Design Decisions: A Microworld for Mathematical Generalisation

Proceedings of the 1st …, 2008

Research in, 2008

The first international conference on Computer support for collaborative learning - CSCL '95, 1995

This article describes one attempt to develop an alter native perspective for designing a computer mi croworld by using a bottom-up approach to instruc tional design. This approach differs from traditional in structional design in two ways. First, the program was intended to augment an existing activity sequence rather than serve as an independent environment sepa rated from the students' regular classroom work. Sec ond, it is considered to be bottom-up in the sense that its aim was to engage students in activities that were consistent with their provisional ways of knowing. The first section of this paper describes how the con structs of reification and distributed intelligences were combined with Freudenthal's three design heuristics to guide the development of the microworld. The second section discusses some data from a project classroom in which the program was used.

2013

This paper draws on findings from a prior study for which I designed and developed a dynamic geometry environment called Configure and used it in the episodes of a teaching experiment to engage children's informal and intuitive topological, or at least non-metric, conceptions and support their development. I found that "Amanda" developed significant and authentic forms of geometric reasoning and have given the name "qualitative geometry" to these findings. These newly identified forms of reasoning were seen to develop as Amanda engaged in mathematical activity mediated by the microworld of Configure. These findings are used to provide a perspective on mathematics thinking and learning as engagement in microworld-mediated mathematical activity. Essential elements of this particular form of mathematical activity are provided.

Journal of Educational Computing Research, 1995

International Journal of Computers for Mathematical …, 1997

Generalization and proof are defining activities within mathematics, yet the focus of "school" proof has often been on form over meaning, on established results rather than exploration and discovery. Computer-based microworlds offer opportunities for students to notice and describe patterns, formulate generalizations, and generate and test mathematics conjectures. This paper examines the work of a group of middle and high school students who used a microworld for transformation geometry to investigate the composition of reflections. The students' conjectures are described in terms of a learning paths chart for the task, as well as through a detailed analysis of the work of one pair of students. A general scheme for describing informal exploration and reasoning prior to formal proof is offered, and the role of social support in the learning of proof is discussed.

Educational Studies in Mathematics, 1992

Proceedings of the 1st International Workshop on Intelligent Support for Exploratory Environments, EC-TEL, 2008

Abstract. Few systems exist that support learners explicitly in the process of learning mathematical generalisation. This paper presents the eX-presser, part of a new system that seeks to address this issue by providing the user with a microworld for the construction and analysis of general patterns. The design includes the provision of sophisticated intelligent support that assists learners and teachers throughout their various interactions with the system. Given the open and exploratory nature of the environment and the resultant ...

JOURNAL OF MATHEMATICAL BEHAVIOR, 17 (1), 53-78, 1998

This paper examines the category of open-ended exploratory computer environments that have been labeled "microworlds." The paper reviews the ways in which the term "microworld" has been used in the mathematics and science education communities, and analyzes examples of specific computer microworlds. Two definitions of microworld are proposed: a structural definition that focuses on design elements shared by the environments, and a functional definition that highlights commonalties in how students learn with microworlds. In the final section of the paper, the notion that computer microworlds can be said to "embody" mathematical or scientific ideas is addressed, within the context of a re-evaluation of the general concept of representation.

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