Mental operations on number symbols by children

Area of Science:

• Cognitive Development
• Developmental Psychology
• Numerical Cognition

Background:

• Early childhood numerical cognition is crucial for mathematical development.
• Understanding how children learn abstract numerical concepts is an ongoing research area.
• Investigating the role of pretraining and association methods in early number learning.

Purpose of the Study:

• To investigate how children aged 4-6 learn number-color associations.
• To determine the effectiveness of different training methods (absolute vs. relative) and pretraining (counting/ordering).
• To model children's decision-making processes using cognitive models.

Main Methods:

• Children were trained on number-color associations using paired associate or choice discrimination methods.
• Half of the participants received pretraining on counting and ordering objects.
• Performance was assessed using "more or less" questions, and data were analyzed with Estes's scanning model.

Main Results:

• Absolute training and counting-ordering pretraining led to better acquisition of numerical associations.
• Estes's scanning model successfully fit the children's response data.
• A response strength model based on Luce's axiom was not supported by the data.

Conclusions:

• Young children possess an inherent ordered numerical scale.
• Children can map numerical scales onto non-quantitative symbols like colors.
• Children can generate, compare, and make ordinal decisions using these symbolic representations.