Analysing signs emerging from students’ work on a designed dependency task in dynamic geometry*

Abstract

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students’ awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design principles used in the study and present analysis of four Danish grade 8 students (age 13–14) working in pairs on the very first task of the sequence. The Theory of Semiotic Mediation frames the design of the study and the analysis of data, which was collected in the form of screencast, video and written products. The results show that grasping logical relationships is not immediate, on the contrary, the results indicate that students expect dependencies to be non-hierarchical in DGE and that low achieving students describing the behaviour of constructions during dragging refer to their global appearance, rather than to geometrical properties. Such results suggest that specific prompts in the task design can shift students’ attention on specific elements of constructions and that explicitly asking the students to explain any unexpected observation seems to be necessary for active reflection.

KEYWORDS:

• Dynamic geometry environments
• task design principles
• mathematical reasoning competency
• design-based research
• theory of semiotic mediation

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The mathematical reasoning competency is one of eight mathematical competencies in the Danish KOM framework (Niss & Højgaard, 2019).

2 We omit the formulation of 1.c., 1.e. and 1.f. since it is not discussed in this article. 1.c. was a repetition of 1.b. in relation to point B, while 1.e. and 1.f. concern choice (v) – explain.

3 Arzarello (2006) introduced and elaborated (Arzarello et al., 2009) the terms semiotic set and semiotic bundle. A semiotic set comprises three components: signs; modes of production/transformation of signs; and relationships among signs. A semiotic bundle is a collection of semiotic sets and a set of relationships between the semiotic sets of the bundle (Arzarello, 2006, p. 281).

4 E.g. Geometer Sketchpad 3, as mentioned in Talmon and Yerushalmy (2004).