Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.

@article{RittleJohnson2001DevelopingCU,
  title={Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.},
  author={Bethany Rittle-Johnson and Robert S. Siegler and Martha W. Alibali},
  journal={Journal of Educational Psychology},
  year={2001},
  volume={93},
  pages={346-362}
}
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. Two experiments were conducted with 5th- and 6th-grade students learning about decimal fractions. In Experiment 1, children's initial conceptual knowledge predicted gains in procedural knowledge, and gains in procedural knowledge predicted improvements in conceptual knowledge. Correct problem representations… Expand

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References

SHOWING 1-10 OF 88 REFERENCES
The conceptual basis of procedural learning
Abstract In the present article, two studies explored the proposal that conceptual knowledge facilitates the acquisition of procedures. The first study examined children's learning of integerExpand
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
Conceptual and Procedural Knowledge : The Case of Mathematics
Contents: Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. The Notion of Principle: The Case of Counting. Children's Mastery of Written Numerals and the Construction ofExpand
Role of Conceptual Knowledge in Mathematical Procedural Learning
Two experiments were conducted to explore the relation between conceptual and procedural knowledge in the domain of mathematics. The simultaneous activation view, which argues that computationalExpand
Instruction, Understanding, and Skill in Multidigit Addition and Subtraction
We traced the emerging relations between children's understanding of multidigit numbers and their computational skill and investigated how instruction influenced these relations. We followed about 70Expand
Teaching mathematics for understanding: what is a number?∗
Curriculum planners in America are reexamining mathematical operations and symbols to discover teaching approaches that connect symbols to meaning, and computation to real‐life problem‐solving. EarlyExpand
Developing Children's Understanding of the Rational Numbers: A New Model and an Experimental Curriculum
A new curriculum to introduce rational numbers was devised, using developmental theory as a guide. The 1st topic in the curriculum was percent in a linear-measurement context, in which halving as aExpand
Eliciting Self-Explanations Improves Understanding
TLDR
It is shown that self-explanation can also be facilitative when it is explicitly promoted, in the context of learning declarative knowledge from an expository text, and three processing characteristics of self-explaining are considered as reasons for the gains in deeper understanding. Expand
Conceptual competence and children's counting
Abstract A framework is presented for characterizing competence for cognitive tasks, with a detailed hypothesis about competence for counting by typical 5-year-old children. It is proposed thatExpand
Beyond competence: The significance of performance for conceptual development
Abstract Conceptual constraints must change with age if they are to account for children's acquisition of kinds of knowledge that do not fall within the initial constraints. A bi-directional relationExpand
...
1
2
3
4
5
...