Multiple Representations in Mathematics


All human beings ‘meaning make’ at different rates and from different models and metaphors. At the point of learning a new mathematical idea, it is the teacher’s role to ensure that as many pupils as possible make sense of the ideas being communicated. We will explore the research and evidence around the use of different representations and then get hands-on working them to explore a diverse range of topics from subitising to simultaneous equations, averages and spread to division and primes, area and perimeter to sequences and graphs.


This course will outline the theoretical basis for using multiple representations in teaching, including the idea of representational fluency. We will explore how rekenerek and other visuals can be used to teach subitising. There will be some exploration of how Cuisenarie can be used to teach linear relationships and statistics, before we look at reasoning using fraction representations.

This course will also include a deep look at ideas including bridging insturction and variation theory. We will take a look at why multi-base arithmetic should be on the curriuclum of every school and explore some of the incredible insights this topic can give pupils and teachers alike. This course will then feature some work using manipulatives and pictorial representations to teach a variety of mathematical ideas from primary and secondary school.

Example Programme

  • 10:00   The theory of representations, including practical examples
  • 11:30   Variation Theory
  • 12:30   Lunch
  • 13:00   Manipulatives and Pictures
  • 14:00   Progression of Representations
  • 15:00   Finish

You will leave the course with...

  • An understanding of the importance of representational fluency in teaching.
  • Practical ideas for the teaching of a variety of topics from the primary and secondary curricula.

This course is appropriate for...

  • Primary, Secondary and FE Teachers
  • Non Specialists
  • Newly Qualified Teachers
  • Maths Subject Leaders

Your Course Leaders

Mark McCourt

Mark is the UK's leading authority on teaching for mastery. He has trained over 2000 schools in mastery models for schooling in the UK and overseas.

A leading figure in mathematics education, Mark has led many large-scale government education initiatives, both in the UK and overseas. Mark was a Director at the National Centre for Excellence in the Teaching of Mathematics (NCETM) and has also been a school leader, an Advanced Skills Teacher, a school inspector and a teacher trainer. He founded and was Chairman of the Teacher Development Trust.

Mark has extensive experience of mathematics teaching and learning across all age and ability groups, having taught students from age 3 to PhD!

Chris McGrane

Chris has 13 years of teaching experience, spread across 3 very different schools. Before becoming Mathematics Lead for La Salle in Scotland he was Principal Teacher of Maths at Hillhead High School and oversaw the design and implementation of a mastery curriculum - the first of its type in Scotland.

Chris has played a role in moving forward professional dialogue regarding mathematics education in Scotland. In addition to conference presentations he uses Twitter daily to share insight, ideas and opinion. He regularly publishes articles on his blog Recently, reflecting his interest in effective task design, Chris launched the website which shares tasks he has written and collated from colleagues.

Jonathan Hall

Jonathan has been teaching Maths in secondary schools since completing his PGCE in 2005. Before becoming a Mathematics Lead for La Salle, he was a successful head of department at Leeds City Academy for over five years and continues to work there as a Lead Practitioner of Mathematics.

Over the past decade, Jonathan has made significant contributions to the maths community by the creation of several well-known websites, most notably MathsBot, used by millions of teachers and students each year.

Jonathan has regularly presented at local and national conferences where he shares his both experiences and ideas from the classroom and the resources he creates. He is a keen Twitter user and is often posting new resources or updates to existing ones based on feedback from the maths community.

Locations and Dates:

  • Middlesbrough

    Unity City Academy (TS3 8RE)

    Thursday, 20th June 2019

Course Fees

£140 / 80

First Attendee / Subsequent Attendees



All Complete Mathematics members benefit from free access to courses and conferences from La Salle Education

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