Concrete, Pictorial, Abstract, Language


This full-day CPD event will include a broad discussion of the importance of connecting learning through multiple representations of concepts and ideas when modelling and teaching.

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.

During this hands-on event, we will take a look at several mathematical ideas and how they might be taught through a CPAL approach.

  • A range of manipulatives for teaching mathematics
  • Detailed exploration of addressing some of the most important concepts in maths through a CPAL approach
  • How to increase pupils' understanding and attainment

Course Leader - 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!

*We cannot guarantee which of the workshop leaders will run this course.

Course Leader - 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. The work was been hailed as sector leading, while attainment improved over this time. Chris is an avid reader of literature relating to mathematics education and has shared both this learning and practice from his own classroom regularly at conferences, where has been a popular speaker. Chris has appeared on recent episodes of Craig Barton’s podcast and is scheduled to appear for an extended interview in the coming year.

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 Chris is the lead of the Glasgow branch of the Association of Teachers of Mathematics (ATM), which regularly puts on events with expert speakers. Recently, reflecting his interest in effective task design, Chris launched the website which shares tasks he has written and collated from colleagues.

*We cannot guarantee which of the workshop leaders will run this course.

Delegates will take away:

  • An appreciation of the research and evidence behind CPAL approaches.
  • Deep understanding of using manipulatives to teach across the age and attainment range.
  • 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.

Outline Programme:

  • Time

  • 10:00 - 10:15

    An introduction to CPAL, its history and the evidence
  • 10:15 - 11:15

    Using Cuisenaire Rods from Early Number to Trigonometry
  • 11:15 - 12:30

    Algebra Tiles from Counting to Algebraic Long Division
  • 12:30 - 13:00

  • 13:00 - 14:00

    Approaches to Equations
  • 14:00 - 15:00

    Using Paper Folding for Geometrical Proof

Locations and Dates:

  • Carlisle

    Upperby Primary School (CA2 4JT)

    Thursday, 16th May 2019

  • Aberdeen

    Oldmachar Academy (AB22 8UR)

    Tuesday, 4th June 2019

  • Leeds

    Leeds City Academy (LS6 2LG)

    Thursday, 11th July 2019

  • Leicester

    Beaumont Leys School (LE4 0FL)

    Friday, 12th July 2019

Course Fees



After the first delegate, any subsequent delegates are only charged £80



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