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Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.
The authors propose that conceptual and procedural knowledge develop in an iterative fashion and that improved problem representation is 1 mechanism underlying the relations between them. TwoExpand
Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.
Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentallyExpand
Promoting transfer: effects of self-explanation and direct instruction.
Both self-explanation and instruction helped children learn and remember a correct procedure, and self-Explanation promoted transfer regardless of instructional condition. Expand
Conceptual and procedural knowledge of mathematics: Does one lead to the other?
ages understand and what they struggle to learn, and examine how instruction influences children's acquisition of both concepts and procedures. The purpose of the present study was to explore theExpand
Learning to spell: variability, choice, and change in children's strategy use.
The overlapping waves model proved useful for understanding the development of spelling, despite the fact that explicit use of backup strategies had a minimal impact on accuracy. Expand
Developing Conceptual and Procedural Knowledge of Mathematics
The chapter reviews recent studies on the relations between conceptual and procedural knowledge in mathematics and highlights examples of instructional methods for supporting both types of knowledge. Expand
Conceptual and Procedural Knowledge of Mathematics : Does One Lead to the Other ?
This study examined relations between children's conceptual understanding of mathematical equivalence and their procedures for solving equivalence problems (e.g., 3 + 4 + 5 = 3 + ). Students in 4thExpand
Compared With What? The Effects of Different Comparisons on Conceptual Knowledge and Procedural Flexibility for Equation Solving
Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages andExpand
Assessing Knowledge of Mathematical Equivalence: A Construct-Modeling Approach.
Knowledge of mathematical equivalence, the principle that 2 sides of an equation represent the same value, is a foundational concept in algebra, and this knowledge develops throughout elementary andExpand