International Journal of Mathematical Education in Science and Technology, 1995
The extension of 2D interactive graphics systems for geometric constructing in secondary schools ... more The extension of 2D interactive graphics systems for geometric constructing in secondary schools through tools for interactive calculations on geometric configurations provides, from a didactic point of view, an opportunity for reflection and analysis. In this article the qualities will be presented which an interactive tool for calculating in planimetry could and should possess. With reference to examples the functioning of a prototype calculation module (calculation module of Cabri‐geometre) will be described. A first evaluation will be made of the didactic potentialities involved and finally special and general problems of the use of such tools will be discussed.
Ordinary interactive dynamic geometry systems (IDGS) cannot generally show, how a measurable prop... more Ordinary interactive dynamic geometry systems (IDGS) cannot generally show, how a measurable property of an interactively constructed geometric figure depends on the determining variables of that figure. With a certain method of “Automated Deduction in Geometry” (ADG), implemented in Geometry Expressions (abbreviated GX, homepage: http://www.geometryexpressions.com/), it is now possible to calculate such a dependency as an algebraic expression consisting of the determining variables. We explain this facility by selected examples, which represent the usage of this tool and evaluate its application in classroom. keywords planimetry, automated calculation, interactive dynamic geometry systems.
An essential procedural aim in secondary education is the learning to solve problems. Problem sol... more An essential procedural aim in secondary education is the learning to solve problems. Problem solving its to be seen as the most complex form of learning, it can include concept learning and rule learning. We hope and believe that the abilities and skills developed through problem solving in secondary schools can be transfered to extra school activities. In geometry teaching we can differentiate between the following typical kinds or ideal types of problems: construction problems, calculation problems, theorem finding problems, proving problems...
International Journal of Mathematical Education in Science and Technology, 1995
The extension of 2D interactive graphics systems for geometric constructing in secondary schools ... more The extension of 2D interactive graphics systems for geometric constructing in secondary schools through tools for interactive calculations on geometric configurations provides, from a didactic point of view, an opportunity for reflection and analysis. In this article the qualities will be presented which an interactive tool for calculating in planimetry could and should possess. With reference to examples the functioning of a prototype calculation module (calculation module of Cabri‐geometre) will be described. A first evaluation will be made of the didactic potentialities involved and finally special and general problems of the use of such tools will be discussed.
Ordinary interactive dynamic geometry systems (IDGS) cannot generally show, how a measurable prop... more Ordinary interactive dynamic geometry systems (IDGS) cannot generally show, how a measurable property of an interactively constructed geometric figure depends on the determining variables of that figure. With a certain method of “Automated Deduction in Geometry” (ADG), implemented in Geometry Expressions (abbreviated GX, homepage: http://www.geometryexpressions.com/), it is now possible to calculate such a dependency as an algebraic expression consisting of the determining variables. We explain this facility by selected examples, which represent the usage of this tool and evaluate its application in classroom. keywords planimetry, automated calculation, interactive dynamic geometry systems.
An essential procedural aim in secondary education is the learning to solve problems. Problem sol... more An essential procedural aim in secondary education is the learning to solve problems. Problem solving its to be seen as the most complex form of learning, it can include concept learning and rule learning. We hope and believe that the abilities and skills developed through problem solving in secondary schools can be transfered to extra school activities. In geometry teaching we can differentiate between the following typical kinds or ideal types of problems: construction problems, calculation problems, theorem finding problems, proving problems...
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Papers by Dr. Heinz Schumann