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Concept-procedure interactions in children's addition and subtraction.

Katherine H Canobi¹

¹Department of Psychology, University of Melbourne, Melbourne, Vic. 3010, Australia. khc@unimelb.edu.au

Journal of Experimental Child Psychology

|September 24, 2008

Summary

Practicing addition and subtraction problems with conceptual sequencing helps children apply math skills to new problems. This structured practice also improves their understanding and explanation of core math concepts.

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Area of Science:

Cognitive Development
Mathematics Education
Child Psychology

Background:

Understanding how children learn mathematical concepts and procedures is crucial for effective teaching.
Previous research highlights the interplay between conceptual knowledge and procedural fluency in mathematics.
The development of addition and subtraction skills in young children involves both understanding underlying principles and mastering calculation techniques.

Purpose of the Study:

To investigate the interaction between conceptual understanding and procedural skills in children's learning of addition and subtraction.
To examine how a structured problem-solving practice phase influences children's mathematical performance and conceptualization.
To determine if conceptual sequencing of practice problems enhances the transfer of learning.

Main Methods:

A 3-week problem-solving practice phase was implemented with 72 children aged 7 and 8.
Participants completed pretests and posttests assessing accuracy, procedures, and conceptual explanations.
Data included performance on addition and subtraction problems, self-reported use of concept-based strategies, and verbalized conceptual understanding.

Main Results:

Conceptual sequencing of practice problems improved children's ability to generalize procedural learning to new problems.
Well-structured procedural practice enhanced children's capacity to articulate key mathematical concepts.
Initial procedural skills were significant predictors of subsequent conceptual advancements in mathematics.

Conclusions:

The findings support an iterative model of development for basic mathematical concepts and skills.
Integrating conceptual and procedural practice is essential for robust learning in addition and subtraction.
Children's mathematical development is characterized by a dynamic interplay between conceptual insights and procedural mastery.