The aim of this study is to achieve a deeper understanding of the repertoire of cognitive resources children can display in the process of learning numbers. Forty-two children attending Age 4 Kindergarten Class or Year-One in Argentina were individually interviewed, based on a semi-structured script requiring them to represent definite and indefinite quantities orally and notationally. Children's responses throughout the interview were categorized according to Scope of conventional knowledge, Non-conventional responses, Playfulness and Progress. Results of a series of Classification Analyses showed three main classes, which capture the tension between using what is known and exploring novelties in order to represent numerical meanings. (author abstract)