Objectifying the adjacent and opposite angles: a cultural historical analysis

ABSTRACT

The angle topic is central to the development of geometric knowledge. Two of the basic concepts associated with this topic are the adjacent and opposite angles. It is the goal of the present study to analyze, based on the cultural historical semiotics framework, how high-achieving seventh grade students objectify the adjacent and opposite angles’ concepts. We videoed the learning of a group of three high-achieving students who used technology, specifically GeoGebra, to explore geometric relations related to the adjacent and opposite angles’ concepts. To analyze students’ objectification of these concepts, we used the categories of objectification of knowledge (attention and awareness) and the categories of generalization (factual, contextual and symbolic), developed by Radford. The research results indicate that teacher's and students’ verbal and visual signs, together with the software dynamic tools, mediated the students’ objectification of the adjacent and opposite angles’ concepts. Specifically, eye and gestures perceiving were part of the semiosis cycles in which the participating students were engaged and which related to the mathematical signs that signified the adjacent and the opposite angles. Moreover, the teacher's suggestions/requests/questions included/suggested semiotic signs/tools, including verbal signs that helped the students pay attention, be aware of and objectify the adjacent and opposite angles’ concepts.

KEYWORDS:

• Geometric concepts
• adjacent angles
• opposite angles
• attention
• awareness
• objectification
• cultural historical semiotics

Disclosure statement

No potential conflict of interest was reported by the authors.