Designing Virtual Worlds for Use in Mathematics Education.

Virtual Reality (VR) is a computer generated, multi-dimensional, inclusive environment that can build axioms of algebra into the behavior of the world. This paper discusses the use of VR to represent part of the algebra curriculum in order to improve students' classroom experiences in learning algebra. Students learn to construct their knowledge of algebra from their interactions with the computer concerning algebraic concepts represented in VR. The VR representation of algebra reported in this document is called Spatial Algebra. Spatial Algebra creates a mapping between algebraic concepts and spatial objects. The example provided in this paper maps numbers and variables to blocks, operations to spatial proximity, and algebraic relations to space partitions. Spatial representations of the operations of addition and multiplication; the commutative, associative, and distributive properties of equality; identities; the additive and multiplicative inverses; calculus of signs; and factoring are provided. A final section presents the following reasons why VR should be used in mathematics instruction: (1) VR worlds engage students cognitively and affectively; (2) interactions with the virtual world is intuitive; (3) the virtual world can be programmed to provide various types of guidance to students; (4) virtual objects behave in concrete ways; (5) virtual worlds allow students to explore the same place repeatedly, building a sophisticated understanding of concepts and procedures; and (6) the system can automate some procedures. (Contains 33 references.) (MDH)