EJMT Abstract

In the first part we will outline that in history of mathematics eight activities proved to be fundamental for generating new mathematical knowledge. They can be taken as a framework for scaffolding mathematical learning environments in classrooms of today. By this, modern learning theories about constructivism as well as procedural and conceptual learning could be augmented and enriched.

In the second part we will demonstrate by some mathematical examples for the middle and upper grades of high school the use of technology which might help to foster productive problem solving and thought processes. Furthermore ideas for a new computer based tool for measuring mathematical problem solving abilities in a PISA-like test are described which simulates some aspects of oral examinations. Finally we try to highlight in which way a computer-simulation of a mathematical lesson might help pre-service teachers to improve their abilities to teach mathematical problem solving.