Garry Clark* & Edward Redden (Australia), gclark@metz.une.edu.au
Using Logo as a Scaffolding to Develop Algebraic Thinking in a Virtual
   Classroom

Literature regarding the introduction of algebra in schools advocates a number
of methods including the use of patterns, modelling, problem-solving and
functions. All have in common the expression of generality which Krutetskii
said was a key concept in identifying mathematical giftedness.  The writers
have been researching the efficacy of Logo in introducing algebraic concepts by
addressing the following research questions a) Can geometric investigations in
a Logo environment provide a suitable context for the generation of algebraic
concepts?  b) Does this environment facilitate notions of expressing generality
in children and how readily are these notions of generality recorded in
symbolic language.

A series of comparative case studies has been developed with 7 students
enrolled in an online talent education development program. The data consists
of a dialogue that is conducted between the online tutor and the participant in
the program. The paper identifies a number of algebraic constructs that emerge
from conducting investigations in a Logo environment. More importantly it
details the intellectual struggle of a number of students as they interact with
the environment.