Home // International Journal On Advances in Intelligent Systems, volume 9, numbers 3 and 4, 2016 // View article

Metacognitive Support of Mathematical Abstraction Processes: Why and How - A Basic Reasoning

Authors:
Hans M. Dietz

Keywords: Abstraction; Mathematical Abstraction; Mathematics Education; Mathematical Reading; Metacognition

Abstract:
A significant and distinctive feature of human beings is the ability of performing abstraction operations, e.g., when forming categories of objects or even conscioulsy creating abstract objects as it is typical in mathematics. Although the possible range of corresponding abilities is certainly pre-determined by individual genetic factors, a high-level abstraction performance will typically be achieved gradually by an intensive long-run practice in solving abstraction prone problems. On the other hand, mathematical abstraction is often considered to be a serious obstacle in mathematics education. As metacognition has turned out to be helpful in overcoming some other obstacles in the students' process of knowledge acquisition, one may ask whether metacognition may also serve as a remedy against the abstraction obstacle and, in particular, whether it may help to accelerate the acquisition of abstraction abilities. The paper provides some inital reasoning w.r.t. this possibility, proposes some basic principles of abstraction that could be taught on a metacognitive level, and presents a concept of a corresponding teaching experiment. Hopefully it will provide more effective teaching as well as a better understanding of cognitive processes underlying mathematical abstraction.

Pages: 352 to 362

Copyright: Copyright (c) to authors, 2016. Used with permission.

Publication date: December 31, 2016

Published in: journal

ISSN: 1942-2679