Steffe et al (1983) made a crucial distinction between counting and the number word sequence.
Counting in the terms of Steffe et al; arises in problem-solving contexts - in addition and subtraction situations. Counting involves the coordination of each spoken number word with the conceptual production of a 'unit item'.
In this context , the term 'counting' is used to describe strategies that coordinate number words and conceptual items; or imagined items that are generated in the act of counting.
The term 'counting' is used in a broader sense than what teachers would typically use.
'Counting' used here can refer to students strategies when solving several kinds of tasks;
counting a collection of objects (eg. counters)
counting to figure out how many altogether in two screened (hidden) collections of counters
counting to figure out how many counters remain when some counters are added or removed from a screened collection.