which make up the curriculum, provide the essential range of activities, learning opportunities and contexts essential for the effective development of these skills (PLTS).

The framework comprises of six PLTS:

  • independent enquirers

  • creative thinkers

  • team workers

  • self-managers

  • effective participators

  • reflective learners.

PLTS underpin the whole curriculum and can transform young people’s engagement with learning. They support learners’ understanding of themselves as well as their relationship with others and the world around them. Effective development of PLTS can raise achievement and make a considerable impact on learners’ ability to succeed, both now and in adult life.

How do we develop PLTS?

The mathematics programmes of study provide a rich and exciting range of opportunities to develop PLTS as an integral part of subject teaching and learning. Explicit and implicit opportunities are present in the key concepts, key processes, range and content, and curriculum opportunities.

Independent enquirers

Learners can develop as independent enquirers when they are provided with opportunities in mathematics to:

  • identify for themselves mathematical aspects of a situation, problem or issue, research answers and find solutions

  • pose their own questions, plan what to do, appreciate the number of different techniques that could be used to anlayse the situation, and select the most appropriate methods, tools and models to use

  • explore and decide how to represent, analyse, interpret, evaluate and process information to work logically towards results, and reach their own supported conclusions

  • develop their independence in selecting the mathematics to use when working on problems in familiar and unfamiliar contexts.

Creative thinkers

Learners can develop as creative thinkers when they are provided with opportunities in mathematics to:

  • create their own solutions to unfamiliar problems by combining understanding, experiences, imagination and reasoning to construct new knowledge

  • adopt a questioning approach and develop their own lines of inquiry and convincing arguments to support decisions and conclusions

  • draw creatively on their knowledge and understanding to model situations

  • challenge assumptions and generate new ideas and ways to solve problems.

Team workers

Learners can develop as team workers when they are provided with opportunities in mathematics to:

  • experience the benefits of working collaboratively to solve mathematical problems in a range of contexts, both in and out of the classroom

  • recognise their own strengths and those of others to allocate roles and tasks and take responsibility for their own contribution to achieve effective outcomes, for example when planning an investigation or presentation

  • extend their work with others using modern communications systems to draw on a wide range of information sources, for example contributing to a class blog

  • provide and respond to constructive feedback, taking account of different views and developing the confidence to resolve issues and achieve their identified goals.


Learners can develop as self-managers when they are provided with opportunities in mathematics to:

  • take responsibility for organising their own time and resources both in and out of the classroom to complete extended tasks, for example planning how to tackle a problem

  • demonstrate perseverance and initiative by trying out their own ideas with confidence and creativity when addressing challenging tasks, for example applying skills or concepts to new or unfamiliar contexts

  • respond to an increasing range and complexity of key processes by changing priorities and managing risks to complete tasks.

Effective participators

Learners can develop as effective participators when they are provided with opportunities in mathematics to:

  • engage personally with issues and problems that demonstrate the relevance and importance of mathematics to their lives

  • experiment with data, mathematical ideas and models to identify and examine issues or problems and develop their critical understanding

  • take an active part in discussions using interpretation and evaluation to develop convincing arguments

  • negotiate and balance diverse views, including their own, making independent decisions and reaching workable solutions.

Reflective learners

Learners can develop as reflective learners when they are provided with opportunities in mathematics to:

  • recognise how adapting and refining their ideas as work progresses can improve outcomes

  • monitor and improve their own performance, inviting and reflecting on feedback from others and learning from their mistakes

  • explore and select different ways of communicating their understanding of mathematics to a range of audiences

  • take responsibility for their own learning and actively engage with opportunities to identify successes and areas for development.


How do we plan for PLTS?

Effective planning for PLTS in mathematics needs to ensure that they are embedded into sequences of work, teaching approaches and learning outcomes. When this is done well, it will enrich the experiences of learners and support their progress in mathematics while increasing coherence across the curriculum.

The following are some questions we might ask to support the development of PLTS through mathematics.

  • Are there planned opportunities for learning and teaching, where the six PLTS can be taught, practised and reinforced in a range of contexts?

  • Are planned experiences sufficiently ‘open’ for learners to draw on personal experiences and set themselves personal challenges?

  • Do activities encourage learners to explore a range of settings, for example collaborative work, individual work, in the classroom, the school and events in the community?

  • Are learners encouraged to communicate in a variety of ways?

  • Are there opportunities to make coherent links to learning in other curriculum areas to effectively connect and enhance learners’ experiences?

  • Are e-technologies used effectively to enable and support such learning?


The teacher plans for the class to investigate and compare different ways of upgrading and paying for a new mobile phone, and also to develop independent enquiry and reflective skills through this task. Learners will work over several lessons to a timeframe and will conclude by making a presentation of their findings to the whole class.

It is important for the learners to develop the skills to become increasingly independent, to make decisions, and take responsibility about the direction and format of their work.

Learners work in groups, taking on specific roles, and are taught ways of enquiring that they apply and use to answer the investigative questions they have set themselves. They are supported and encouraged to develop appropriate success criteria and reflect on how their inquiry might have been improved. They complete individual and group evaluation forms at the end of the task to help them reflect on their contribution.

This activity involves learners in:

  • identifying questions to answer and problems to solve, planning and carrying out research to compare pay-as-you-go phones with contract phones from different sources (independent enquirers)

  • generating ideas and constructing mathematical models, exploring possibilities by carrying out calculations, varying values and following their own ideas through (creative thinkers)

  • proposing practical ways forward, analysing the problem, inviting feedback and revising their ideas to agree manageable steps (effective participators, reflective thinkers)

  • collaborating with others to plan and deliver their class presentation, discussing their findings, reflecting on and communicating what they have learnt (team workers, reflective learners)

  • evaluating their own performance using feedback from other learners and identifying their own targets for improvement (independent enquirers, reflective thinkers)

  • showing perseverence in working with others to complete the project on time (team workers, self-managers).

Are we achieving our aims?

In planning for progression, it is important to develop a clear picture of how learners demonstrate PLTS in the context of teaching and learning in mathematics and how those skills can raise achievement in this subject. For example, learners may demonstrate that they are:

  • making personal choices about their learning and identifying ways to improve their work, for example by posing questions and developing convincing arguments

  • increasingly selecting and applying their mathematics in real-life and beyond-school contexts

  • extending and transferring their understanding, for example by using mathematics in increasingly complex or unfamiliar contexts, exploring ideas, and using mathematics to model and interpret situations.

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