A vision for mathematics in your school

This activity provides a structure for reflection on the vision and aims for mathematics in your school, and the influence that your own pupils and school context have on an approach to designing a new curriculum. To study this aspect in depth, refer to the Excellence in Mathematics Leadership materials highlighted at the end.

Hand out a selection of mathematics 'vision and aims' statements. You could use those on Resource Sheet 1. Include a copy of your existing vision statement for mathematics in your school. You might find it helpful to anonymise it first if necessary.

As individuals:
Read through the statements.

In pairs:
Ask your team to share their thoughts about the examples. What do they particularly like? Are there any comments that they disagree with? What do they find interesting?

As a team:
Discuss the outcomes of these conversations. Consider the commonalities that exist in the responses. Reveal the fact that your own school's vision and aims were provided. Was it recognised by anyone?

There is a good opportunity to restate your school's vision for mathematics in line with the 2014 curriculum. Keep a note of the strongest feelings that emerge, and perhaps key words or phrases that you identify in the discussions. Aim to include these in your new vision and aims statement.

Discussion point 1

How does your mathematics curriculum fit into your school curriculum?

Discussion point 2

Is every member of your team aware of the contextual information summarised in the school's RAISEonline report (e.g. number on roll, gender split, proportion of pupils with EAL, average point score on entry to a Key Stage)?

How do you assess pupils experience and prior achievement before they begin the curriculum in your school?

Do pupils' starting points influence the vision for mathematics?

Knowing the requirements

This activity provides a structured approach to exploring the aims, structure, terminology and expectations of the new programmes of study for mathematics. To study this aspect in more depth, the ‘take it further’ activities suggest ways to explore the specific content of the programmes of study in more detail.

Structure

The first two pages of ‘National Curriculum in England: mathematics programmes of study’ explain the purpose of study and aims of mathematics.

In pairs:
Ask pairs to discuss and write down five reasons why pupils study mathematics.

As a team:
Compare the responses with the ‘purpose of study’ and ‘aims’ in the document.

These two pages also explain the expectations for use of information and communication technology (ICT), spoken language, the school curriculum and attainment targets. Ensure staff appreciate that although the programmes of study are set out year-by-year for Key Stages 1 and 2, schools are however,

‘only required to teach the relevant programme by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study.’
(National curriculum in England: mathematics programmes of study)

Terminology

In groups:
Ask your team to compare the attainment target language of the 2014 curriculum with existing national curriculum documents. What is the same? What’s different? (For example, do we still have ‘Handling data’, ‘Using and Applying’, ‘Shape, Space and Measures’ sections?)

As a team:
Feedback responses and ensure consistency of understanding of the new terminology:

Discussion point: Using and applying

• Why is there no longer a ‘Using and Applying’ section?

This is a very important opportunity to:
a) reiterate two of the aims of the 2014 National Curriculum:

‘The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.’

(National curriculum in England: mathematics programmes of study)
 

b) stress the need for these aims to permeate the day to day provision of mathematics (see Activity 4: Designing a scheme of work)

Expectations

Now raise awareness that although the Key Stage 1 and 2 programmes of study are year-by-year, they are grouped into the phases ‘Key Stage 1, ‘Lower Key Stage 2’ and ‘Upper Key Stage 2’.

In groups:
Ask your team to name five aspects of mathematics that they feel are important to develop conceptual understanding in, and to become fluent in, during any of:

• Key Stage 1
• Lower Key Stage 2
• Upper Key Stage 2
• Key Stage 3

As a team:
Compare responses with the holistic descriptors:

• Key Stage 1
• Lower Key Stage 2
• Upper Key Stage 2
• Key Stage 3

Finally, discuss the following excerpt with your team:

‘The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.’
(National curriculum in England: mathematics programmes of study)

Take it further:

The following activities are useful to help teachers explore the differences in the content and expectations of the programmes of study for key stages 1 and 2 (year-by-year structure) and key stage 3 programme (grouped by subject content)

In pairs:
Name the strand and year group for a group of randomly chosen 2014 National Curriculum statements such as:

• multiply simple pairs of proper fractions, writing the answer in its simplest form
• record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
• recall multiplication and division facts for multiplication tables up to 12 × 12
• add and subtract one-digit and two-digit numbers to 20, including zero

Solution:

• multiply simple pairs of proper fractions, writing the answer in its simplest form (Year 6 - Fraction, decimals and percentages)
• record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale (KS3 - Probability)
• recall multiplication and division facts for multiplication tables up to 12 × 12 (Year 4 Number: Multiplication and division
• add and subtract one-digit and two-digit numbers to 20, including zero (Year 1 – Number: Addition and Subtraction)

In pairs:
Use these bar charts to explore the range and content of the statements for different strands in different key stages. For example:

a) Fractions, decimals and percentages

Year group

This bar chart emphasises the difference in the number of statements in a particular strand.

Warning: Depending on the nature of the statements, this may or may not mean that less curriculum time is needed to develop conceptual understanding in a year group for a particular strand.

b) Geometry – Position and Direction

Year group

This bar chart emphasises that strands do not have statements for particular year groups, for example, Year 3.

c) Statistics

Year group

This bar chart emphasises the reduced number of statements in some strands and hence potentially less curriculum time compared to current programmes of study.

Ask pairs to analyse other strands, make a presentation to the team and discuss the implications.

Strengthening subject knowledge

Exploring the requirements of the 2014 curriculum may well result in some surprise – or even concern - amongst colleagues. Some aspects which have been seen for some time as within the realm of secondary mathematics will now first be encountered in upper Key Stage 2. Others, particularly within probability and statistics, will now be introduced in Key Stage 3. For example, 'multiply simple pairs of proper fractions, writing the answer in its simplest form' appears in the statutory requirements for Year 6. In Key Stage 3, 'use trigonometric ratios in similar triangles' is included in the programme of study. This activity is an opportunity to introduce and explain support provided by the NCETM to strengthen subject knowledge, and therefore access to the internet will be required. It is likely that teachers will want to study this aspect in more depth beyond the PDM. The NCETM Microsite ‘Video material to support the implementation of the National Curriculum’explores how children might access the more challenging concepts through the use of representations.

Introduce your team to the National Curriculum Resource Tool. This resource is designed to help teachers plan lessons in line with the new curriculum.

Select Y6 Fractions (including decimals and percentages) and click ‘show selection’. Explain that the page is now displaying all statements in the National Curriculum at that level of expectation. Each tab provides information as follows:

• Making Connections: The relevant areas of mathematics in adjacent year groups are displayed, along with cross-curricular and real-life connections.
• Articles: Relevant reading from the NCETM and other sources.
• Activities: A wide variety of ideas for the classroom that can be used when teaching the concept.
• Exemplification: Questions designed to exemplify the learning outcomes in that area of mathematics at this level of expectation.
• Video: Relevant videos from the NCETM and other sources.

Depending on the number in your team, assign a section to each individual or pair.

As individuals or in pairs:
Ask members of your team to spend ten minutes exploring the content within Y6 Fractions, with a particular focus on 'multiply simple pairs of proper fractions, writing the answer in its simplest form'.

As a team:
Ask each pair to explain and demonstrate their findings.

Discussion point

The existing National Curriculum levels are disappearing. Schools are free to adopt their own assessment approaches. See 'assessing without levels' on the DfE website.

• How do members of your team feel about the removal of level descriptors from the curriculum?
• How will summative assessment operate in your new school curriculum?
• Can the exemplifications explored above help with assessment in your school?

Take it further:

• NCETM National Curriculum resource tool: This activity only explores one area of the curriculum and in one year group. Members of your team may want to explore other aspects of mathematics, particularly any identified while exploring the structure of the 2014 curriculum earlier in the meeting.

Designing a scheme of work

Introducing a new curriculum is of course a challenge, but it’s also an opportunity for schools to review their existing practice in core areas of mathematical learning, such as arithmetic in primary, and algebra in secondary, and use this review to develop their own schemes of work to ensure effective practice for pupils. This activity is intended to encourage a debate about the design of a scheme of work and result in a personalised template that can be used in your school.

As a team:
Complete some or all of these activities:

a) What’s your reaction to these brief summaries of the changes in the curriculum?

• Primary: higher expectations overall; a greater emphasis on arithmetic, and written (as well as mental) methods; less prominence given to data, with probability removed altogether; a steer away from use of calculators until the later primary years.
• Secondary: higher expectations overall, with increased requirements in the areas needed for calculus in the sixth form, for example algebra, geometry, proportion and rates of change.

b) Discuss these points of view:

• The curriculum is a mastery curriculum and although this is not achievable immediately, it should be something that is worked towards. The aim is that there is a narrower spread of attainment. The more able should be catered for through deepening their reasoning and problem solving skills rather than being accelerated into new curriculum content. Representations/resources are key to enable all children to access and make sense of the concepts being taught.
• The class should work as a whole and the scheme of work should identify the programme of study for each year group.

Now remind your team that an important intended outcome of this PDM is to start the process of designing a scheme of work for your school that takes account of these changes and structures a mathematical journey for your pupils. Share the template provided on Resource Sheet: Scheme of work template (PDF)  (Word). Explain that this template includes an idea for a long term plan on page 1, and a potential medium term plan on page 2. Further emphasise the following:

• Key learning intentions: Selected from a larger list of learning intentions for a unit, these would be the 'big idea' for that particular unit.
• Making connections: This section would be based around the learning intentions for a unit in Year X, based on (at least) the statements in the National Curriculum. Connected learning intentions from the previous year, Year W, would give information about prior learning. Intentions from the next year, Year Y, would give an indication of where the learning is going next.
• Teaching strategies: examples of approaches that have worked well in your school previously.
• Suggested activities: examples of activities that have been shared in your school, or links to online resources; e.g. NRICH
• Opportunities for investigation and discussion: specific suggestions for developing reasoning and problem-solving throughout the curriculum.
• Probing questions: specific suggestions for improving mathematical dialogue and encouraging verbal reasoning.
• Mistakes and misconceptions: signposts for the teacher to indicate common mistakes and misconceptions to be aware of when teaching.
• Assessment: learning outcomes for the unit based on the learning intentions.
• Mathematical language: key mathematical vocabulary and notation that will be encountered during the unit.

Depending on the number in your team, assign sections to each individual or pair.

As individuals or in pairs:
Ask them to spend ten minutes discussing what the content of a section might look like. You could create the skeleton of a unit by first providing a list of statements as the learning intentions.

As a team:
Ask each pair (or individual) to share their thoughts.

Conclude my emphasising the importance of identifying key learning intentions and any connections for a unit of work.

Note: It is also important that the scheme of work should spend longer time on key topics to develop depth before moving on. This will mean that there is less opportunity to revisit topics and so making connections to topics taught previously will be important to consolidate learning and develop fluency. The NCETM Progression Maps contain some connections (for example, Algebra PDF) and there is also a making connections document within each year group and topic within the NCETM planning resource, (for example, National Curriculum: Algebra Year 6 - Making Connections)

Taking it further:

• Ofsted subject-specific guidance for mathematics survey visits

Designing a calculation policy

Arithmetical proficiency is a key component of the 2014 National Curriculum. This activity provides an opportunity to focus on the greater emphasis placed on this aspect of mathematics and reflect on the effectiveness of a schools’ current calculation policy; in particular, expectations and the models and representations used throughout the school. To study this aspect in more depth, the ‘take it further’ activities provide exemplification of approaches being adopted by schools to meet the new expectations, and also ways to explore the specific progression within each of the four operations in more detail.

As a team:
Consider the following introduction from the NCETM Microsite ‘Video material to support the implementation of the National Curriculum’

‘Research by the Department for Education demonstrates that a key feature of high performing jurisdictions is that the development of quick recall, accuracy and fluency in parallel with the development of understanding and reasoning are all required to promote sound mathematical development (DfE 2012 p70). Procedural fluency and conceptual understanding are not mutually exclusive. The Ofsted Survey of Good Practice in Primary Mathematics (Ofsted 2011) found that many of the successful schools sampled teach fluency in mental and written methods of calculation, alongside understanding of the underlying mathematical concepts.’

As an individual:
Complete the following calculations:

As a team:
Compare and contrast the methods used to complete the calculations with

• a) each other
• b) the school’s current calculation policy
• c) the examples in National Curriculum Mathematics Appendix 1(PDF)

Reminder: The appendix sets out examples of formal written methods for all four operations to illustrate the range of methods that could be taught.

Discuss the expectations of the 2014 National Curriculum for written and mental calculations using the NCETM progression maps:

• Addition and Subtraction (PDF)
• Multiplication and Division (PDF)

In pairs:
For each operation, write down five types of models and images that can be used to support conceptual understanding throughout the primary phase. Compare responses with another pair.

In groups:
Compare and contrast responses from the pairs activity with the contents of the National Primary Strategy ‘Models and images’ documents. Discuss which ones are useful in the current school policy and identify any missing ones.

As a team:
Discuss the essential features that need to be included in the renewed calculation policy, including the new expectations for calculating with fractions and decimals.

As a team:
Compare the responses with the template provided in Resource Sheet: Calculation Policy Template v1 (PDF) (Word) and Resource Sheet: Calculation Policy Template v2 (PDF) (Word) to develop a new calculation policy.

Take it further

In pairs
Explore the NCETM videos: Video material to support the implementation of the National Curriculum

As an individual
Explore the ‘Maths to share’ articles in the NCETM Primary Magazines to develop strategies in addition, subtraction, multiplication and division

As an individual
Explore ‘Teaching mental calculation strategies, guidance for teachers at key stages 1 and 2’

As an individual
Explore ‘Teaching written calculations strategies, guidance for teachers at key stages 1 and 2’

Planning for the future and further support

As subject leader consider the following:

Next steps

• What role should the individuals in your team play in curriculum development?
• How can you continue to ensure full support from your colleagues?
• Regarding the curriculum changes, what should you plan to achieve:
  • Within the next week,
  • Within the next month,
  • With the next year?

Evaluation

• How can you evaluate the changes you are making?
• On what timescales will you carry out any evaluation?
• When should any refinements be made to your planned curriculum?

Further support

• NCETM Primary and Secondary Magazine
• Ofsted Generic grade descriptors and supplementary subject-specific guidance for inspectors on making judgements during subject survey visits to schools