The Role of Reflective Abstraction in Mathematical Problem-Solving and Conceptual Development

Dr. Tracy Goodson-Espy

Department of Education
University of Alabama in Huntsville

October 19, 2001

Abstract

This presentation describes the application of the theory of reflective abstraction to the development of an Internet-based edu-tainment resource based on a Massively Multi-Player Role Playing Game, similar to Everquest or Asheron's Call. The goal of this product is to convey middle-school mathematics, including beginning algebra, in a game-based environment. Serving as a mathematics learning and content consultant for Physitron, Inc., of Huntsville, AL, the author has participated in the development of a single-player system with advanced 3D computer rendering capabilities as well as high quality 3D artwork. This was achieved as the result of a Phase I SBIR award from the U.S. Department of Education. The Phase II SBIR program is on-going. A critical aspect of the Phase I prototype is that it integrates National Council of Teachers of Mathematics standards-based content with the 3D RPG setting. Students assume a character in the virtual world and then discover mathematical challenges that are carefully integrated with the storyline and setting. In the virtual world, the student initiates a pre-defined, text-based conversation with a mentor that presents the first educational challenge. Subsequent challenges are communicated to the student by magical items occupying the virtual world. The effectiveness of the prototype was demonstrated through a pilot test in which the students tested indicated a preference for learning mathematics via a format similar to the prototype than through standard methods. Several students noted that seeing the problem in a 3D situational context was beneficial, as were the immediately available, online hints.