Addition and Subtraction Mental, Informal, Standard written Method s

We have little or no experience of teaching mental calculation in this country and a conspicuous dearth of publications recommending suitable tried and tested teaching strategies Thompson, 2000

3 Key Messages – Mental Calculation Involves rapid recall Use of rapid recall facts and strategies to derive new facts May involve pencil and paper jottings Choice of strategy depends on the numbers involved, known facts and personal preference

Their characteristics…. feel for number bank of known facts range of strategies can match strategy to calculation can articulate and explain what they have done

5 General Strategies Counting on and counting back Partitioning

Particular Strategies Reordering Bridging Near doubles Compensation 6

The benefits….. reflects intuitive ways in line with what we do naturally promotes independent thinking allows for discussion

8 Number Line Images 33 – – 87 £3.29 – £1.59 Find how long between 4:30 and 9:15

9 The ‘empty’ number line Addition: Subtraction: 62 – – 289 £ £5.90

Informal written methods Addition Expanded addition Subtraction Counting up Negative numbers 10

Calculation skills should develop in such a way that a child first uses procedures which are rather long winded and even tedious compared with methods used by adults. However, these procedures are so designed that the child can see each step and can justify it at his own level of understanding. Lowry, 1965

The ‘adult’ methods…..

The ‘bugs’….

14 Progression: Mental with jottings Non standard written methods Formal / compact / standard method

Progression in Calculation “It seems unrealistic to expect that there will be a smooth progression from idiosyncratic mental methods to the standard written algorithms for the four basic operations” (Thompson, 1999, p. 170)

Key Features of Standard Algorithms Plunkett Written Standardised Contracted Efficient Automatic Symbolic General Analytic Not easily internalised Encourage cognitive passivity Clarke Traditional Powerful Reliable Precise Contracted Fast Provide a written record Mental image Instructive Easy to mark and manage