Non-formal mechanisms in mathematical cognitive development: The case of arithmetic

Area of Science:

• Cognitive Psychology
• Developmental Psychology
• Educational Psychology

Background:

• The traditional view posits cognitive development involves a shift from non-formal to formal reasoning, particularly in mathematics.
• This study challenges the notion that non-formal mechanisms in arithmetic are phased out with age.

Purpose of the Study:

• To investigate the role of non-formal reasoning mechanisms in children's arithmetic development.
• To examine whether reliance on non-formal strategies increases or decreases with age.

Main Methods:

• Analysis of over 50,000 Dutch primary school children's performance on arithmetic expressions via an online platform.
• Identification and analysis of 'foil errors' resulting from violations of formal evaluation order.

Main Results:

• Foil errors were more prevalent when lower-priority sub-expressions were perceptually grouped or easy to compute.
• Reliance on these non-formal mechanisms (perceptual grouping, opportunistic selection) significantly increased with grade level.
• These non-formal strategies persisted and became more influential despite causing systematic rule violations.

Conclusions:

• Cognitive development in arithmetic may involve an increased reliance on non-formal reasoning, not a complete shift to abstraction.
• Findings challenge established theories of cognitive development in mathematics and have implications for educational practices.