Depth for all in maths
I recently delivered a session titled, ‘Primary Maths: Differentiation through scaffolding and adaptation’ at the #PrimaryEssentials conference on Saturday 8th May. Recordings of the event are still available for purchase here.
The talk focussed on the importance of high-quality differentiation that allows the vast majority of children within the classroom setting access to the same content with tangible real-life examples of how to do so. Instead of creating 30 different tasks/lesson plans for the 30 children in the class teachers should instead use strategies to ensure children are accessing age-related curriculum expectations.
This can be done in a multitude of ways but I have found focusing on the following has been successful:
Proactive Instruction
High-quality, explicit instruction is of the utmost importance when teaching new content. Explicit instruction is going to be appropriate for the majority of the pupils in your class. We cannot underestimate the impact that quality first teaching has for children
Qualitative not Quantitative
There has been a historical assumption that differentiating instruction means giving some pupils more work to do, and others less. So a higher attaining child may be given more maths equations and word problems and a lower attaining is given 2 equations. A pupil who has already demonstrated proficiency in five equations, doesn’t need five more with no progression in their learning. Simply adjusting the quantity of a task will generally be less effective than altering the nature of the task itself through scaffolds, constraints and adaptations to match the actual pupil needs.
Rooted in Assessment
Assessment has to be the bread and butter of teaching and learning. It is not merely the summative assessment that happens at the end of a unit to determine "who got it." Or your end of term assessment data. Assessment has to be constant and formative.
Diagnostic pre-assessment should take place before and as a unit begins, to shed light on individuals' needs and strengths and weaknesses. Assessment is constant within lessons through effective questioning, checking for understanding, paired work, whiteboard work, I, We, You model. Every step of the lesson should be checking for understanding and using that to make proactive steps to plug gaps, extend learning and address misconceptions.
Accommodate learning over time
Teachers should take into account effective planning, sequential small step learning. How do children move on from their starting point and what is the next small step? What are the enabling factors that allow that to happen and what provision is being provided to enable that to take place?
This was how most classrooms were differentiated under the old NC. When I began my teaching career this is how I was training to differentiate. Even at this early stage in my career it confused me. Surely this widened attainment for the class, rather than narrowing it?
At this time there was an attainment gap in the UK in the world and part of this may have been due to how we were differentiating as evidenced in PISA. The Program for International Student Assessment (PISA) is an international assessment that measures 15-year-old students' reading, mathematics, and science literacy every three years.
The PISA 2015 data showed socio-economic correlations with attainment. Only 11% of UK participants in the study were found to be ‘higher attainers’ vs 22% ‘lower attainers’. There was a strong correlation between socio-economic background and attainment in the UK: the majority of lower attainers found to come from lower socio-economic backgrounds; the majority of higher attainers come from higher socio-economic backgrounds.
Ultimately if some of our pupils consistently access less complex or less challenging learning than their peers when do they get to reach the age-related expectations (ARE)? If in Year 1 they are constantly exposed to learning experiences that are just below ARE, what happens to them in Year 2? Year 3? The gap continues to get bigger. What happens to this child when they reach Year 6?
So what do we do?
Well, as much as we can we should be creating equitable environments where all pupils are given access to the same curriculum content. Pupils should be given appropriate amounts of learning time that allows them to focus on the skill/concept being taught. This means we need to ensure that the learning is cumulative. A well designed maths curriculum will mean that key concepts and skills are built upon over time and create conditions in which pupils are given the opportunity to deepen their understanding. Providing a firm and secure foundation in those fundamental mathematical skills means that pupils are able to secure their understanding of the mathematical concept they are learning.
Steps for Depth
As teachers, we need to pitch our teaching, questioning and tasks at the appropriate level for our pupils. Tasks that are too easy give no challenge to our pupils and tasks that are too hard can lead to confusion, misconceptions and ultimately frustration and disengagement. Task design needs to be considered thoughtfully so that pupils are given appropriate levels of challenge.
This is a resource I have designed that can be used with all pupils within the classroom who have varied attainment levels. Here you can see there are eight boxes that contain ‘steps’ for pupils:
What’s the same? What’s different?
If the answer is ___ what is the question?
Write a maths story for this equation.
What would happen if ________? Finish the sentence and prove it.
Create a ‘spot the mistake’
How could this be shown with a diagram or concrete materials?
Find the pattern.
Create a pictorial representation.
The resource provides a structured way to provide depth for all children with varying degrees of independence. Once pupils have been introduced to the box tasks and know how to navigate them they can be used to develop reasoning, conceptual understanding, language and deeper mathematical thinking. The box tasks are designed to be used fluidly within lessons in a range of ways. Teachers can use the tasks to:
provide depth within teacher modelling
form an independent activity
used within teacher led small group work
Extension activities for different children (task can be given to specific children based on prior pupil knowledge and understanding
pupil self selection (ensure they are pre-trained in this)
retrieval activities
starters/plenaries
live marking (give pupils a task box when live marking within the lesson)
marking next steps
Whole class feedback next steps
Essentially, we as teachers need to remember not to place glass ceilings on our pupils and ALL pupils deserve access to the same content. The task we have is to ensure we are creating situations via our modelling and task design where we are enabling this to happen.
You can download the Steps for Depth resource below or find it on my TES page here.