Thinking out of the box on the symbol-grounding problem: Not cardinality but ordinality and the link with calculation! Cause or consequence?

For many daily life activities we rely on calculation and insight in mathematical relations. Many factors contribute to the math achievement level of an individual, one of them being efficient symbolic number (i.e. digits and verbal number words) processing. Despite the importance of symbolic number processing for math achievement, it is yet unclear how we acquire the meaning of symbols. The most popular account states that numerical symbols are learned by being ‘mapped’ onto their corresponding (innate) non-symbolic magnitude representation (i.e. arrays of dots). Several recent findings which do not reconcile with this account, however, have led us think out of the box and reconsider a disregarded alternative view. In this view, numerical symbols acquire meaning not by being associated or mapped with their cardinal value (i.e. the number of items in a set they represent), but by being based on ordered relations (i.e. four comes after three, three after…). Although studies have indeed demonstrated a correlation between symbolic order knowledge and math achievement, it remains to be investigated whether order representations are the cause or the consequence of math achievement. In this project, we describe a series of intervention and longitudinal studies with adults and children that will evaluate whether order representations are a core system for math achievement or whether learning simple additions result in better order knowledge.