What does research say about mental computation?
Ann Heirdsfield
Heirdsfield was involved in a study to develop curriculum related to mental computation. To assist teachers she created a fantastic concept map to help understand the areas involved in mental computation. The initial branches include, numeration, number facts, estimation and effect of operation on number. These four points create a structure that helps better understand the processes of mental computation. The was a large emphasis on "...the importance of enhancing children's math reasoning processes and ability to represent, communicate, and connect ideas cannot be overestimated." (Heirdsfield, 2011). The academic terms canonical and non-cannonical mean the normal/standard form and non-standard with an understanding that we work with a base 10 number system. The terms 'subtrahend' and 'addend' refer to the operations for subtraction and addition.
Dale farron
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Barbara ReysBarbara Reys (1985) emphasises three main ideas that are practical and pedagogical benefits of 'Mental Computation'.
Despite the article being written in 1985 it still provides sound reasoning and explainations surrounding the pedagogies and strategies used for mental computation. |
In 1957, Wandt and Brown found that 75% of calculations done by adults in their daily lives involved mental computation. Northcote and McIntosh (1999) found that, in an age in which calculators are commonplace, this percentage had increased to 85%. (Cited in McIntosh, 2004).
ALISTAIR MCINTOSH
"...mental computation demands active thought about numbers and operations rather than unthinking recall of procedures. It is a creative and problem-solving approach to numbers. The essence of problem-solving is to use all one knows about a situation in order to come up with an optimum solution strategy." (McIntosh, 2004).
"It is extremely important that teachers have a coherent programme for assisting students to become familiar with, and to acquire confidence in using, a flexible range of strategies. The process through which students acquire mental strategies most effectively is:
Students who are visual thinkers are likely to maintain the link with the visual images; others will progress to the symbols and leave the mental images behind." (McIntosh, 2004).
- first present specific strategies in the form of actions on objects
- these in turn lead to mental images and mental models which can be operated on mentally
- these mental images in turn are often eventually replaced by actions on symbols without recourse to images.
Students who are visual thinkers are likely to maintain the link with the visual images; others will progress to the symbols and leave the mental images behind." (McIntosh, 2004).
DEECD
"...research over the last several decades has shown that students who are encouraged to use efficient mental computation strategies develop deeper understanding of number relationships." (DEECD, 2009)