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

  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},
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

Figures and Tables from this paper

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
Individual differences in conceptual and procedural knowledge when learning fractions.
Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learnExpand
Procedural and conceptual knowledge acquisition in mathematics: where is collaboration helpful?
It is argued that the effectiveness of collaboration may depend on the type of knowledge the instruction targets, and the elaborative meaning-making activities ascribed to collaboration may facilitate learning. Expand
Conceptual and Procedural Knowledge of a Mathematics Problem : Their Measurement and Their Causal Interrelations
Some learning theories see conceptual knowledge as a source of children’s procedural knowledge. Others assume the opposite to be true or posit bi-directional causal relations. Empirical tests ofExpand
Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving
It is proposed that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of doubt, mediate interactions between procedural and conceptual knowledge. Expand
Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers
The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look atExpand
In pursuit of knowledge: comparing self-explanations, concepts, and procedures as pedagogical tools.
Investigating how type of instruction affected self-explanation quality and subsequent learning outcomes for second- through fifth-grade children learning to solve mathematical equivalence problems found conceptual instruction led to higher quality explanations, greater conceptual knowledge, and similar procedural knowledge compared with procedural instruction. Expand
Conceptual and Procedural Knowledge in Mathematics of Preservice Teachers in the Countryside
Mathematical competence rests on developing knowledge of concepts and procedures. It is, therefore, the aim of mathematics instruction to develop conceptual and procedural knowledge of students. ThisExpand
Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge.
This work modeled the three constructs in the domain of equation solving as latent factors and tested whether the predictive relations between conceptual and procedural knowledge were bidirectional, whether these interrelations were moderated by prior knowledge, and how both constructs contributed to procedural flexibility. Expand
Combining Exploratory Learning With Structured Practice to Foster Conceptual and Procedural Fractions Knowledge
Investigating in two quasi-experimental studies whether a combination of both task types fosters robust knowledge more than structured tasks alone confirmed this hypothesis and indicated that students learning with a combinationof tasks gained more conceptual knowledge and equal procedural knowledge compared to studentslearning with structured tasks only. Expand


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
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