• Article

Specialist Knowledge for Teaching Mathematics (SKTM)

For secondary non-specialists: a new Maths Hubs CPD programme for 2021/22

Specialist Knowledge for Teaching Mathematics (SKTM)
  • Published: 29/04/2021
Are you teaching maths outside your own specialism? Or is someone in your maths department a non-maths specialist? Of course, there’s much more to teaching maths than knowing how to do the maths. And it’s not always obvious how teaching skills from other subjects can be adapted for the maths classroom.

The Maths Hubs Network is launching a new national professional development programme in 2021, which aims to provide non-specialist maths teachers with the specialist knowledge they need to support students to acquire mathematical understanding.

Specialist knowledge such as:

How to use representations to expose mathematical structure

These images can help students to understand the equivalent fractions:

Bar models are powerful images that can be used to represent many areas of maths, including ratio. In the example below, of a class of 30, with a 2:3 ratio of boys to girls, it can clearly be seen that 2⁄5 of the class are boys and 3⁄5 are girls:

These blocks, and place-value counters, can assist students' understanding of place value:

How to go beyond teaching knowledge and encourage students to use what they know to reason mathematically? The following are two popular examples:

‘Always, sometimes, never true’ activities begin to develop reasoning that forms the basis of mathematical proof:

Answer these statements using: Always, Sometimes or Never

  1. If a number is a multiple of 10, it is also a multiple of 5. ________
  2. If a number is a multiple of 4, it is also a multiple of 8. ________
  3. If a number is a multiple of 9, it is also a multiple of 2. ________
  4. Multiples are positive integers. ________
  5. Adding two consecutive multiples of 5 will give a multiple of 10. ________
  6. Adding 5 consecutive multiples of 2 will give a multiple of 10. ________

Questions such as this encourage students to interrogate and defend their understanding of algebraic expressions:

Which is bigger, 3n or n+3?

How to weave problem solving into all maths topics. Here are three possible ways:


When a certain four-digit number is rounded to two significant figures, the answer is 8000.

  1. What is the greatest value the number could be?
  2. What is the smallest value the number could be?


Mark and Ahmed share some sweets in the ratio 1:3.

Ahmed has eight more sweets than Mark.

How many does Mark have?

Area of a circle

This shape is cut from a square piece of card measuring 12 cm by 12 cm. Approximately what area of card remains?

The new programme draws on best practice established by the Teacher Subject Specialism Training (TSST), previously managed locally by individual schools or trusts. 18 sessions have been designed for six full days, or the equivalent in part-days or twilights. The programme will be run locally by Maths Hubs for small groups of up to 20 teachers, with a common outline across the country. Groups will work collaboratively, led by an experienced secondary teacher.

Each participating teacher will be provided with a hard-copy workbook for each session full of useful representations for the classroom that can be annotated and used for reflection. They will also work with a school-based mentor between sessions to reflect, plan and think deeply about mathematical concepts and how these are most effectively used in maths lessons.

To find out more about the programme and to register your interest, or to forward details to a colleague, please visit the SKTM – Secondary Non-specialists page in the Maths Hubs area of our website

All images used in this article are taken from the NCETM Secondary Mastery Professional Development Materials on which the SKTM programme draws heavily.

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