Deeper Understanding in Mathematics


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.

Example Programme

  • 10:00   Research, Evidence and Myth-Busting
  • 11:00   Higher Order Questions and Mutiple Representations
  • 12:30   Lunch
  • 13:00   Exemplar Topic: Exploring Simultaneous Equations
  • 14:00   Mathematical Connections and Models
  • 15:00   Finish

You will leave the course with...

  • How to better utilise a range of tasks.
  • How to question types to develop opportunties for deeper thinking in pupils.
  • Practical solutions for embedding approaches for a deeper understanding in your classroom.

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:

  • Coming soon


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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