Adaptive variability in children's conceptual models of division

Area of Science:

• Cognitive Psychology
• Mathematics Education
• Developmental Psychology

Background:

• Children often struggle with whole number division, relying on the partitive model.
• This reliance can hinder understanding when transitioning to fraction division.
• Prior research indicates a need to explore diverse division strategies.

Purpose of the Study:

• To investigate how different mathematical tasks influence children's whole number division strategies.
• To assess the adaptive use of division models by elementary school children.
• To identify potential representations that bridge whole number and fraction division concepts.

Main Methods:

• Sixty-three elementary school children solved whole number division problems.
• Problems were presented in three contexts: objects, story problems, and number lines.
• Children's problem-solving strategies and conceptual models were analyzed.

Main Results:

• Children demonstrated multiple division models, with strategy use varying by context.
• Story problems primarily elicited partitive models; number lines elicited quotative models.
• Objects elicited both partitive and quotative models, showing adaptive strategy use.

Conclusions:

• Elementary students adapt their division strategies based on the mathematical task context.
• Number line representations may facilitate conceptual links between whole number and fraction division.
• Supporting adaptive strategy use can enhance the integration of children's mathematical knowledge.