Concrete, Pictorial, Abstract, Language


In order to secure greater depth of understanding and to give the highest possible chance for pupils to make meaning of mathematical structure, new learning should always include opportunities to explore ideas through concrete and image based manipulatives, all the time making connections to efficient symbolic and abstract approaches with explicit and precise mathematical language. This course draws upon the ideas of Bruner, Skemp and Dienes amongst others.


During this hands-on event, we will take a look at several mathematical ideas and how they might be taught through a CPAL approach. The course will explore how Cusineaire rods can be used to develop understanding of key concepts in number and early algebra.

This course will also outline how Algebra Tiles can be used in an axiomatically robust way to teach integers, algebra and equations. Finally, the course involves some work on paper folding to support the teaching of geometry ideas.

Example Programme

  • 10:00   An introduction to CPAL, its history and the evidence
  • 10:15   Using Cuisenaire Rods from Early Number to Trigonometry
  • 11:00   Algebra Tiles for Integers and Equations
  • 12:30   Lunch
  • 13:00   Algebra Tiles for distribution, factorisation, completing the square
  • 13:45   Using Paper Folding for Geometrical Proof
  • 15:00   Finish

You will leave the course with...

  • A deep understanding of using manipulatives to teach across the age and attainment range.
  • An appreciation of the research and evidence behind CPAL approaches.
  • Lots of example resources and manipulatives to use in the classroom.
  • Ways to embed CPAL approaches in programmes of study and individual lessons.
  • An approach to teaching, learning and assessment resources for all key stages.

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:

  • Ayr

    Prestwick Academy (KA9 2LB)

    Thursday, 23rd January 2020

  • Dumfries

    Wallace Hall Academy (DG3 5DS)

    Friday, 12th June 2020

Course Fees

£140 / 80

First Attendee / Subsequent Attendees



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

Contact Us

By phone:
020 8144 4748
By email:
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Or find us at:
121 King's Cross Road