The results of a questionnaire that should reveal students’ knowledge about the use of computers in mathematics and the relevance of applications of mathematics in our society clearly show that current math teaching does not provide adequate ideas about the importance of computers. We describe the results and give examples of mathematical activities that are suitable to both foster mathematical concepts and widen the mathematical view. Possible changes in the curriculum are discussed.

Zugl.: @Diss.

Univ., Diss.--Freiburg, 2000.

The results of a questionnaire that should reveal students’ knowledge about the use of computers in mathematics and the relevance of applications of mathematics in our society clearly show that current math teaching does not provide adequate ideas about the importance of computers. We describe the results and give examples of mathematical activities that are suitable to both foster mathematical concepts and widen the mathematical view. Possible changes in the curriculum are discussed.

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Univ., Diss.--Freiburg (Schweiz), 2005.

dreimal im Jahr erscheinende Zeitschrift über aktuelle Themen der TU Chemnitz

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Das Buch argumentiert, dass Descartes seine Metaphysik von Körpern durch ein zweistufiges Argument begründet hat: Ersteres (letztendlich auf der Theorie der Ideen beruhend) soll beweisen, dass Körper erweiterte Substanzen sind; Letzteres (das die gesamte Naturphilosophie von Descartes nutzt) sollte beweisen, dass Körper nichts anderes als erweiterte Substanzen sind. Das Buch zeigt, dass es für Descartes keine Argumente aus der „ersten Philosophie“ gibt, die beweisen könnten, dass Körper nichts als erweiterte Substanzen sind. Es zeigt, dass Descartes’ Argument, alle „realen Qualitäten“ und „wesentlichen Formen“ der Scholastiker zu eliminieren, letztendlich ein Argument für die beste Erklärung ist, die auf ontologischer Sparsamkeit beruht. Mit anderen Worten, ein Rasiermesser. Insbesondere war es die Visionstheorie, den Paradigmenfall für Descartes’ Ontologie materieller Substanzen zu liefern. Die Arbeit kam zu dem Schluss, dass – entgegen der Behauptung praktisch aller kartesischen Gelehrten – die These, dass Körper nichts als erweiterte Dinge sind, nicht der Ausgangspunkt von Descartes’ Physik ist, sondern ihre Krönung. / The work argues that Descartes established his metaphysics of bodies by means of a two-step argument: the former (ultimately grounded on the theory of ideas) being intended to prove that bodies are extended substances; the latter (which takes advantage of Descartes’ entire natural philosophy) aimed at proving that bodies are nothing but extended substances. It shows that for Descartes there are no arguments from ‘first philosophy’ that could prove that bodies are nothing but extended substances. The work shows that Descartes’ argument to eliminate all “real qualities” and “substantial forms” of the Scholastics is ultimately an argument to the best explanation driven by ontological parsimony. In other words, a razor. More in particular, it was the theory of vision to provide the paradigm case for Descartes’ ontology of material substances. The work concluded that, contrary to what claimed by virtually all Cartesian scholars, the thesis that bodies are nothing but extended things is not therefore the starting point of Descartes’ physics, but its crowning achievement.

As a full-time Professor of Mathematics Education, as well as a part-time eighth grade (13 and 14 year olds) mathematics teacher, I have the opportunity to experience the teaching profession from “both sides of the fence.” My university courses are enhanced by my work in the field, while my eighth graders’ learning is strengthened by educational principles studied at the university. In this paper (and presentation), I will explain this partnership and the benefits to both audiences.