Teaching Maths

Introduction to teaching maths

Understanding people’s motivations in learning maths

Many people say that they had negative experiences of learning maths in the past – usually at school.  For someone to return to education in maths is often a huge step and can be motivated by a number of factors, such as:

  • needing to pass a course that requires mathsassessment
  • needing to pass a one-off test, such as an entry test for a course or job
  • wanting to help children with their school work
  • wanting to learn something that they always wanted to crack – common topics that learners mention are long division and fractions
  • wanting to better themselves generally

If someone wants to return to learning they have probably overcome many barriers already.  If someone needs to learn then they might have some anxiety.

Of course for some learners maths may be something they never had the chance to learn formally or achieve certificates in, so don’t assume that everyone has been scarred.  Some people even enjoy it!


“Maths Anxiety”

Many tutors recognise the phenomenon known as “maths anxiety”, “fear of maths” or “mathsphobia”.  Students often avoid maths because of what appears to be a genuine fear of a subject they associate with worry, demoralisation and even humiliation.

Recent research from the University of Chicago identifies that people who experience anxiety about doing maths register actual pain during brain scans.

Tutors need to recognise, but not over-dramatise, the emotional baggage that some of their learners might bring to their learning.

Ask potential or new learners about their purposes in returning to learning and to ask, simply, “How did you find learning maths in the past?”

If they tell you that they had a difficult time:

  • explain that they are not alone in having had an unpleasant experience of mathslearning
  • describe the way in which they can learn mathswith you and what they can expect
  • explain that if they struggle with understanding mathsyou will do your best to explain in different ways and never to be afraid to ask for help again and again
  • try to encourage them to focus on the mathsthey already use in their daily lives and say that you will build on what they already know and do

It is a sad fact that, although people use a lot of maths in their daily lives, when you point this out to them they will say, “That’s just common sense.”  It seems that many of us see maths as being, by definition, the “difficult stuff” that we cannot do.


Preparing to tutor maths

Maths tutors need to have the language to describe concepts in several different ways, and make connections with learners’ existing knowledge and between different maths topics. If you’re new to tutoring numeracy/maths, it would be worth taking time to prepare yourself with a few refresher exercises for yourself.  Try these challenges:

  • explain in no more than 50 words what a percentage is
  • draw a picture that describes how 0.5 means the same as half
  • explain the connection between decimals, fractions and percentages – and give examples of times when you would use one rather than another
  • explain “place value” up to thousands
  • explain how the metric system makes calculations easier than the imperial
  • show a friend how to use “number bonds” and a “number line” to make their mental addition or subtraction skills more efficient
  • explain when you would use a pie chart to display data


It’s possible that you won’t be familiar with some of the terms in these challenges above.  If that’s the case, look them up on the internet.


Starting with what the learner can already do, or already understands

Adults bring to learning a wealth of maths knowledge and experience, often without realising it.  For example, in spite of a lack of skills, many people will have:

  • managed personal and household budgets
  • used timetables
  • shopped and cooked
  • chosen a mobile phone and
  • read a gas meter


They are likely to have used a range of strategies, often successful but sometimes flawed, as they manage the numbers in their lives.

The first job of the maths tutoring is to establish what people want or need to learn.   The next is to identify what they already know, understand and can do.

As with all of us, learners might have picked up misconceptions or have gaps in their knowledge.  It is important to uncover these misconceptions by observing how learners approach tasks, and by asking questions to check for understanding of method.

Approaches to Teaching Maths

Research has found that learning which is not passive but active is most effective for teaching maths.

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Analysing Mistakes

The best way to find out where a student has gone wrong is to ask them how they did the task.

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Key topics

This section will give you ideas for teaching various topics, regardless of the level your learners are working at.

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