Professional Focus Paper
Course: Mathematics
1.
Level: National 4
Who is this paper for and what is its purpose?
This paper is for teachers and other staff who provide learning, teaching and support as learners work towards
Mathematics National 4.
Curriculum for Excellence is a unique opportunity to raise achievement and to ensure that all learners are better
prepared than they have been in the past for learning, life and work. This is because the new curriculum gives real
scope to build learning 3–18 in a joined-up, seamless way. As a result, progression in learning can be much
stronger, with a strong focus on the attributes and capabilities, skills (including higher-order thinking skills), and
knowledge and understanding. These are delivered through the experiences and outcomes of the 3–15 Broad
General Education (BGE) and, at the senior phase, through programmes that build directly on the BGE leading to
qualifications. Because of a strengthened focus on the nature and quality of learning experiences, self-motivation is
likely to be increased and learners will be more engaged and enthused. To ensure continuity and progression,
qualifications at the senior phase have been changed to embrace this unambiguous focus on high-quality learning.
Curriculum for Excellence has the flexibility to meet the needs of all learners in their local circumstances, enabling
each to achieve their very best. For example, some schools may take the opportunity to offer National Courses
over two years which might involve bypassing qualifications at a given level, whereas others may work towards a
qualification within one year. In both cases, this advice is relevant to the learning and teaching approaches that
learners will encounter. This paper, then, is intended to stimulate professional reflection and dialogue about
learning. It highlights important features of learning which are enhanced or different from previous arrangements at
this SCQF level.
How will you plan for progression in learning and teaching, building on the Broad General Education, to meet the
needs of learners?
2.
What’s new and what are the implications for learning and teaching?
Mathematics National 4 consists of four Units providing learners with the opportunity to develop and apply a range
of mathematics skills for life and work within real life contexts.
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Expressions and Formulae
Relationships
Numeracy*
Added Value Unit: Mathematics Test
*This Unit is common to both Mathematics National 4 and Lifeskills Mathematics National 4.
MATHEMATICS
To achieve Mathematics National 4, learners must pass all of the required Units, including the Added Value Unit.
What are the key aspects of Mathematics National 4?
Increased emphasis on skills development
Mathematics National 4 has an increased emphasis on skills development and higher-order thinking skills. This is
developed through the understanding and application of straightforward operational skills in algebra, geometry,
trigonometry and statistics within familiar mathematical contexts. These transferrable skills will support learning
within other areas of the curriculum, including the sciences and technologies. Learners will develop a range of
mathematical techniques and reasoning skills and use these to solve mathematical problems. Learning and
teaching approaches will focus much more on a broader range of skills including, for example: resilience in problem
solving; increased analytical skills; the ability to communicate solutions; making informed decisions; and using
creativity and deduction. Learners will develop their literacy skills through appropriate use of mathematical
language and abstract terms.
Wider range of evidence of learning
Previous approaches to assessment were directed by the need to achieve end of unit NABs. These have been
replaced by a new emphasis on naturally occurring evidence and combined assessments, building on approaches
developed in the BGE. Staff can now make use of a wider range of evidence including, for example: written
evidence generated during supervised class work; tests; oral evidence; computer-generated class work; and
photographs of project or investigative work. Evidence of the use of mathematical reasoning skills can be gathered
either separately or combined with evidence of other outcomes and assessment standards. This will allow scope
for planning well-designed experiences that enable learners to interpret a situation where maths can be used and
communicate a solution relating it to the given context.
Hierarchy of Units
The Numeracy Unit at National 4 is in a hierarchy with the Numeracy Units at National 3 and National 5.
Mathematics National 4 is in a hierarchy with the Mathematics National 5 Course. The hierarchical nature allows for
flexible approaches to learning and teaching. Programmes of learning can be designed to enable learners to
experience learning within and across SCQF levels as appropriate to their needs. This approach has the potential
to encourage all learners to achieve at the highest level and build a strong platform for further learning at the next
level.
Added Value Unit
The Added Value Unit offers scope for learners to demonstrate knowledge and skills acquired from across the
course. It will allow for further development and application of the literacy and thinking skills developed within the
BGE. For example, learners will be required to interpret, communicate and manage information in mathematical
form.
What are the key features of learning in Mathematics National 4?
Active learning
Learners will be expected to take an active role in the learning process, extending their reasoning and analytical
skills through a range of mathematical tasks and activities. Learning activities, linked to their own interests or
aspirations, will develop their ability to analyse, to evaluate, to solve problems and to apply their learning in other
aspects of their lives.
MATHEMATICS
Through active learning learners should experience tasks and activities that require them to analyse and make
decisions, explain their thinking and synthesise aspects of their existing skills. When learners are increasingly
active in their learning, they think deeply about mathematical ideas and concepts and construct their own
understanding about them. They use existing skills and knowledge in different contexts, test out their ideas and
solve problems.
How will you plan opportunities for learners to take a more active role in their learning?
Learning independently
Learners undertaking Mathematics National 4 will continue to develop as independent learners either working on
their own or in groups. Learners can develop confidence and self-motivation through activities that offer a choice of
approaches and resources and which encourage them to be self-reliant. This could nurture their leadership skills
and promote responsibility and team working – essential skills for learning, life and work.
For example, within project-based or investigative tasks, learners could develop their communication and
presentation skills when using probability to assess risk.
How will you plan opportunities for learners to work independently?
Responsibility for learning
Learners should be expected to take responsibility for, and plan, their own learning based on an understanding of
how best they themselves learn. Opportunities for personalisation and choice will enable learners to show what
they can do. This will promote motivation and ensure that individuals are challenged appropriately.
Within Mathematics National 4, well-planned approaches to learning will enable learners to develop a positive
attitude towards the use of mathematics within learning, life and work. For example, understanding the practical
importance of accuracy and reliability in the use of numerical data within scientific experiments or evaluating and
interpreting raw data to make informed decisions on real-life situations.
How will you support learners to take responsibility for, and plan, their own learning?
Collaborative learning
Mathematics National 4 builds on collaborative approaches to learning from the BGE. Collaborative learning
challenges learners to think independently and engage in discussion, debate and activity to achieve specific
outcomes. For example, collaborative approaches will support learners to develop confidence in the use of abstract
terms and mathematical language to explore mathematical ideas. In planning activities, staff should provide
opportunities for learners to collaborate more widely with others. This is a key change that recognises that learning
takes place both within and beyond the classroom. The statistical and geometric skills within the Expressions and
Formulae and Relationships Units provide rich opportunities to plan projects and problems that draw on the
expertise of a range of employers and businesses. For example, learners could work with a range of different
businesses to investigate the use of symmetry in design or the importance of reliable data in the workplace. These
links will strengthen learners’ positive attitudes towards the use of mathematics in real-life situations.
MATHEMATICS
Working with partners provides the relevant and real-life contexts and situations that promote investigative and
problem-solving approaches. For example, learners could work in teams developing their reasoning and geometric
skills within a design and packaging context. Staff can also use such opportunities to enhance learners’
exploratory, analytical and creative skills, allowing them to engage in a variety of roles and making effective
contributions as part of a team.
How will you ensure that learners have the confidence to take on appropriate roles and responsibilities in
collaborative tasks?
How will you ensure that learners can access opportunities to work with a wide range of partners?
Applying learning and skills development
Mathematics National 4 has a greater emphasis on enabling learners to apply their learning across a wider range
of mathematical contexts. For example, learners use of numerical data and mathematical language to explore
mathematical ideas will be consolidated when practised in a range of meaningful contexts.
Learners should develop their confidence in applying skills, as appropriate to context, through both non-calculator
activities and available technology. For example, learners could make effective use of technology including
application software, blogs and social media to engage with others and to access links to creative learning
experiences in mathematics.
Links with other curricular areas, such as the sciences, technologies and social subjects, are essential to help
learners apply and make connections in their learning. This will ensure their skills are reinforced and transferrable.
For example, using contexts developed by organisations such as STEMNET will bring relevance and coherence to
learners overall experiences as well as enhancing learning in the science curriculum area.
How can we ensure that learners can access opportunities to apply their learning in other curricular areas?
MATHEMATICS
3.
Qualification information
The SQA website provides you with the following documents:
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Assessment Overview
Course Specification
Unit Specification
Support Notes
Course Assessment Specification
Unit Assessment Support Packages
Full information on arrangements for this qualification is available at the SQA website:
Mathematics National 4: http://www.sqa.org.uk/sqa/47417.html
4.
What other materials are available on the Education Scotland website which staff
could use?
http://www.educationscotland.gov.uk/nationalqualifications/subjects/mathematics.asp
http://www.educationscotland.gov.uk/learningteachingandassessment/curriculumareas/mathematics/nqs/index.asp
Support materials have been produced over the last year to support Curriculum for Excellence and further support
materials and events are planned. This downloadable list is updated quarterly with the most up-to-date details
available from the page below.
Published and planned support for Curriculum for Excellence:
http://www.educationscotland.gov.uk/publishedandplannedsupport
T +44 (0)141 282 5000 E enquiries@educationscotland.gov.uk W www.educationscotland.gov.uk
Education Scotland, Denholm House, Almondvale Business Park, Almondvale Way, Livingston EH54 6GA
© Crown copyright, 2012
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