Coming to Understand Angle and Angle Measure: A Design-Based Research Curriculum Study Using Context-Aware Ubiquitous Learning

Crompton, Helen

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March 22, 2019

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Crompton, Helen
- Affiliation: School of Education

Abstract

This study uses design-based research (DBR) to develop an empirically-substantiated instructional theory about students' development of angle and angle measure, with real-world connections and technological tools through the use of context-aware ubiquitous learning. The research questions guiding this research are: 1.How do students come to understand angle and angle measure through the use of real-world connections and technology enabled learning tasks? 2.What are effective means of support to facilitate students' understanding of angle and angle measure? A conjectured local instruction theory was developed from a thorough review of the literature in chapter two. This review encompassed research-based developmental trajectories and effective instructional supports for promoting students' understanding of angle and angle measure. It was conjectured that context-aware u-learning was a good support for students coming to understand angle and angle measure. Context-aware u-learning in this study involves the use of real-world connections and a Dynamic Geometry Environment. The local instruction theory was subject to a cyclical iterative process of anticipation, enactment, evaluation, and revision (Gravemeijer & van Eerde, 2009). This process contributes to the theories of how students come to understand angle and angle measures, while also developing a set of instructional activities which can be utilized and adapted by educators to meet the needs of the students in their classrooms. The instructional sequence was implemented in one classroom-based teaching experiment in the first macro cycle of the DBR process. A second macro cycle was implemented using revised instructional materials in one classroom-based teaching experiment. Findings indicate that context-aware u-learning is a valuable mathematical context for introducing students to angle and angle measure. Common misconceptions about angle can be avoided as the students study angles in the real world which presents them with angles with rays of different length and in various orientations. Good foundations were built by having the students consider angle by the generalizable properties and over the seven days the students showed good movement across the van Hiele levels of geometric thinking. A revised local instruction theory is presented as a result of the findings from this study.

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