Cognitive development in advanced mathematics using technology

@article{Tall2000CognitiveDI,
  title={Cognitive development in advanced mathematics using technology},
  author={David Tall},
  journal={Mathematics Education Research Journal},
  year={2000},
  volume={12},
  pages={196-218}
}
  • D. Tall
  • Published 1 December 2000
  • Psychology
  • Mathematics Education Research Journal
This paper considers cognitive development in mathematics and its relationship with computer technology, with special emphasis on the use of visual imagery and symbols and the later shift to formal axiomatic theories. At each stage, empirical evidence is presented to show how these forms of thinking are enhanced, changed, or impeded by the use of technology. 

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References

SHOWING 1-10 OF 44 REFERENCES

Knowledge construction and diverging thinking in elementary & advanced mathematics

This paper considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum and shows how students cope with the transition to advanced mathematical thinking in different ways leading once more to a diverging spectrum of success.

Interrelationships Between Mind and Computer: Processes, Images, Symbols

The article considers the relationship between processes carried out by the computer, images generated by thecomputer and in the mind of the individual, and the resultant relationship with mathematical symbols and their mental manipulation.

A conceptual approach to the early learning of algebra using a computer

The findings of this research show that the use of a module based on a computer environment, with its many advantages for conceptual learning, prior to the more formal introduction of algebraic techniques, is of great cognitive value and suggest that for the production of a versatile learner in mathematics, more attention should be paid to the integration of the global/holistic abilities of the individual with his/her serialist/analytic abilities.

The psychology of learning mathematics

Contents: Part A:Introduction and Overview.The Formation of Mathematical Concepts. The Idea of a Schema. Intuitive and Reflective Intelligence. Symbols. Different Kinds of Imagery. Interpersonal and

Duality, Ambiguity and Flexibility in Successful Mathematical Thinking

In this paper we consider the duality between process and concept in mathematics, in particular using the same symbolism to represent both a process (such as the addition of two numbers 3+2) and the

The School Mathematics Project

The School Mathematics Project is one of several organizations for the improvement and renewal of parts of the school curriculum in Britain. It is now concerned with problems of application as well

Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic

In this paper we consider the duality between process and concept in mathematics, in particular using the same symbolism to represent both a process (such as the addition of two numbers 3+2) and the

Information Technology and Mathematics Education: Enthusiasms, Possibilities and Realities.

Abstract This presentation addresses critical issues in the use of information technology in Mathematics Education. By reflecting on human thinking processes, it will consider developments of

CONSTRUCTION OF CONCEPTUAL KNOWLEDGE: THE CASE OF COMPUTER-AIDED EXPLORATION OF PERIOD DOUBLING

This research focuses on students using an experimental approach with computer software to give visual meaning to symbolic ideas and to provide a basis for further generalisation in the theory of geometric convergence.

Advanced Mathematical Thinking

Preface. Introduction. 1. The Psychology of Advanced Mathematical Thinking D. Tall. I: The Nature of Advanced Mathematical Thinking. 2. Advanced Mathematical Thinking Processes T. Dreyfus. 3.