Reference
Reference information: As mathematics educators know, ‘counting on’ is an apparently simple (but actually, quite sophisticated) strategy used for finding the answer to an addition problem.
Young children often progress to it after using the self-explanatory ‘counting all’ strategy for a brief period. It comes in two forms: ‘count on from first’ and ‘count on from larger’. An example of the latter strategy to find, say, 5 + 8 would be: “Eight…nine, ten, eleven, twelve, thirteen. It’s thirteen.”
Reference: http://www.atm.org.uk/your-say/previous/ATM-Opinion-Thompson...
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