“Mastery’ just isn’t working”

“Mastery’ just isn’t working”

We fundamentally believe that … “All children can achieve in mathematics; the question is only - to what depth?”

“Mastery’ just isn’t working”

 

We know teaching that focuses on developing secure and deep understanding, including the use of practical resources and iconic representations has proved to be highly successful. 

 

However, through our experience working with teachers and school leaders across the UK, there are clearly some issues with schools successfully implementing ‘mastery’.

 

 

‘Mastery’ just isn’t working

 

Individual teachers, or even the whole staff, feel frustrated despite their best efforts trying to implement ‘mastery’. All they have experienced is gaps getting bigger, children who ‘couldn’t’ before, still ‘can’t’ and an increase in workload.

 

In many instances, teachers have been given a scheme to follow which seems to have everything they need to implement ‘mastery’ successfully… the curriculum is mapped out in ‘small steps’, the lessons are planned, some with videos, and there is a variety of resources.  All that’s left to do is deliver it! So, if it’s not working, they believe it’s down to their ability as a teacher.

 

They were previously trying to do their best for the children. Since they have implemented a ‘mastery’ scheme, they know they are definitely not doing the best for the children. 

 

“Other schools are using the scheme successfully (or are they?) so it must be me!”

 

In fact, there are a wide range of factors that can be contributing to ‘mastery ‘not working in a school.

 

Too big

 

The ‘Small Steps’ Curriculum 

 

We’ve been in schools where the medium term plan suggests a single lesson should cover “multiply and divide numbers by 10 and 100”. Unsurprisingly this feels overwhelming for children – it does not feel like a ‘small step’ - and some children don’t leave the lesson feeling that they have succeeded, it is a lot to cover in one go, for example

 

Whole numbers: 34 x 10 (just add a zero!)

Decimals: 3.4 x 10 (oh the answer’s not 3.40!)

Whole number: 560 ÷ 10 (just remove the zero!)

Decimals: 0.56 ÷ 10 (oh the answer’s not .56!)

 

… and that’s just multiplying by 10. We’ve still got to multiply and divide both whole numbers and decimals by 100 in this lesson!!!

 

Just because someone has decided to call this a ‘small step’ does not mean it is small enough to teach and learn conceptually to any depth. 

 

Some teachers we’ve worked with just don’t feel confident with ‘mastery’ and being asked to deliver the ‘small steps’ has made them even more nervous.  They can’t see how to teach so much in one lesson… even though they are called ‘small steps’- they are just too big, and therefore not having the desired impact. It’s an awful feeling when you notice that you’re losing children within the lesson, but you don’t have the time to support them because you have to move on to a new step every day.

 

So ‘small’ steps are the issue here – steps need to be manageable - manageable for the teacher to teach and manageable for the learner to learn. 

 

For example, in the above example, “multiply and divide numbers by 10 and 100” we would suggest breaking this step down into at least eight manageable steps. This may seem like an ‘overreactive’ swing in the other direction, but there is a lot of new, (and important) conceptual understanding for the children to grasp here and time is needed to explore, reason and make connections. 

 

Oh, and yes there is time and room for 8 manageable steps in a medium term plan … if and only if, all 39 weeks of the academic year are thought through and used carefully. We should not be cramming the maths curriculum into convenient blocks of 2 week units for each year group, 6 week terms, etc. 

 

If you break the ‘small steps’ down into a more manageable size, this gives you one thing to focus on each day, allowing the teacher and the children to feel comfortable tackling one bit of new learning in each lesson. In our experience, the result is, teachers feel more confident… and they enjoy teaching maths more … and all children achieve!

 

 

We will explore designing a coherent maths curriculum at a macro and micro level using manageable steps in another blog…

 

Retention

 

 

Children’s retention of their learning isn’t great

 

A series of conversations with school leaders have highlighted to us that many have concerns about the retention of the learning within their school. 

 

Given the nature of the ‘small steps’ curriculums they were using, it was clear to see why they felt that they didn’t’ have the time to practise, consolidate and apply their learning whilst still progressing through the curriculum. 

 

Maybe you are coming up against the same issues with your learners? In the lessons you know that they are moving through the ‘small steps’ as suggested by the scheme but it is not having the impact on long term memory. 

 

It’s important to make the time to practise and consolidate learning, but how do you do this when you feel your scheme keeps moving on regardless and there are only so many hours available for maths in the curriculum?

 

We believe you need to be bold enough to make a structural change to your school timetable with a smarter use of curriculum time for maths: two sessions a day for maths!! Shorten the amount of time for a maths lesson by focusing on one manageable step and introduce a shorter second maths session to keep maths on track, not for new learning. The different emphasis means this second session is not just another maths lesson, call it something else – a Maths Meeting perhaps – and use it for: 

 

  • Revisiting and embedding arithmetic skills
  • Recalling and securing key number facts
  • Deliberate practising current or previous learning
  • Same day / week ‘prevent the gap’ immediate intervention  
  • Pre-teaching
  • Improving strategies to solve problems (e.g. use of bar model)
  • Responding to a ‘surprise’

 

We have witnessed a huge change in schools that have implemented this structure and it is the missing piece in many schools. Lingering longer in a maths lesson and then using a maths meeting to make the learning last longer results in all children making more sustainable progress. 

A Maths Lesson/Maths Meeting structure will make the world of difference to your learners, and you. 

 

We will explore the effective use of Maths Meetings in another blog...

 

Differentiation

 

 

It’s hard to differentiate for different ‘abilities’

 

If ‘mastery’ has been introduced as ‘all children must do the same thing at the same time’ then this will lead to problems. Likewise, children being labelled and/or grouped with fixed ability labels (usually based on historic prior attainment) will also lead to the progress of some children being artificially capped. 

 

Trying to balance supporting all learners to achieve in every lesson is an ongoing challenge and one of the most frequent questions we are asked is…

 

“How do I differentiate and bring learners along together?” 

 

The use of labels is the BIG issue here: 

 

  • The use of ‘ability’ labels. Typically, pupils are labelled ‘less able’, ‘more able’, etc based on their prior attainment. Historic data can be interesting but it only tells you about the past not the future. 

 

  • The use of the label ‘mastery’. It is used in different ways by different people. It feels some resources have simply used the label ‘mastery’ to make them sound relevant and/or trendy. We believe ‘mastery’ is about teaching for secure and deep understanding. At each stage, the aim is to support all pupils to have a secure understanding of mathematical concepts and to challenge pupils by deepening their understanding.

 

Therefore, the issue boils down to the difference between differentiating by depth of understanding and differentiating by ‘tasks for different abilities’. The manageable step for the lesson is the intended new learning for all the children, so how do I know ahead of the lesson who will need to be challenged to deepen their understanding and who will need support to secure their understanding? Be ready to be surprised

 

If we challenge the learners who can ‘do it’/give the answers quicker than others by moving onto ‘bigger numbers’, ‘harder questions’ or ‘more maths’ then we are actually moving onto maths that is conceptually different to the key learning of the day. This can lead to future problems as the learning is not secure and has not been explored to sufficient depth. It can also contribute to ‘gaps’ getting bigger and harder to manage.

 

Differentiating by depth keeps the focus on the conceptual learning of the day, and creates challenge through the use of non-examples, reasoning about misconceptions and solving problems. All your learners are still focussed on the same learning. Some may have moved on from the ‘do it’ part of the lesson to explore the learning to greater depth before other pupils, depending on the manageable step. 

 

Not only does this approach to differentiation help secure and deepen their understanding of today’s learning, it’s also an inclusive approach that empowers ALL children. Some may have previously had low confidence in maths. Working on the same mathematical concept as the rest of the class fosters a sense of belonging and purpose for all pupils. When children start to feel a sense of achievement in mathematics every day, they then start to believe they ‘can do maths’, and this becomes the start of a positive mindset to learning mathematics.

 

We will explore differentiation by depth in another blog…but this lesson design blog gives you a great starting pointhttps://candomaths.org/blog/doit-twistit-solveit-teaching-mastery/

 

 

Resources

 

What ‘Mastery’ resources are used and why

 

We’ve found that there are great risks in asking teachers to implement a ‘plug and play’, off the shelf, downloadable ‘mastery’ scheme and this can lead to one (or more) of …

 

  1. Teachers haven’t thought through the key conceptual understanding for themselves and any potential barriers to learning
  2. Teacher explanation focuses on task completion rather than developing conceptual understanding
  3. Teachers feel ‘straight-jacketed’ into the plans and resources that have been provided 
  4. The resources provided simply don’t support the teacher as much as they had hoped
  5. Teachers and pupils become overwhelmed by the amount, and variety, of resources

 

… resulting in teachers become disengaged from the curriculum and feeling disempowered.

 

It may sound like an obvious statement, but it’s important to know ‘why you use a particular resource/scheme’ (i.e. the principles that are underpinning it) and not simply ‘what resource you use’.

 

It’s also important to pay attention to how, and why, certain questions have been designed within a scheme/resource you are using. There are subtle differences that can make your job of teaching for a secure and deep understanding so much more effective. For example, number choice in examples and tasks can play a huge role in securing the concept of the lesson, guiding the children towards key noticing. A small set of well-crafted questions using Variation Theory is more effective than a wide (and sometimes random) variety of questions.

 

In some cases, we’ve seen when teachers are asked to use the ‘done for you’ lesson plans from a scheme, they miss out on doing any of the deeper thinking around the concept they are about to teach. Not having engaged with the intended learning for today’s lesson and not being clear where the lesson sits within a learning journey, the teacher is not fully prepared for the bumps in the road that may crop up during the lesson. 

 

Yes, a ‘scheme’ can plan a lesson based on a ‘small step’ in learning for a fictional class, but the authors don’t know yourchildren. Don’t forget, the teacher is the most important person to help your children learn, with all your insight and experience. Of course, there will be times when you need some advice/guidance with how to approach something, but that’s not the same as being told how to teach every lesson. Resources can’t teach your children, but they can support you in getting the best out of the lesson.

 

We will explore using Variation Theory to craft questions and activities that put bumps in the road in another blog

 

Reasoning

 

 

Not all my learners are getting to the ‘Reasoning and/or Problem Solving’ parts of the lesson

 

The aims of the National Curriculum weren’t designed to be designated tasks to tick-off, they are overarching aims. Reasoning and solving problems just become integral every day, in every maths lesson, for all children.

 

One of the issues is that reasoning is seen merely as the ‘Do you agree?’ type question demanding a written response for the child to complete in a lesson. Reasoning is a way of thinking, not a task. Reasoning is the golden thread running through a lesson. The quality of the questions you ask and the examples you chose to model will make all the difference here. Driving for ‘noticing’ in order to make connections and generalisations is key.

 

ALL children must have opportunities to explain, discuss, reason, justify and convince throughout the lesson. 

 

The other issue is that problem solving is often seen as merely completing a ‘problem’. Problem solving is much more than this … more than solving a word problem!! To develop problem solving strategies, there need to be regular opportunities to think about, grapple with and explore a range of well-designed problems throughout the lesson. Rich, non-routine problems (sometimes with more than one solution) are a great way to challenge and deepen understanding and build resilience.

 

ALL children must have opportunities to apply their learning, positively struggle and persevere with solving problems.

 

We will explore reasoning and solving problems in another blog

 

‘Mastery’ only works if … 

 

A thread that cuts across all the above factors is ‘mastery’ only works if current classroom practice is transformed and not just tweaked.  It’s important to talk about what we will stop doing as much as what we will start doing. This is a great and exciting opportunity to draw the line on some current practices and/or old thinking ….

 

  • stop using differentiated learning objectives
  • stop sending the ‘less able’ to work outside the classroom with the TA
  • stop children self-selecting chilli challenges
  • stop using problem solving as a ‘thing’ we do on Friday
  • stop judging the success of a lesson by the amount of work in a book
  • stop using ‘mastery’ as a category on a tracker
  • stop using so much time on next step marking and spend it on quality planning (we agree with Debbie Morgan, NCETM Primary Director when she says “the next step is the next lesson” … but only of course if the manageable steps are well designed!)

 

One of the best starting points is to be really clear on an agreed understanding of what you mean when you use the word ‘mastery’ or maybe don’t use it at all! Put the focus on the effective use of representations, language and well-crafted questions and tasks to secure and deepen children’s understanding of mathematics at every point of the journey. 

 

So, if you think that ‘mastery’ isn’t working, we hope that it has shown you that you are not alone in this. There are many teachers going through the same problems and encountering similar issues.

 

In our next blog post, we will explore in more detail how you can address these problems in your classroom, and join us in the belief that All children can achieve in mathematics.

 

This was written by Buzzard Publishing based on an interview with Liz Hopkins and Steve Lomax, CanDoMaths

Website created by Digital Trading