Effective maths instruction

This blog post by Clare Sealy, she outlines the principles of maths instruction and an approach based on cognitive load theory. Citing Craig Barton’s book, ‘How I wish I’d taught maths’, she lists five principles of maths instruction:

  1. Present new information in small steps with pupil practice after each step
  2. Ask a large number of questions and check the response of all pupils
  3. Provide models
  4. Guide pupil practice
  5. Provide scaffolds for difficult tasks

These are based on Rosenshine’s Principles of Instruction, in particular: guided practice, everyone is successful, new material in small steps and lots of models. We have been working on an approach to planning maths in Year 1 that takes the whole class on a journey of instruction from modelling and explanation to guided practice to small group teaching alongside independent practice.

Year 1 approach

In this approach, the teacher introduces a model (for example, adding two groups by combining using a part part whole model). This is a large format version that everyone can see how it works – it could be an A3 version. The whole class stay together and all work, through guided practice, on the same model using ‘My Turn Your Turn’ or ‘Talk To Your Partner’ type strategies. The important thing is that everyone is working with the teacher and everyone has apparatus. When the learning is constructed in this way from the right starting point, everyone can come on board and everyone can be successful. After a cycle of tasks and interaction as a whole class (and only when the teacher feels the learning is secure), a group of children work with the teacher on a small group version of what we’ve been doing as a whole class – a bit like guided writing in English. Meanwhile, the other children work on a model and learning from previous days. When the teacher feels the children are ready to be independent, they then work on a mini version of the model that they complete in the exercise books. Here are some examples so you can see how it works.

Subtraction as take away • Addition as counting on

This approach provides a lesson structure but it requires good subject knowledge to identify the progression of maths learning in a specific domain. The image below shows the progression of number sentences from counting on orally, to counting on using common vocabulary to increasingly symbolic notation.

Progression of addition by counting on

 

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