Developing a dynamic geometry task platform for accessing students' perceptions of geometric properties through analysis of example spaces

Abstract

Geometry learning at the junior secondary level should focus on the connection between students’ intuitive, spatial thinking and formal, deductive reasoning. It is crucial for students at this stage to develop abstract concepts based on knowledge of and reasoning with geometric properties. Dynamic geometry tools are promising resources in classroom teaching for enriching students’ experience in geometry.

Studies about students’ learning with dynamic geometry tools usually focus on the long-term development of tool use in the contexts of problem solving and explorations. Data are mostly obtained from interviews and observations with students working in small groups or individually.

This study begins with an original approach. It aims at understanding students’ perceptions of geometric properties in simple dynamic figures without assuming any prior experience of students with dynamic geometry tools. A special web-based platform was developed to capture students’ results of dragging in dynamic figures. Quantitative and qualitative data were obtained for analysis from this platform and task-based interviews respectively.

In a set of 8 tasks designed in this study, students were asked to drag free points in pre-constructed figures to create examples of geometric configurations with parallel lines. Results of the tasks were collected through the web-based platform from 1,589 secondary 1 to 4 Hong Kong students in 11 schools of different backgrounds. In the next stage, 24 secondary 2 students from another 6 schools took part in task-based interviews, enabling detailed observations and analysis of their reasoning.

The basic assumption of this design is that students working on the tasks will generate examples of geometric figures that reflect their understanding of relevant geometric properties. Their results could then be analyzed in the form of collective and personal example spaces with critical dimensions of variation to be identified (Watson & Mason, 2005).

The findings of the study indicate how participating students vary in their ways of discerning critical geometric properties in dynamic figures. In particular, the results reflect students’ general limited awareness of basic geometric properties, such as equal opposite sides or angles, while manipulating and interpreting pre-constructed figures. Graphical representations of collective example spaces, developed in this study, provide useful means for revealing dimensions of variation in examples generated. It is hoped that the findings and method of the study can inform classroom teaching with dynamic geometry tools that capitalizes on variation in students’ perceptions.