Developing Conceptual and Procedural Knowledge of Mathematics

@inproceedings{RittleJohnson2015DevelopingCA,
  title={Developing Conceptual and Procedural Knowledge of Mathematics},
  author={Bethany Rittle-Johnson and Michael Schneider},
  year={2015}
}
Mathematical competence rests on developing knowledge of concepts and of procedures (i.e. conceptual and procedural knowledge). Although there is some variability in how these constructs are defined and measured, there is general consensus that the relations between conceptual and procedural knowledge are often bi-directional and iterative. The chapter reviews recent studies on the relations between conceptual and procedural knowledge in mathematics and highlights examples of instructional… 

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References

SHOWING 1-10 OF 106 REFERENCES

Conceptual and procedural knowledge : the case of mathematics

Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis is presented, which examines the relationship between initial Meaningful and Mechanical Knowledge of Arithmetic and the Acquisition of Decimal Number Knowledge.

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. Two

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 learn

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.

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 the

The developmental relations between conceptual and procedural knowledge: a multimethod approach.

The results reveal substantial problems with the validities of the measures, which might have been present but gone undetected in previous studies and are essential for theoretical and practical progress in the field.

Individual differences in conceptual and procedural fraction understanding: the role of abilities and school experience.

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 computational

Advances in Instructional Psychology

The contributors to this volume address reasoning and problem solving as fundamental to learning and teaching and to modern literacy. The research on expertise and the development of competence makes

In pursuit of knowledge: comparing self-explanations, concepts, and procedures as pedagogical tools.

...