Approaches to teaching maths

Traditionally, maths has been taught using a ‘transmission’ model, where a teacher, in a position of authority and expertise, relays information from the board to a passive class. The learners listen then repeat exercises on their own without collaboration.

Research has found that learning which is not passive but ‘active’ is most effective for teaching maths.  Active learning can be used in any context, including vocational contexts, with learners working at any level.  It encourages learners to be actively engaged in talking and collaborating to solve problems.  Questions come from not only the teacher but the learners themselves, and they tend to be higher-order, seeking deep understanding through exploration and broad application.  Question start with words such as: “Is it always the case that …?” and “Can you suggest a time when this would not be the case …?”


Active learning tasks

Active learning does not necessarily require learners to be physically active. suggests a range of activities that will enable students to learn actively.  These include:

  • “Hands-on” activities with concrete materials
  • Project work
  • Problem solving
  • Quizzes and games
  • Use of information and communication technologies, in particular multimedia
  • Structured discussion
  • Surveys, for example using questionnaires
  • Presentations
  • Debates
  • Fieldwork


A checklist for active learning

Examine your teaching practice, looking at session plans for specific sessions.  To what extent do you include:

  • activities which require learners to collaborate or co-operate with one another
  • space and time for discussion between learners
  • higher-order questions
  • time and space for learners to explore problems, making and correcting mistakes as they find them


Specific learning difficulties affecting maths ability


“Dyscalculia is the term used for a specific learning disability affecting numbers and maths. Students with dyscalculia have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number facts and procedures. Dyslexia and dyscalculia can co-exist or they can exist independently of one another.”

Research on the internet suggests that there are conflicting understandings (and beliefs) about dyscalculia’s nature and its status as a specific learning difficulty.

Formal research into dyscalculia stretches from psychological approaches involving brain scans to locate activity in the brain, which appears to have identified dyscalculia as a genuine and measurable phenomenon, to discussion around whether it might be linked to a whole spectrum of specific learning difficulties and anxiety about maths.

Teaching and reinforcement methods suggested for supporting learners “diagnosed” with dyscalculia are often very effective and sensible teaching approaches that would benefit all learners of mathematics.

Tips for teaching learners who show signs of possible dyscalculia (from include:

  • Focus on understanding (especially of quantity)
  • Use concrete materials to help link mathematical symbols to quantity
  • Start at a level which the child is comfortable at, so that they experience some success, and slowly move to more difficult areas
  • Provide a lot of practice for new skills/concepts
  • Reduce the need for memorisation, especially initially
  • Ask a lot of questions to get the child engaged and thinking about their own thinking
  • Make learning as active and fun as possible – a positive experience


To read more about dyscalculia, and for useful links, see:


Dyslexia and maths

People with dyslexia are likely to have difficulties with learning and using maths, especially when they need to read and extract information from text, or memorise information and work with sequences.

Some more information about how dyslexia affects someone’s maths learning can be found here:


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