By Corrinne Fraser
Corrinne Fraser is a mathematics education consultant who works to support MATS, boroughs and individual schools strengthen their provision for mathematics. Corrinne has worked across institutions and key stages to align maths teaching and learning to new curriculum requirements and the drive for mastery in UK schools. Corrinne is passionate about inspiring teachers and young people through dynamic yet accessible approaches to learning and loving mathematics.
Starting secondary school can be daunting. There are countless new demands on young people as they transition from being the ‘top dogs’ in primary school to the ‘littlest fish’ in their secondary setting; most new Year 7 students will be navigating an unfamiliar building, taking greater responsibility for managing their own time, and perhaps even studying new subjects.
Ahead of all these pressures, how can we as Year 6 teachers make sure students feel confident to build upon their mathematics learning from Key Stage 2 as they start Key Stage 3? I believe there are a few key concepts which are integral to preparing students to access the secondary curriculum and thrive in their mathematics lessons. By incorporating them into primary teaching, we can ensure that Year 7 maths feels like a continuation of students’ prior learning, rather than a brand-new start.
Support students to select and evaluate problem-solving strategies, and to explain their thinking.
Looking ahead to GCSE, up to 60% of the assessment marks will come from questions that require students to communicate their reasoning clearly, or problem solve and apply their mathematical skills in unfamiliar contexts. Alongside mathematical proficiency, they will need to be able to justify their methods and be brave enough to tackle problems that do not seem straightforward.
The most recent reforms to the GCSE course were designed to encourage a ‘deeper and wider’1 approach to teaching mathematics, and the exams at the end of Key Stage 4 certainly reflect this goal. Becoming successful mathematicians is about more than just recalling mathematical facts and carrying out procedures fluently. Students must also be able to explain their thinking, outline why the processes work, move between real-life applications of mathematics and make judgement calls on what maths to use and when. Building confidence in applying mathematical learning to a wide range of situations is not something that can be crammed into Years 10 and 11 – all teachers have a responsibility to support students in developing these skills as early as possible. The primary setting is the ideal space to foster a habit of explaining reasoning and justifying approaches – not least because the physical layout of classrooms facilitate discussion and group work.
Encourage students to use precise mathematical language to establish a shared maths vocabulary between Key Stages 2 and 3.
At the heart of clear communication is a strong command of language. Dr Kovarik wrote an insightful paper outlining the benefits of expanding on students’ use of correct terminology and the common barriers to success in this endeavour.2
In secondary school, students will be expected to explain their thinking using precise and sophisticated mathematical vocabulary. Sometimes teachers, across all key stages, shy away from mathematical vocabulary, worrying that it will overcomplicate lessons or make the topic seem intimidating or inaccessible.
However, it is vital that we give students the correct tools to explain their thinking and make their reasoning clear; to do this we must integrate the correct vocabulary into their day-to-day language. Modelling the precise use of mathematical words and promoting it in the classroom provides an excellent foundation for students upon which to build their logic and reasoning skills upon.
There is often a disconnect between the words used at primary and secondary school – important terms such as ‘regroup’, ‘number families’ and ‘partitioning’ are familiar to Key Stage 2 teachers and students, but may not be so to our Key Stage 3 and 4 colleagues. This means an opportunity to build on these concepts using the correct terminology may be missed. There are also occasions where oversimplifying or omitting terminology at primary can lead to terms being re-learnt at secondary unnecessarily – a frustrating experience for students and teachers alike. Sharing key terms and teaching strategies between teachers as part of the transition process is incredibly beneficial in supporting students moving between settings.
Empower students to continue a concrete–pictorial–abstract approach to mathematics in Key Stage 3.
The EEF has documented how powerful manipulatives can be when used to support learning.3 Being able to represent problems using diagrams can also support students in overcoming vocabulary issues or help them to find a solution strategy. Disappointingly, the use of manipulatives is rare and often stigmatised in secondary settings. This shortcoming is partly due to a lack of awareness among secondary school teachers of the importance of concrete and pictorial representations in securing strong understanding of mathematical concepts.
However, if students are encouraged throughout primary to use manipulatives or pictorial representations to support them in accessing and expanding conceptual notions, then they will take these strategies with them to secondary school. Then, as more and more empowered students move into Key Stage 3, perhaps we will see a shift in secondary colleagues realizing how useful these learning aids are.
The Maths Anxiety Trust reports that many students fall out of love with, or worse, become more anxious about the subject as they get older,4 which is disheartening for any maths teacher, at any key stage, to read. But, by building the above considerations into our planning for the transition to secondary, and by finding opportunities to collaborate with our secondary school colleagues to nurture competent and creative mathematical thinkers across the key stages, I hope we can break the cycle of underachievement and lack of confidence that exists in too many secondary school classrooms.
Corrine Fraser is one of the expert authors behind MathsBeat, Oxford’s digitally-led maths mastery resource. MathsBeat can provide you with a clear and consistent teaching and assessment spine designed to engage all children and set them up for success with maths throughout primary, into secondary and beyond.
MathsBeat also includes dedicated Secondary Progression Units that are focused on consolidating knowledge from Key Stage 2 and developing children’s fluency, logic and communication through mathematical investigation. Accompanying each unit is also a Reflection Journal so students can be supported in developing their metacognitive skills.
Find out more about MathsBeat at www.oxfordprimary.co.uk/mathsbeat
1 ‘Reformed GCSE subject content consultation: Government response’, November 2013. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/254513/GCSE_consultation_-_government_s_response.pdf
2 Dr Madeline Kovarik: ‘Building Mathematics Vocabulary’ in International Journal for Mathematics Teaching and Learning, Oct 2010 https://www.cimt.org.uk/journal/kovarik.pdf
3 Education Endowment Foundation: ‘Improving mathematics in Key Stages Two and Three: Guidance report’, 2017. https://educationendowmentfoundation.org.uk/public/files/Publications/Maths/KS2_KS3_Maths_Guidance_2017.pdf
4 Carey et al: ‘Understanding mathematics anxiety: Investigating the experiences of UK primary and secondary school students’, March 2019. http://bit.ly/2QGTzU6