Supertasks and numeral systems

In the design of computer microworlds as media for children's mathematical action, our basic and guiding principle was to create possible actions children could use to enact their mental operations. These possible actions open pathways for children's mathematical activity that coemerge in the activity. We illustrate this coemergence through a constructivist teaching episode with two children working with the computer microworld TIMA: Bars. During this episode, in which the children took turns to partition a bar into fourths and thirds recursively, the symbolic nature of their partitioning operations became apparent. The children developed their own drawings and numeral systems to further symbolize their symbolic mental operations. The symbolic nature of the children's partitioning operations was crucial in their establishment of more conventional mathematical symbols.

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Numerical Methods I

10.20850/9781716344954 ◽

2021 ◽

Author(s):

Boris Obsieger

Keyword(s):

Numerical Methods ◽

Computer Program ◽

Iterative Methods ◽

Error Propagation ◽

Random Variables ◽

Regression Analyses ◽

Practical Application ◽

Numeral Systems ◽

Roots Of Polynomials ◽

Digital Computers

Textbook of several universities. 2nd edition. The color edition is also available at Glasstree Bookstore. It is recommended for students. The series of books Numerical Methods is written primarily for students at technical universities, but also as a useful handbook for engineers, PhD students and scientists. This volume introduces the reader into numeral systems and representation of numbers in digital computers. Possibly the most important part of this book are descriptions of differences between constant and random variables, related types of errors and error propagation. These topics are supplemented with various types of regression analyses. Finally, direct and iterative methods for finding roots of polynomials are explained. Practical application is supported by 77 examples and 13 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be included in any computer program.

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