# 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} }

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.

## 62 Citations

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- Computer Science
- 2000

This presentation considers a theoretical cognitive development in arithmetic, algebra and the calculus and reflects on empirical research to show how the computer can be used both well and badly in supporting mathematical learning.

### THEORETICAL-COMPUTATIONAL CONFLICTS AND THE CONCEPT IMAGE OF DERIVATIVE

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Recent literature has pointed out pedagogical obstacles associated with the use of computational environments on the learning of mathematics. In this paper, we focus on the pedagogical role of…

### What Mathematics is Needed by Teachers of Young Children ?

- Education
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There has long been a dichotomy between the mathematics that is learned by trainee teachers ‘for their own personal development’ and the mathematics they will need to teach to young children. My…

### USING THEORETICAL-COMPUTATIONAL CONFLICTS TO ENRICH THE CONCEPT IMAGE OF DERIVATIVE

- Computer Science
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The pedagogical role of the computer's inherent limitations in the development of learners' concept images of derivative is focused on, and how the approach to this concept can be designed to prompt a positive conversion of those limitations for the enrichment of concept images.

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- Education
- 2010

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the…

### Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

- Education
- 2011

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the…

### Representational Fluency and Symbolisation of Derivative

- Education
- 2001

The nature of mathematical concepts has been the subject of some scrutiny in the mathematics education literature. One of the key ideas described in the literature is the distinction between the…

### A framework for examining characteristics of computer-based mathematical tasks

- Computer Science
- 2011

A tool which allows teachers, researchers and task designers to isolate, a priori, the possibilities and limitations of computer-based tasks is developed in the form of a framework that supports the notion that the use of technology in a task may afford the design of high-order thinking activities.

### USING TECHNOLOGY TO INTEGRATE CONSTRUCTIVISM AND VISUALISATION IN MATHEMATICS EDUCATION

- Education
- 2002

This paper provides a discussion of the pros and cons of instructivism and constructivism in the mathematics classroom, and endeavours to show why the latter is a preferable methodology to the former…

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