NOMAD 11(2), 2006. A less radical constructivism

Skapad: 2006-06-30. Ändrad: 2006-11-02  

NOMAD 11(2), 2006. A less radical constructivism

JESSICA CARTER

Abstract

This paper poses two problems for von Glasersfeld's Radical Constructivism. The first problem concerns the rejection of the idea that it is possible to share meanings. The second problem is that Radical Constructivism rejects the notion of an objectively existing reality of which we can have objective knowledge. Yet with respect to mathematics, von Glasersfeld seems to claim that it is possible to obtain objective knowledge. We propose an alternative position - Constructive Realism - that gives a description of what mathematical objects are and gives an account of why knowledge in mathematics is objective. Furthermore, we argue that some of the assumptions, used in von Glasersfeld's description of how numbers are formed, support the claim that some meanings are objective and that communication is possible. Finally, we consider some of the implications this position has for mathematics education.

Sammendrag

Artiklen formulerer to problemer for von Glaersfeds Radikale Konstruktivisme. Det f¯rste problem vedr¯rer forkastningen af ideen om mulighed for delagtigg¯relse af mening. Det andet problem er, at den Radikale Konstruktivisme benÊgter eksistensen af en objektiv ydre virkelighed, som vi kan have objektiv viden om. Dog ser det ud til, at von Glasersfeld mener, at vi kan have objektivt gyldig viden i matematik. Vi prÊsenterer en alternativ position - Konstruktiv Realisme - som beskriver hvad matematikkens objekter er og redeg¯r for hvorfor viden i matematik er objektiv. Desuden argumenterer vi for, at nogle af de antagelser som von Glasersfeld bruger i beskrivelsen af hvordan tallene dannes, st¯tter pÂstanden om at nogle meninger er objective og at kommunikation er mulig. Til sidst giver vi nogle forslag til hvilke implikationer denne position har for undervisning i matematik.

JESSICA CARTER
Jessica received her Ph.d. at the Center for Educational Development in University Science, University of Southern Denmark (SDU) in 2002. She works mainly in Philosophy and History of Mathematics, where she tries to give a description of mathematical objects that agrees with mathematical practice. She is currently assistant professor at the Department of Mathematics and Computer Science and member of the Science and Mathematics Education Research Group at SDU.