ABSTRACT. This paper suggests that from a cognitive-evolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical. This progression was driven by three cognitive advances: the ability to “represent ” events, the development of symbolic reference, and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture: a “virtual ” culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills.

ISBN: 0-8330-3477-4 RAND white papers are authoritative publications that draw on a strong body of prior research to summarize key findings relevant to pending decisions or policy problems. White papers are reviewed by RAND’s corporate management to assure that they adequately represent RAND’s best work in the subject as well as significant differences of opinion. RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND ® is a registered trademark. RAND’s publications do not necessarily reflect the opinions or policies of its research sponsors. © Copyright 2003 RAND All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from RAND.

The Dissertation Committee for Kenneth Ray Austin certifies that this is the approved version of the following dissertation:

In countries around the world the power of the central state over the educational system has diminished in the past two decades. In educational systems where control was formerly

To my father who died mid-dissertation. I know you would have been proud. To my parents. Who gave me the lust for inquisitiveness and learning and a critical eye. To the students not receiving the education they have a right to. To the amazing women who participated in this study. A las mujeres extraordinarias que participaron en este estudio. Without you, this would not have been possible. Sin ustedes, esto no hubiera sido posible. Acknowledgements I owe appreciation to a number of special people. First and foremost, thank you to Jay Scribner who encouraged me from inception to completion and did not allow me to wallow unnecessarily in those dark moments in which doctoral students sometimes find themselves. Thanks to my committee for your feedback and positive reaction to my work. Thanks to the academic community, including my professors and my policy and planning

While digital library development has greatly advanced in the past five years, there is as yet little research demonstrating the efficacy of digital library technology on teaching and learning. This paper presents an initial articulation of a model of the critical dimensions of digital library implementation in educational settings, based on the development of the Digital Library for Earth System Education (DLESE). It also suggests how such a model may contribute to an understanding of how digital libraries are used and valued. 1

This publication would not have been possible without the dedicated efforts of many individuals. Deep appreciation is extended to each of the writers. Their knowledge of the research findings and effective practices for at-risk populations has helped to provide educators with the knowledge and information they need to include these students in standards-based reform efforts. Sincere thanks also go to the members of the planning committee, who provided the vision and guidance for the design and planning of the roundtable and this publication. In the spirit of interagency collaboration, we also would like to acknowledge contributions made by the staff of the Region IX Comprehensive Center at McREL, the

How we design a classroom makes a powerful statement about how we view education. Whether a classroom has straight rows of desks or is filled with sofas and computer workstations tells us much about how teaching occurs, how learning takes place, and to what extent students are engaged in their studies. As educators come to view learning as an active process of engagement, classroom design is being reexamined. Educational Trends Educational reformers have tinkered with classroom design throughout the history of public education. At the turn of the 20th century, educators devised the Lancastrian system, using bleacher-style seating and sloped floors to aid the teacher’s supervision of the classroom. By the 1920s, however, today’s standard, rectangular classrooms