Why can’t I just plough through the textbook? Those authors know what they are doing, otherwise why would the publishers have employed them?
According to Ofsted’s summary report, Mathematics: understanding the score:
Good schemes of work were rare in secondary schools. It was not uncommon for teachers to use only examination specifications and textbooks to guide their lesson planning, focusing on content rather than pedagogy. Few schemes included guidance on matters such as the most effective teaching approaches, how to meet the full range of pupils’ needs or on what constitutes an appropriate level of challenge. They provided insufficient support for teachers who were at an early stage in their professional development or for staff who were not mathematics specialists.
The best schemes of work included guidance on approaches, interesting activities and resources that help nurture pupils’ understanding. They were seen as living documents, subject to regular discussion and review, which helped staff to develop their expertise.
So, a good textbook will provide some guidance on content, and may even promote effective pedagogy, but a scheme of work should be the vehicle through which the department’s vision, ethos and learning intentions are made clear to teachers. It will be developed through mutual discussion and sharing of ideas, should ease the planning process for teachers, and must support new, inexperienced and non-specialist staff. Such a scheme of work is never complete!
The NCETM’s EiML materials describe an effective structure for curriculum planning and as showing how mathematics is planned for at the long-, medium- and short-term level. From this, some implications for the development of a scheme of work can be extracted:
Long Term Planning should
- clearly state an expected pathway of progression across the Key Stage
- break down the Key Stage progression into a yearly plan
- reflect the department’s vision and national priorities.
Medium Term Planning should:
- link clearly to the long term-plan
- make clear what is to be taught and when
- contain differentiated teaching objectives
- give clear links to rich and interesting activities and resources
- indicate teaching approaches which will engage and interest the students
- contain a schedule for various assessment items in line with a departmental or whole-school policy
- reflect the department’s vision and national priorities.
Getting started: the first decisions
The National Curriculum was originally based on the concept of one national curriculum level progress every two years. Recent secondary school improvement target-setting strategies have expected at least three national curriculum levels between year 7 and year 11, some schools adopting an expectation of two thirds of a national curriculum level of progress each year. In practice, it is not easy to take the statutory Programmes of Study and create the previously mentioned ‘expected pathway of progression’ from scratch. That is where the lines of progression created by the National Strategies can be helpful. They provide learning objectives broken down into groups for each year that are pitched at the appropriate level for this aim to be worked towards:
- Year 7: consolidating level 4 and introducing level 5
- Year 8: consolidating level 5 and introducing level 6
- Year 9: securing level 5, mostly level 6 and introducing some level 7
- Year 10: Securing grade C / level 7 and introducing grade B / level 8
- Year 11: Securing grade B / level 8 and introducing grade A / level EP
- Year 11+: Securing grade A and introducing grade A*
Of course, with this long-term planning scenario, it is essential to focus on the stage of learning the leaner is at rather than just simply the age of the learner and it may well be that some pupils will follow a pathway based on the lines of progression for alternative year groups; the most obvious example being the most able mathematicians in Year 7 who should be targeting an A* by the end of Year 11.
The example schemes of work for Year 7 and Year 9 use the learning objectives (from the lines of progression) for the stated year group to ensure that the units of work are pitched at the right level for thelearner operating at age related expectations.
Choosing a structure
By cross-referencing the objectives within the lines of progression, related objectives from adjacent years can be found. These have been included, and labelled as ‘past experience’ and ‘where next?’ This serves two purposes: firstly it is important to understand the bigger picture of where a particular piece of mathematics progresses, and also, consideration of these can be used to guide teachers towards appropriate differentiation.
Note that the lines of progression start at Year 7. To create the ‘past experience’ section for the Year 7 scheme of work, cross-referencing with the primary framework has been carried out. This might be particularly enlightening for secondary teachers as there is considerable overlap between Years 5/6 and Year 7. An awareness of this might influence the way in which certain topics are approached in Year 7.
As a unit is created by grouping objectives it is almost inevitable that a ‘big idea’ for each grouping is guiding this process and the choice of timing. As departments work on this it would help if this was formally noted; both for the benefit of future teachers who have not been involved in the process, and to guide in the ongoing development of the unit. Space has been left for each unit in the Year 7 and 9 schemes of work and an interesting exercise might be to consider the provided groupings and discuss what the big ideas were as they were created. This can then be included in both the long and medium term plans.
The suggested structure for the medium term plan then also includes:
The ‘rich and interesting activities and resources‘ chosen to be included in a scheme of work will obviously reflect the vision and ethos of the department. The example Year 7 and 9 schemes of work include links to many of the ideas and resources available on the NCETM portal. In particular, the Secondary Departmental Workshops, Self-evaluation Tools, and Secondary Magazines, have been referenced extensively.
While certain activities and resources are suggested in each scheme of work structure, it is also worth having in mind 'types' of activities that students might experience in order to develop their understanding. These could be either short (maybe starter) activities or longer activities that might take a lesson or more.
Once these types of activity are considered and included in the scheme of work, lesson planning should become less problematic and, as students become familiar with the types of activity, they will learn strategies and approaches that will support them in further problem solving.
These types of activities are taken from Improving Learning in Mathematics and the Maths4Life resource Thinking Through Mathematics.
The pedagogy suggested by these activities may require some CPD – you might find the activities suggested here a useful starting point for this.
Correct use of mathematical vocabulary can significantly aid progression in the subject. What are the ‘key words’ that will be encountered during the unit and what approaches in the classroom develop learners’ knowledge and use of them? This resource produced by the National Strategies may be helpful.
Criteria for success
A phrase that is interpreted in various ways, in this context it is intended to refer to the ‘steps to success’ required in order to be successful with the particular learning outcomes. While there will often be too many to be worth listing (and therefore be something that teachers would draw out during a lesson rather than list during planning) there may be key criteria for success that you feel it is necessary to flag up in the medium term plans. As an example, to be successful with many problems involving the area and circumference of a circle, learners need to be able to round to a given number of decimal places. This has been left blank in the example schemes of work as in part it depends on the chosen learning outcomes.
Approaches to assessment
The content for this section will depend on the policies and procedures in your school. However, a blend of formative and summative approaches is likely, and the Assessing Pupils’ Progress (APP) assessment criteria are likely to be an underpinning feature. Examples include:
Pupil self-assessment sheets
- Set homework tasks
- APP ‘moments’ – key criteria that should be assessed formatively during the unit
- Extended learning assignments
- Key questions
The example schemes of work have flagged up times for ‘periodic review’ – a phrase developed by QCDA as part of the theoretical APP process. This periodic review could be the opportunity to stand back, consider the bigger picture of progress shown by a class, and act accordingly on the results. This might include the use of a criteria-referenced test, and it may well be linked to any reporting procedures in your school.
These are different from learning objectives in that they show examples of how a learner could demonstrate what they are able to do rather than describe the knowledge, skills and/or understanding the learner is expected to acquire . The objective should ensure that the pitch of the work is correct while the outcome supports in developing an understanding of what a piece of mathematics looks like. Considering the learning outcomes at the medium-term part of the process is important as it should prompt deep thinking about how to guide a learner’s journey where they develop the knowledge and understanding to be able to tackle the problem confidently and successfully. Again, the example schemes of work have this section left blank for departments’ own development. More guidance can be found here