Key Principles for Teaching Maths

Some of the key principles behind the approach used by Steve Chinn to teach maths

1. Some children and adults cannot remember maths information, despite many hours of practice. We don’t know why this is, but we do know some ways to try and rectify this. More rote learning is NOT one of the ways.

2. We need a range of approaches because no one way works for all learners.

3. Maths builds and links so gaps in knowledge can prevent progress (see below).

4. Any first learning experience, what we learn when we meet new information, is a dominant entry to the brain. Despite ‘new’ learning we tend to return to the first learning, whether it is right or wrong. We need to teach how to unlearn.

5. New learning needs to be cognisant of the wrong learning and offer powerful alternative learning.

6. Frequent re-visits, refreshing, is needed to keep that new learning uppermost in the brain.

7. Know the pre-requisites of any topic and make sure your students have secured these before you teach the new topic.

8. Maintain motivation and encourage learners to take risks, so ….

9. Avoid giving negative evaluations, be that a look, a word or the comment that accompanies a mark. Don’t humiliate, especially publicly.

10. Encourage meta-cognition and flexible thinking. Encourage learners to discuss and explain their methods and how they perceive your methods.

11. Encourage risk taking. Have that as a key component of your classroom ethos.

11. Link the learning. Maths builds and links.


a. From basic facts to algebra. Use the secure knowledge to build new knowledge. That gives the new knowledge a cognitive foundation that will support memory.

number bonds for 10 7 + ___ = 10 to algebra 7 + y = 10

multiplication facts 7 x 8 = 5 x 8 + 2 x 8 to algebra 7y = 5y + 2y

b. Link the operations. Use addition as counting on to subtract.

Use multiplication to divide as ‘What do I multiply 6 by to get 42?’

c. Link fractions, decimals and percentages, so that examples such as 25% = 25/100 = 0.25

This make learning more efficient and, hopefully, quicker.

(There are many examples of this approach in the Maths Explained tutorials).

12. Beware of the pressure any demand for speed of working creates. Manage this. For example, set fewer questions for homework, but make sure they still cover the topic effectively.

14. Make sure the numbers used for each maths question are not a barrier to success. You are testing the concept, not recall of basic facts.

14. Actively address the problems created by a poor short-term memory. Don’t give out too much information at one time. Repeat information, especially the key information that the learner needs to start the task.

15. Actively address the problems created by a poor working memory, for example, don’t ask mental arithmetic problems that require more steps to solve than working memory can manage.

16. Use manipulatives and visual images, alongside the maths symbols, to explain concepts and procedures.

(There are many examples of this in the Maths Explained tutorials).

17. Match the manipulative and visual image to the concept. This means having a maths ‘kit box’ to hand.

18. Whenever possible, do an error analysis. It is possible to use examples in set work that can generate ‘common’ errors, such as 53 – 18, where ‘take the little from the big results’ in an answer of 45. This is not to create failure, but to expose mis-conceptions.

19. Intervention often needs to go back much further than you might think. Foundation knowledge may not be there.

20. Build a positive attributional style (see Martin Seligman’s work).

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