Fluency in mathematics combines both increasing efficiency in the use of different methods (procedural efficiency) with deepening conceptual understanding, so that children are capable of applying their understanding to the ensure the selection and accurate use of the appropriate strategies for different situations.

Deep conceptual understanding is needed in all aspects of number and the four operations, and understanding the connections between them during the primary years. For example, children need a strong conceptual understanding of the different manipulative structures symbolised by same operation, the concept of ratio and 1:many relationships in number.

Rich and varied experiences of manipulatives and visual images are indispensable for children to develop this. Intelligently designed practice develops fluency so they become confident in making decisions about which strategies to use most efficiently for calculations, as well as with manipulating the continuum of the number system itself, including fractions, decimals and percentages.

These are usually best explored with teachers practically through a series of workshops in:

  • Number and calculation - progression in Year R and KS1
  • Addition and subtraction - progression in KS2
  • Multiplication and division - progression in Year R and KS1
  • Multiplication and division - progression in KS2
  • Fractions - progression in KS1
  • Fractions, decimals, percentages - progression in KS2

In each of these workshops the focus is upon how manipulative and visual images are used by all learners to explore and express their conceptual understanding of the operations. Teachers will develop their own capacity for modelling and reasoning examples of their own. These provide the means for children to develop deeper understanding which they can reason and communicate with others,  and develop their fluency in the formal written methods.