Abstract
The research study described here was conducted with a small group of 5- and 6-year-old children in a 35-pupil rural school in the Langdale Valley (Lake District, UK) over a period of 14 weeks. It considers the theoretical implications of children inventing their own signs for their counting actions instead of using the culturally inherited signs of conventional arithmetic. It also raises questions concerning ‘transformational addition’ in which ordinals (‘position numbers’) are distinguished from cardinals (‘size numbers’), and suggests that the invented signs may have a consistency and validity comparable with the signs of conventional arithmetic.