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Young children's reasoning about many-to-one correspondences
Catherine Sophian1, Samara Madrid
1Department of Psychology, University of Hawaii at Manoa, USA. csophian@hawaii.edu
Child Development
|October 14, 2003
Summary
Seven-year-olds showed improved understanding of many-to-one correspondence after training, demonstrating a key step in developing multiplicative numerical knowledge. However, some children struggled to apply learned concepts to new problems.
Area of Science:
- Cognitive Development
- Mathematics Education
- Child Psychology
Background:
- Understanding numerical concepts is crucial for mathematical development.
- Many-to-one correspondence is a foundational concept linking additive and multiplicative reasoning.
- The transition to multiplicative thinking involves understanding repeated quantities.
Purpose of the Study:
- To investigate young children's grasp of many-to-one correspondence problems.
- To explore the developmental shift from additive to multiplicative numerical knowledge.
- To assess the impact of training on understanding iterative mappings.
Main Methods:
- Two experiments were conducted with children aged 5 to 7 years.
- A training procedure focused on the iterative nature of many-to-one mappings.
- Performance was evaluated on experimental and generalization problems post-training.
Main Results:
- 5- and 6-year-olds did not benefit from the training.
- A subset of 7-year-olds showed improvement after the training.
- 7-year-olds demonstrated training effects on generalization tasks, though some application difficulties persisted.
Conclusions:
- Seven-year-olds are beginning to develop an understanding of many-to-one correspondence.
- Training can facilitate the transition towards multiplicative reasoning in young children.
- Challenges remain in applying learned mathematical concepts to novel situations.