Number Sense Maths Principle 3

Using a derived fact strategy approach is the best way to commit addition and subtraction facts to memory.

Research Finding

An alternative approach to developing fluency in these facts is a ‘memorisation only’ approach. However, the total set of facts to be learnt is 242 and rote memorisation of facts involving similar numbers is challenging [7]. Comparison of a derived facts approach with a traditional memory based approach showed that the derived fact approach was more successful at leading to gains in speed and fluency in addition and subtraction facts, and crucially benefits of this approach are retained for longer once teaching has finished[4]. In fact, children who use derived fact approaches do over time memorise some of the facts they are repeatedly deriving [1]. Deriving facts is a more effective route to memorisation than teaching through memorisation directly. Another disadvantage to a memory only approach is the missed opportunity to teach number relationships which a derived fact strategy approach provides [8] (see Principle 6).

Application to Number Sense Maths

Number Sense Maths explicitly teaches number relationships and linkages, encouraging children to avoid seeing calculation in isolation, and rather to look to "use what they know to work out what they don't yet know".


[1] GRAY, E. and TALL, D., 1994. Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic, The Journal for Research in Mathematics Education, 26 (2), 115–141.

[4] THORNTON, C.A., 1978. Emphasizing Thinking Strategies in Basic Fact Instruction The Journal for Research in Mathematics Education, 9 (3) 214-227.

[7] DEHAENE, S. (2011). The number sense: how the mind creates mathematics.

[8] MA, L., 2011. Three approaches to one-place addition and subtraction: Counting strategies, memorized facts, and thinking tools. Available at