Many adults have gone through the trials and tribulations of learning to drive. Whilst some take to it immediately, others need more time and space to hone their skills. During our multiplication research project, Making Sense of ‘X’, we have similarly found that some pupils acquire new facts with relative ease, with others needing extra support to develop multiplicative fluency.
In the Herts for Learning maths team, we have been supporting schools and pupils by using this model to reflect on how curriculum time is spent. In our new online training programme, launching this term, we have used the learning to drive analogy to break down the crucial stages:
Taking a mock driving test every week without any instruction or support between tests is unlikely to improve driving skills. Whilst assessment is an important element of any learning, we believe there are important stages which need to be prioritised before pupils are ready to be assessed in their multiplication tables. Just like focusing on a new manoeuvre, for the start of each multiplication table, pupils will need time to go back to learn and rehearse before mastering the new skills.
When learning to drive, novice drivers need to begin with expert instruction. They need plenty of time dedicated to hands-on experience and discussion, with support to make connections to prior knowledge and skills. We believe it is the same for multiplication, with time needed to build, deconstruct, draw and talk about the structure behind the facts.
Throughout our ESSENTIALmaths plans, we use speaking frames such as this to support pupils to describe the structures they have built and drawn. We would want pupils to be able to move between different representations which could involve manipulatives such as counters, cubes, beadstrings and everyday objects. Our previous blog looked specifically at this phase in detail.
Once you have been taught the basics of mirror, signal, manoeuvre, it is time to rehearse the different elements, starting with easier manoeuvres and building up stamina over time. There are countless ways of rehearsing multiplication tables but one way of providing daily opportunities is to use a counting stick for your focus times table. As well as building fluency in counting up, down and out of order, there is also the chance to build in reasoning.
This example shows possible questions and responses to describe a missing value. To begin with, pupils may produce simple responses such as “I know it is 28 + 4”. However, once they are familiar with the concept, pupils often come up with ever elaborate responses which show a level of much deeper understanding.
Once there has been plenty of time for varied rehearsal, it is time to for the learner driver to recall how to perform a range of manoeuvres in increasingly complex situations. Learners may need to go back to the ‘learn’ or ‘rehearse’ stage before progressing on. Part of the recall stage in terms of multiplication could involving low-threat gaming opportunities. This could start with a simple bingo board where the ‘caller’ reads out a product, with the players finding the corresponding calculation. Alternatively the players could be provided the product and the ‘caller’ calls out the calculation.
Other gaming opportunities could involve dice or playing cards, either for a focus times table or a mixed set of calculations. It is essential that pupils have the underlying understanding from the ‘learn’ and ‘rehearse’ stage and are not attempting to recall disconnected facts and, in some cases, inadvertently practising incorrect facts.
Like teachers, driving instructors use on-going assessment to inform which further teaching, rehearsal or practice opportunities are needed before the final assessment of the driving test.
It is up to schools how they use purposeful assessment to support teaching and learning but we would encourage all teachers to use testing as a brief stocktake opportunity, with the bulk of teaching time being spent on the stages that precede ‘assess’. One aspect of the MTC which we are regularly asked about is the timed element of it. This is something that many pupils may need building up to, to ensure a focus on speed is not brought in too early; inadvertently impeding the learning.
By the end of the progression, we aim for pupils to be able to take the wheel and recall and apply their facts with independence and confidence. There are often bumps in the road, and obstacles to overcome, but it has been fantastic to see pupils across the schools we work in building their skills to then apply their increased understanding across the maths curriculum.
- reflect on the ‘learn, rehearse, recall, assess’ model. What is already going well for you? Is there any aspect that could be enhanced to support your pupils?
- are all year groups playing their part to ensure pupils have the pre-requisite skills to allow pupils to be fluent by the end of Year 4?
- what aspects of the ‘learn, rehearse, recall, assess’ model could be used for pupils in UKS2 who are yet to secure all the multiplication facts up to 12 x 12?
Is this a key focus in your school? We are launching a new digital training offer with pre-recorded modules for delegates to access at a convenient time. This course will explore the phases of learning, rehearsal and recall to develop pupils' retrieval of these multiplication facts with understanding and confidence. Delegates will also have the chance to explore the most up to date guidance from the Department for Education (DfE) about the Multiplication Tables Check (MTC) and implications for the 2020/21 academic year.
Supporting pupils to learn multiplication facts: effective strategies for rehearsal and recall’ is a digital training package available to access between 22nd October and 20th November 2020. Full details are available: www,cpd.hertsforlearning.co.uk/elearning/Course/Detail?CourseId=259 or please contact: firstname.lastname@example.org.
More information is available at:
Further professional development opportunities:
Making Sense of ‘X’ project
After running the project with 45 schools across 2019-2020, we will soon be recruiting schools keen to participate in 2021. Please follow the link or get in touch if you would like further information: