Deeper Understanding in Mathematics

Drawing on the best evidence in mathematics education research

The effective teaching of mathematics is a well understood process, with extensive and robust evidence of what works well available from important researchers such as John Mason, Anne Watson, Malcolm Swan, Margaret Brown and, more recently, meta-analyses which succinctly capture impactful practice (for example, the excellent recent report from The Education Endowment Foundation, Hodgen et al - see our blog and the NCETM report Mathematics Matters).

Mathematics teaching is more effective when it recognises both what has been learned and what needs to be learned, which means teachers must use assessment to build on pupils’ existing knowledge. Questions that reveal whether or not learning has occurred are complex, rich and explorative. Tasks should encourage reasoning rather than simple ‘answer getting’.

In this workshop, we will explore a range of higher-order questions, which can be addressed in a variety of ways including multiple representations and the use of mathematical manipulatives.

These rich questions exposes common misconceptions and other surprising phenomena, giving opportunities for extension, discussion and further learning.

We will use tasks which make connections between topics both within and beyond mathematics and with the real world and which engage pupils in collaborative learning that develops mathematical language through communicative activities.

A misconception has arisen in recent years that mathematics is about wading through questions and answering closed, simplistic problems. We will explore mathematical problems, suitable for all age and ability groups, which confront difficulties rather than seeking to avoid or pre-empt them. Such approaches also result in increased pupil independence and motivation.

The session will also link to the Complete Mathematics mastery model of learning, to illustrate how all pupils can learn all of school level mathematics.

Join us for a day of thought-provoking discussion and practical solutions for embedding approaches for deeper understanding in your classroom.


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.

*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.

Outline Programme:

  • Time

  • 10:00 - 11:00

    Research, Evidence and Myth-Busting
  • 11:00 - 12:30

    Higher Order Questions and Mutiple Representations
  • 12:30 - 13:00

  • 13:00 - 14:00

    Exemplar Topic: Exploring Simultaneous Equations
  • 14:00 - 15:00

    Mathematical Connections and Models

Locations and Dates:


Leeds City Academy, Leeds

Hurlingham Academy, London

Hillhead High School, Glasgow


Wednesday, 7th March 2018

Monday, 19th March 2018

Thursday, 22nd March 2018

Course Fees



£80 for subsequent delegates from the same school



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