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Are blocks of longer units the way forward when planning maths?

Tuesday, 5 April 2016
There has been some recent advice to teach maths topics in longer blocks of time, even though the majority of schools in the UK (and around the world) still use a spiral approach, often consisting of 1, 2 or 3 week units of work. So what should you do in your classroom?
Some of the schools using my Maths Planning Menu have 'blocked' together units giving a longer focus on number, that lasts 4-6 weeks at the start of the year in September. This is then followed by teaching addition and subtraction units together in another longer period of 4-6 weeks on calculation.

My Maths Planning Menu is based on a flexible two-week unit structure, I suggest a spiral approach of revisiting and developing a maths skill or concept later in the year. However it was written with the intention of giving maths support in a framework that schools can adapt to plan in their own way, so I have been pleased that schools feel confident to try new approaches.
So how should you plan your maths topics?

Spending longer on a maths topic isn't necessarily the answer, although it can be a help for some topics. 
The essence of a mastery approach is that a specific step in a topic is taught until it is mastered by the whole class. No matter how you structure your planning for the year, with a spiral or blocked approach, if the children in your class haven’t understood a particular concept or skill then a decision needs to be made whether to spend longer on it using a different approach, go back a few steps to fill gaps or, in a spiral curriculum, leave it until later in the year when they may be ready for it. 

Most maths schemes give advice on timing for the teaching of a topic, whether it is a few days, a week or a month. This may be helpful as a guide but you, the teacher, must decide what is right for your class and it will vary depending on their learning needs. Whatever scheme you are using the key part is that teachers take control and carefully monitor the children’s learning. 

 Blocking maths topics into longer units

In Shanghai one topic is taught at a time in depth over longer periods. The advantage given is that you don’t have to re-teach a topic when you visit it again and there is time to teach small steps within a 'one lesson, one exercise' approach. There is a greater emphasis on number, especially in the children's first few years at school, with many areas of our curriculum such as shape not introduced in Shanghai classrooms until later which allows extra time for this concentration on number.

It may be beneficial, especially in the first term, to focus purely on number and calculation to give a solid grounding in these areas. The topics that follow throughout the year on measures, shapes and fractions will use and reinforce these skills. Two 2-week units could be combined to make 4-week blocks, however careful planning is needed to ensure good coverage of the skills throughout the year alongside other maths topics. 

Other factors to consider are whether the children (and you) can keep an interest in the same topic for an extended period of time. Many of the same models and images will be used throughout (which can be a positive thing) and although new contexts can keep the subject interesting this may make planning harder. With a spiral approach children will be learning the next step in the same topic when they are older and may be more ready. 
If, as it is claimed, time is wasted as re-teaching is needed within a spiral approach, then it must be asked if this would be a greater problem if there is no structured revisiting within the year.

Teaching maths within a spiral curriculum

The mathematics teaching in Singapore is heavily based on a spiral approach. Topics are re-visited over time, building on previous learning to explore with greater depth, to solve more complex problems or to move on to the next step in learning a procedure or skill. If a mastery approach is taken within a spiral curriculum and children are taught well and understand the previous step, after a quick recap, they should be ready to move on without wasting precious time.  

The time between each spiral will vary. Some topics such as shape and measures could have a termly focus but with regular opportunities to use previously learnt content between each focus. Other content, particularly number and calculation, will involve shorter spirals with visits and re-visits over several weeks so the small steps of progression build up over time.

In conclusion

There is a great desire to adopt elements of the East Asia teaching methods for primary maths as their scores at international test are higher than our own. However, this sometimes means too narrow a focus on one or two of their strategies, such as teaching maths topics in longer blocks or using textbooks, rather than looking at all the factors. 

This simple approach may not work without making effective use of their pedagogy, including excellent subject knowledge so that teaching and learning has a very specific focus, a good understanding of small steps of progression, appropriate use of models and images, carefully considered repetition (‘intelligent practice’), use of a textbook and the ‘one lesson, one exercise’ approach. In addition there are other factors such as shorter teaching hours and a different cultural starting point that may have a greater impact on results and are unlikely to be transferred to our system.

As teachers we are good at looking at new ideas that will help teaching and learning and so I'm sure you will be looking at your class and using whatever strategies you think will help. 

I have spent much of this year meeting with educationalists to discuss mastery and advising schools on Shanghai/Singapore approaches, which has certainly been very interesting. However it has also made me realise how good our creative UK teaching can be as well. So by all means use the new, but keep your existing methods that are working well. 

A word about this article

I get asked frequently about the idea of blocking maths topics and teachers seem to have little real information about where it has come from or if it is better than the more commonly used spiral approach.

This article is to help as a starting point for teachers to go on and find out more about this alternative approach. It is not in any great depth - that article would have been too long! 

If I was teaching I would stay with the spiral approach, which is the structure given in my Maths Planning Menu. However within that spiral approach I have suggested spending (a flexible) 2 weeks on a maths topic. This is a good length of time to teach in depth, consolidate skills, apply through problem solving and assess progress - and it also allows time for revisiting a topic and building on it later in the year. 

Don't get swept along by every 'new' idea from East Asia. A mastery approach is about allowing children time to grasp a new concept, skill or procedure and mastering it before moving on. This is great teaching within any curriculum design, whether block, spiral or anything in between.

However for Broadbent Maths schools that wish to give it a try, there is a suggested outline of how to structure the units into blocks

‘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.’

NC 2014 Introduction
Breaking down a topic into small steps and teaching each step until the children have a good understanding and are ready to move on is a sound approach to take. Bruner sees this fitting within a spiral curriculum:

‘A curriculum as it develops should revisit the basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them’.
Bruner (1960)
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Mastery in maths - how can schools plan for this?
Some suggestions for teachers to plan for a mastery approach
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