Modelling problem-solving situations into number theory tasks: The route towards generalisation

2010 ◽  
Vol 22 (3) ◽  
pp. 85-110 ◽  
Author(s):  
Ioannis Papadopoulos ◽  
Maria Iatridou
Keyword(s):  
Number Theory ◽  
Problem Solving ◽  
Modelling Problem

Even Perfect Numbers—An Update

1981 ◽  
Vol 74 (6) ◽  
pp. 460-463
Author(s):  
Stanley J. Bezuszka
Keyword(s):  
Number Theory ◽  
Problem Solving ◽  
History Of Mathematics ◽  
Independent Study ◽  
History Of ◽  
Perfect Numbers ◽  
Excellent Resource

Do you have students who are computer buffs, always looking for a new problem to program efficiently? Do you have students who do independent study projects? If so, motivate them with this topic that is rich in the history of mathematics and number theory—perfect numbers. They provide an excellent resource for theoretical as well as computerized problem solving.

Teaching Engineering Field Theory Using IT

1997 ◽  
Vol 25 (1) ◽  
pp. 1-12
Author(s):  
H. W. Gretton ◽  
J. T. Callender ◽  
N. V. Challis
Keyword(s):  
Field Theory ◽  
Heat Conduction ◽  
Problem Solving ◽  
Computer Technology ◽  
Engineering Practice ◽  
Two Dimensional ◽  
Mathematical Skills ◽  
Repetitive Tasks ◽  
Engineering Mathematics ◽  
Modelling Problem

In this paper it is argued that modern developments in technology, such as the spreadsheet, open out possibilities for different approaches to topics in engineering mathematics, for example field theory. The aim here is not to reduce mathematics for engineers to the level of pressing buttons, but it is to encourage a deeper understanding. The visualization capabilities of computer technology, and its strength in performing repetitive tasks, can allow and indeed encourage a review both of what mathematical skills and understanding are required of engineers now and also of the best approach to nurturing that understanding. For example in an approach to two- dimensional heat conduction, the initial emphasis may be shifted away from heavy manipulation and towards modelling, problem solving and building a conceptual framework. This allows students to develop an intuitive feel for typical problems before becoming entangled in some of the more complex analytical and mathematically sophisticated issues. The current example is only one of many where modern developments in technology may lead to a review of educational as well as engineering practice.

Teaching Teachers to Teach Mathematics

1996 ◽  
Vol 178 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Rika Spungin
Keyword(s):  
Number Theory ◽  
Problem Solving ◽  
Prospective Teachers ◽  
Problem Solving Strategies

Group investigations from the areas of number theory, probability, and geometry. are presented and discussed. By working in groups, sharing ideas, and making and testing conjectures, prospective teachers gain confidence in their own ability to do mathematics and develop a variety of useful problem-solving strategies.

Polygons, Stars, Circles, and Logo

1986 ◽  
Vol 33 (9) ◽  
pp. 6-11
Author(s):  
Bill Craig
Keyword(s):  
Middle School ◽  
Elementary School ◽  
Number Theory ◽  
Problem Solving ◽  
Elementary School Students ◽  
Upper Elementary ◽  
School Students ◽  
Know How ◽  
Elementary And Middle School ◽  
Mathematical Topic

Many teacher are excited about the potential uses of Logo with elementary school students. The language give students access to mathematical topic they have not previouly explored. The following activitie uae Logo in the study of geometry, number theory, and problem solving. The activities assume that tudents are familiar with turtlegraphic commands (FORWARD, BACK, RIGHT, LEFT) and know how to define procedures. The activitie are designed for students in the upper elementary and middle school grades. The star procedure and explorations are adapted from Discovering Apple Logo by David Thornburg. The book contains excellent ideas for the use of Logo as a tool for mathematical explorations. See the Bibliography for additional resources.

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