Validation of Solutions of Construction Problems in Dynamic Geometry Environments

This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’ in DGEs and the use of only straightedge and compass in classic Euclidean geometry. We then demonstrate that the drag test criterion may permit constructions created using measurement tools to be considered valid; however, these constructions prove inconsistent with classical geometry. This inconsistency raises the question of whether dragging is an adequate test of validity, and the issue of measurement versus straightedge-and-compass. Without claiming that the inconsistency between what counts as valid solution of a construction problem in the two geometry worlds is necessarily problematic, we examine what would constitute the analogue of the straightedge-and-compass criterion in the domain of DGEs. Discovery of this analogue would enrich our understanding of DGEs with a mathematical idea that has been the distinguishing feature of Euclidean geometry since its genesis. To advance our goal, we introduce the compatibility criterion , a new but not necessarily superior criterion to the drag test criterion of validation of solutions of construction problems in DGEs. The discussion of the two criteria anatomizes the complexity characteristic of the relationship between DGEs and the paper-and-pencil Euclidean geometry environment, advances our understanding of the notion of geometrical constructions in DGEs, and raises the issue of validation practice maintaining the pace of ever-changing software.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42932/1/10758_2004_Article_6999.pd

Artigue M., Gras R., Laborde C., & Tavignot P. (Éds) (1996). Vingt Ans de Didactique des Mathématiques en France - Hommage à Guy Brousseau et Gérard Vergnaud. Grenoble, La Pensée Sauvage

Straesser R. Artigue M., Gras R., Laborde C., & Tavignot P. (Éds) (1996). Vingt Ans de Didactique des Mathématiques en France - Hommage à Guy Brousseau et Gérard Vergnaud. Grenoble, La Pensée Sauvage. In: Didaskalia, n°11, 1997. Expérimentation et modélisation. pp. 192-193

Students' constructions and proofs in a computer environment Problems and potentials of a modelling experience

SIGLEAvailable from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Geometrie und graphische Darstellungen in der Berufsschule Versuch eines Ueberblicks und didaktischen Kommentars

Copy held by FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Mathematics in technical and vocational education in the Federal Republic of Germany (FRG)

Seminar given in Sydney, 6 Sep 1984SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Mathematics teaching in technical and vocational colleges - professional training versus general education

SIGLEAvailable from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman