Abstract number and arithmetic in preschool children

Area of Science:

• Cognitive Science
• Developmental Psychology
• Mathematics Education

Background:

• Humans use language to express abstract number concepts.
• The origin of numerical abstraction, whether language or innate ability, remains debated.
• Evidence for pre-linguistic numerical knowledge requires demonstrating abilities across disparate entities without formal instruction.

Purpose of the Study:

• To investigate whether preschool children possess numerical abstraction abilities independent of language and formal education.
• To determine if young children can compare and add quantities in non-symbolic formats.
• To explore cross-modal numerical processing in early childhood.

Main Methods:

• Preschool children participated in experiments involving visual arrays of dots and auditory tone sequences.
• Tasks included comparing quantities between two visual arrays and adding successive arrays.
• Cross-modal tasks involved integrating quantity information from both visual (dot arrays) and auditory (tone sequences) stimuli.

Main Results:

• Children successfully compared and added large sets of items without counting.
• Performance was unaffected by guessing strategies or continuous variables, indicating true numerical processing.
• Accuracy correlated with the ratio of quantities, consistent with approximate number system representations.
• Addition accuracy matched comparison accuracy, even without symbolic understanding.

Conclusions:

• Preschool children exhibit abstract numerical knowledge, including addition, prior to formal mathematics instruction.
• These findings suggest that an innate approximate number system may underpin later mathematical learning.
• Abstract numerical cognition appears to precede and potentially guide language-based mathematical education.