LEARNING TO THINK SPATIALLY

Committee on Support for Thinking Spatially: The Incorporation of Geographic Information Science Across the K–12 Curriculum

Geographical Sciences Committee

Board on Earth Sciences and Resources

Division on Earth and Life Studies

NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES

THE NATIONAL ACADEMIES PRESS
Washington, D.C.
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Learning To Think Spatially LEARNING TO THINK SPATIALLY Committee on Support for Thinking Spatially: The Incorporation of Geographic Information Science Across the K–12 Curriculum Geographical Sciences Committee Board on Earth Sciences and Resources Division on Earth and Life Studies NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES THE NATIONAL ACADEMIES PRESS Washington, D.C. www.nap.edu

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Learning To Think Spatially THE NATIONAL ACADEMIES PRESS 500 Fifth Street, N.W., Washington, DC 20001 NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This study was supported by Environmental Systems Research Institute, Department of Interior/U.S. Geological Survey Grant No. 00HQAG0011, National Aeronautics and Space Administration Grant No. NAG5-9857, National Geographic Society Education Foundation Grant No. 200-0123, and National Science Foundation Grant No. BCS-0076284. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project. Library of Congress Cataloging-in-Publication Data Learning to think spatially : GIS as a support system in the K-12 curriculum. p. cm. Includes bibliographical references and index. ISBN 0-309-09208-6 (pbk.)—ISBN 0-309-53191-8 (PDF) 1. Space perception—Study and teaching. 2. Geographic information systems. I. National Academies Press (U.S.) BF723.S63L43 2006 370.15′2—dc22 2005032115 Additional copies of this report are available from the National Academies Press, 500 Fifth Street, N.W., Lockbox 285, Washington, DC 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu. Cover designed by Van Nguyen. Photo © Blauel/Gnamm—ARTOTHEK. Courtesy of the Städelsches Kunstinstitut, Frankfurt. Copyright 2006 by the National Academy of Sciences. All rights reserved. Printed in the United States of America

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Learning To Think Spatially THE NATIONAL ACADEMIES Advisers to the Nation on Science, Engineering, and Medicine The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Ralph J. Cicerone is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Wm. A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Harvey V. Fineberg is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Ralph J. Cicerone and Dr. Wm. A. Wulf are chair and vice chair, respectively, of the National Research Council. www.national-academies.org

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Learning To Think Spatially SUPPORT FOR THINKING SPATIALLY: THE INCORPORATION OF GEOGRAPHIC INFORMATION SCIENCE ACROSS THE K–12 CURRICULUM ROGER M. DOWNS, Chair, The Pennsylvania State University, University Park SARAH WITHAM BEDNARZ, Texas A & M University, College Station ROBERT A. BJORK, University of California, Los Angeles PETER B. DOW, First Hand Learning, Inc., Buffalo, New York KENNETH E. FOOTE, University of Colorado, Boulder J. FREEMAN GILBERT, University of California, San Diego, La Jolla REGINALD G. GOLLEDGE, University of California, Santa Barbara KIM A. KASTENS, Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York GAEA LEINHARDT (member until February 28, 2002), University of Pittsburgh, Pennsylvania LYNN S. LIBEN, The Pennsylvania State University, University Park MARCIA C. LINN, University of California, Berkeley JOHN J. RIESER, Vanderbilt University, Nashville, Tennessee GERALD M. STOKES, University of Maryland and Pacific Northwest National Laboratory, College Park BARBARA TVERSKY, Stanford University, Palo Alto, California National Research Council Staff ANTHONY R. DE SOUZA, Director, Board on Earth Sciences and Resources KRISTEN L. KRAPF, Program Officer (until November 2004) YVONNE P. FORSBERGH, Research Assistant (until November 2002) MONICA R. LIPSCOMB, Research Assistant (until June 2004) VERNA J. BOWEN, Financial and Administrative Associate RADHIKA S. CHARI, Senior Project Assistant (from November 2002 to November 2003) AMANDA M. ROBERTS, Program Assistant (from April 2004) TERESIA K. WILMORE, Project Assistant (from November 2003 to April 2004)

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Learning To Think Spatially GEOGRAPHICAL SCIENCES COMMITTEE ROGER M. DOWNS, Chair, The Pennsylvania State University, University Park BRIAN J. L. BERRY, The University of Texas at Dallas, Richardson SUSAN L. CUTTER, University of South Carolina, Columbia RUTH S. DEFRIES, University of Maryland, College Park WILLIAM E. EASTERLING III, The Pennsylvania State University, University Park PATRICIA GOBER, Arizona State University, Tempe MICHAEL F. GOODCHILD, University of California, Santa Barbara SUSAN HANSON, Clark University, Worcester, Massachusetts JONATHAN D. MAYER, University of Washington, Seattle EMILIO F. MORAN, Indiana University, Bloomington DAVID L. SKOLE, Michigan State University, East Lansing National Research Council Staff HEDY J. ROSSMEISSL, Senior Scholar VERNA J. BOWEN, Financial and Administrative Associate

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Learning To Think Spatially BOARD ON EARTH SCIENCES AND RESOURCES GEORGE M. HORNBERGER, Chair, University of Virginia, Charlottesville M. LEE ALLISON, Office of the Governor, Topeka, Kansas STEVEN R. BOHLEN, Joint Oceanographic Institutions, Washington, D.C. ADAM M. DZIEWONSKI, Harvard University, Cambridge, Massachusetts KATHERINE H. FREEMAN, The Pennsylvania State University, University Park RHEA L. GRAHAM, Pueblo of Sandia, Bernalillo, New Mexico ROBYN HANNIGAN, Arkansas State University, State University V. RAMA MURTHY, University of Minnesota, Minneapolis RAYMOND A. PRICE, Queen’s University, Ontario, Canada MARK SCHAEFER, NatureServe, Arlington, Virginia STEVEN M. STANLEY, Johns Hopkins University, Baltimore, Maryland BILLIE L. TURNER II, Clark University, Worcester, Massachusetts STEPHEN G. WELLS, Desert Research Institute, Reno, Nevada THOMAS J. WILBANKS, Oak Ridge National Laboratory, Tennessee National Research Council Staff ANTHONY R. DE SOUZA, Director DAVID A. FEARY, Senior Program Officer ANNE M. LINN, Senior Program Officer RONALD F. ABLER, Senior Scholar ELIZABETH A. EIDE, Senior Program Officer HEDY J. ROSSMEISSL, Senior Scholar ANN G. FRAZIER, Program Officer SAMMANTHA L. MAGSINO, Program Officer TANJA E. PILZAK, Research Associate CAETLIN M. OFIESH, Research Assistant VERNA J. BOWEN, Financial and Administrative Associate JENNIFER T. ESTEP, Financial Associate JARED P. ENO, Program Assistant JAMES B. DAVIS, Program Assistant AMANDA M. ROBERTS, Program Assistant

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Learning To Think Spatially Acknowledgments This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the National Research Council’s Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making its published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge. The review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. We wish to thank the following individuals for their review of this report: Tanya M. Atwater, University of California, Santa Barbara Victor R. Baker, University of Arizona, Tucson Angelo Collins, Knowles Science Teaching Foundation, Haddonfield, New Jersey Mary D. Gunnels, National Highway Traffic Safety Administration, Washington, D.C. Mary Hegarty, University of California, Santa Barbara Roberta L. Klatzky, Carnegie Mellon University, Pittsburgh, Pennsylvania Mark Monmonier, Syracuse University, New York M. Duane Nellis, Kansas State University, Manhattan Herbert L. Pick, Jr., University of Minnesota, Minneapolis Nancy Rankin, Hillview Middle School, Menlo Park, California Cary I. Sneider, Museum of Science, Boston, Massachusetts Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions or recommendations nor did they see the final draft of the report before its release. The review of this report was overseen by David J. Cowen, University of South Carolina, Columbia, and Lyle V. Jones, The University of North Carolina, Chapel Hill. Appointed by the National Research Council, they were responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authoring committee and the institution.

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Learning To Think Spatially Frontispiece: Young students in a GIS learning laboratory.

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Learning To Think Spatially Preface The title of this report, Learning to Think Spatially, is a description of its contents and, at the same time, a description of the process that led to the report. Although the original charge to the committee appeared clear and definitive when the study proposal was approved by the National Academy of Sciences, the writing process has been a less linear path than we expected. To begin with, the committee comprised a wide range of disciplinary backgrounds: astronomy, education, geography, the geosciences, and psychology (for biographical sketches, see Appendix A). Learning about and from each other took considerable time and effort. It became clear that the original charge had to be reshaped; we could not address that charge until spatial thinking itself had been explored and explained. Only after that was done could we focus on the second part of the title: GIS as a Support System in the K–12 Curriculum. Spatial thinking—one form of thinking—is based on a constructive amalgam of three elements: concepts of space, tools of representation, and processes of reasoning. It is the concept of space that makes spatial thinking a distinctive form of thinking. By understanding the meaning of space, we can use its properties (e.g., dimensionality, continuity, proximity, and separation) as a vehicle for structuring problems, for finding answers, and for expressing solutions. By expressing relationships within spatial structures (e.g., maps, multidimensional scaling models, computer-assisted design [CAD] renderings), we can perceive, remember, and analyze the static and, via transformations, the dynamic properties of objects and the relationships between objects. (Abbreviations are spelled out in full at their first use in the body of the report and are defined in Appendix I.) We can use representations in a variety of modes and media (graphic [text, image, and video], tactile, auditory, kinesthetic, and olfactory) to describe, explain, and communicate about the structure, operation, and function of objects and their relationships. Spatial thinking is not restricted to any domain of knowledge, although it may be more characteristic of architecture, medicine, physics, and biology, for example, than of philosophy, business administration, linguistics, and comparative literature. Although spatial thinking is a universal mode of thinking, it has distinctly different manifestations in different disciplines. Part of the nonlinear committee process involved understanding and

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Learning To Think Spatially taking advantage of those differences. Committee members presented interpretations of the process of spatial thinking from their disciplinary perspective. Spatial thinking uses space to integrate and structure ideas. Many of the committee meetings were, therefore, seminar exercises in the representation and integration of ideas from different disciplines. In this respect, we were fortunate to receive the support of numerous individuals (see Appendix B for a list of people who contributed to the committee’s work). Without their support, the committee could not have constructed an amalgam of ideas about space, representation, and reasoning, especially as they relate to geographic information systems. We have lost count of the times that contributors responded to yet another e-mail containing another (small) request. That people were so willing to respond is one measure of the importance of the topic. Another is the willingness of committee members to provide draft materials and comments on the drafts of other committee members. Two of us—–Roger Downs and Anthony de Souza—took the responsibility for creating the overall report structure, for weaving together the disparate pieces, and for writing the final report. However, Learning to Think Spatially represents the collective belief of an interdisciplinary group of scholars that spatial thinking merits—if not demands—the focused and systematic attention of scientists and educators alike. We must understand the process of spatial thinking, we must develop systems for supporting the process, and we must ensure that all students have the opportunity to learn about spatial thinking. We need to invest in a systematic educational program to enhance levels of spatial thinking in K–12 students. Our goal must be to foster a generation of students (1) who have the habit of mind of thinking spatially, (2) who can practice spatial thinking in an informed way, and (3) who adopt a critical stance to spatial thinking. These conclusions and recommendations were driven by the breadth and depth of the educational experiences of members of the committee. Three of us had been K–12 school teachers and most of us had worked extensively at the intersection of research and educational policy, helping to develop national standards, curricula, assessments, and specific educational programs for federal, state, and local education agencies. As with any committee process, Learning to Think Spatially would not have been possible without the generous support, patience, and active encouragement and participation of our five sponsors. The committee gratefully acknowledges the support of the Environmental Systems Research Institute (ESRI), the National Aeronautics and Space Administration (NASA), the National Geographic Society (NGS), the National Science Foundation (NSF), and the U.S. Geological Survey (USGS). Anthony de Souza and I would also like to thank the numerous staff members at the National Academies who helped during the committee, writing, and publication processes: Kristen L. Krapf, program officer; Yvonne P. Forsbergh, research assistant; Monica R. Lipscomb, research assistant; Verna J. Bowen, financial and administrative associate; Jennifer T. Estep, financial associate; Radhika S. Chari, senior program assistant; Amanda M. Roberts, program assistant; and Teresia K. Wilmore, program assistant. Through the committee process, we all came to realize the extent to which spatial thinking pervades our lives as scientists, our roles in the workforce, and our everyday lives. To a person, we enjoyed the challenges of learning about thinking spatially. That it took us more than three years to produce this report is a testament to the size, importance, and difficulty of the topic. The road has been long and winding, but if we reach the goal of spatial literacy for American students then our time has been well spent. Roger M. Downs Department of Geography The Pennsylvania State University

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Learning To Think Spatially Contents EXECUTIVE SUMMARY   1 1   INTRODUCTION   11     1.1  The Challenge to Learn,   11     1.2  Spatial Thinking,   12     1.3  Charge to the Committee,   13     1.4  An Outcome of the Report: Fostering Spatial Literacy,   15     1.5  Audiences for Learning to Think Spatially,   20     1.6  Structure of This Report,   21 PART I:   THE NATURE AND FUNCTIONS OF SPATIAL THINKING     2   THE NATURE OF SPATIAL THINKING   25     2.1  Introduction,   25     2.2  Approaches to Spatial Thinking,   25     2.3  The Use of Space as a Framework for Understanding,   28     2.4  The Three Functions of Spatial Thinking,   33     2.5  Space as the Basis for Spatial Thinking,   36     2.6  The Process of Spatial Thinking,   40     2.7  Conclusion,   48 3   SPATIAL THINKING IN EVERYDAY LIFE, AT WORK, AND IN SCIENCE   49     3.1  Introduction,   49     3.2  Spatial Thinking in Everyday Life,   49     3.3  Spatial Thinking at Work,   52     3.4  Spatial Thinking in Science,   55     3.5  Spatial Thinking in Astronomy,   56

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Learning To Think Spatially     3.6  Spatial Thinking in Geoscience,   68     3.7  Thinking Spatially in Geoscience: The Seafloor Maps of Marie Tharp,   83     3.8  Thinking Spatially in Geography: Walter Christaller’s Discovery of Central Place Theory,   88     3.9  Conclusion,   93 4   TEACHING AND LEARNING ABOUT SPATIAL THINKING   94     4.1  Introduction,   94     4.2  Expertise Differences in Spatial Thinking: The Effects of Experience,   95     4.3  The Challenge of Developing Expertise in Spatial Thinking,   103     4.4  The Transfer of Spatial Thinking Across Subjects in the Curriculum,   105     4.5  The Fostering of Expertise in Spatial Thinking,   107     4.6  Conclusion,   109 5   RESPONDING TO THE NEED FOR SPATIAL THINKERS   110     5.1  Introduction,   110     5.2  The Increasing Need for Spatial Thinking Skills,   110     5.3  Providing Skilled Spatial Thinkers,   111     5.4  The 1999 Trends in International Mathematics and Science Study (TIMSS),   113     5.5  Spatial Thinking in the National Education Standards,   114     5.6  Spatial Thinking and Education for the Next Generation,   131 6   TOOLS FOR THOUGHT: THE CONCEPT OF A SUPPORT SYSTEM   135     6.1  Introduction,   135     6.2  The Nature of a Support System,   135     6.3  The Functions of a Support System,   140     6.4  Tools for Thought: The Limits to Power,   141     6.5  General Criteria for the Design of a Support System in the K–12 Educational Context,   145     6.6  The Need for Support Systems for Spatial Thinking (SSST),   147     6.7  The Requirements of a Support System for Spatial Thinking,   148     6.8  Support Systems for Spatial Thinking in the K–12 Context,   150     6.9  The Implementation of a Support System for Spatial Thinking in the K–12 Educational Context,   151 PART II:   SUPPORT FOR SPATIAL THINKING     7   HIGH-TECH SUPPORT SYSTEMS FOR SPATIAL THINKING   155     7.1  Introduction,   155     7.2  High-Tech Systems for Supporting Spatial Thinking,   156     7.3  The Nature and Functions of GIS,   158     7.4  The Current Status of GIS,   164 8   AN ASSESSMENT OF GIS AS A SYSTEM FOR SUPPORTING SPATIAL THINKING IN THE K–12 CONTEXT   166     8.1  Introduction,   166     8.2  The Capacity of GIS as a Support System for Spatial Thinking,   167     8.3  The Design of GIS as a Support System for Spatial Thinking in the K–12 Educational Context,   176

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Learning To Think Spatially     8.4  The Implementation of GIS as a Support System for Spatial Thinking,   203     8.5  Mechanisms for the Redesign of GIS Educational Software,   214     8.6  Conclusion,   216 9   GIS AS A SUPPORT SYSTEM FOR SPATIAL THINKING   217     9.1  Introduction,   217     9.2  The Necessary Requirements of a Support System for Spatial Thinking,   217     9.3  The Design of GIS as a Support System for Spatial Thinking in the K–12 Educational Context,   218     9.4  The Implementation of GIS as a Support System for Spatial Thinking,   219     9.5  The Redesign of GIS Educational Software,   220     9.6  Conclusion,   220 PART III:   SUPPORTING SPATIAL THINKING IN THE FUTURE     10   CONCLUSIONS AND RECOMMENDATIONS   229     10.1  Introduction,   229     10.2  Charge to the Committee,   229     10.3  The Nature and Functions of Spatial Thinking,   230     10.4  Support for Spatial Thinking,   233     10.5  Conclusion,   235 11   THE SPATIAL THINKER   237     11.1  GIS and the Challenge of Thinking Spatially,   237     11.2  An Example of Using GIS to Think Spatially,   237     11.3  Meeting the Challenge to Learn to Think Spatially,   241     REFERENCES   243 APPENDIXES     A   Biographical Sketches of Committee Members and Staff   259 B   Oral Presentations and Written Statements   264 C   Individual Differences in Spatial Thinking: The Effects of Age, Development, and Sex   266 D   The Role of Spatial Representations in Learning, Problem Solving, and Transfer   281 E   Software Descriptions and Resources   285 F   What Is GIScience?   287 G   The Introduction of GIS into K–12 Education   289 H   Seasonal Differences: A Customized Eighth-Grade GIS Module   293 I   List of Acronyms   298     INDEX   301

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Learning To Think Spatially LIST OF BOXES 1.1   Mapping of Cholera in Nineteenth-Century England,   14 1.2   Mapping of Arsenic in Twenty-First-Century Bangladesh,   16 1.3   Role of GIS in Spatial Thinking,   18 2.1   Browsing in Library Space,   34 2.2   A Personal Guidance System,   38 4.1   Reconceptualizations of the Concept of Transfer,   106 5.1   Spatial Thinking and the National Geography Standards,   116 6.1   Ocean Navigation in Micronesia,   137 6.2   Vehicle Navigation Systems in the United States,   142 6.3   Thinking Inside the Box,   151 7.1   High-Tech Systems to Support Spatial Thinking,   156 8.1   Functions of a GIS,   175 8.2   Students Analyzing a Real-World Problem with GIS: Characteristics and Potential Problems of a School’s Tree Population,   180 8.3   ArcVoyager,   185 8.4   Open Versus Closed Software System Architectures,   188 8.5   Illustrative Difficulties That Teachers and Students Confront When Working with GIS,   194 8.6   What Teachers Should Know to Be Successful with GIS in the Classroom,   206 9.1   Technological Evolution in GIS,   222 C.1   Use of the Terms Sex and Gender,   269 C.2   Shadow Projection Task,   274 LIST OF FIGURES     Frontispiece: Young students in a GIS learning laboratory   ES.1   Diagram of the DNA structure,   2 ES.2   James Watson and Francis Crick with their DNA model,   2 1.1   Snow’s 1855 map showing the areas of south London served by two water companies,   15 1.2   Spatial distribution of arsenic levels in wells in Arailhazar Upazilla, Bangladesh,   17 2.1   Spatial visualization items,   26 2.2   Underneath a typical urban street corner,   29 2.3   Units of length arrayed in a scalar progression from the micro to the macro,   31 2.4   A concept map depicting how various information sources are used to synthesize a geophysical gravity model,   32

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Learning To Think Spatially 2.5   An information landscape depicting demographic similarities and differences between the 50 states,   33 2.6   Visual browsing query process,   34 2.7   Spatialized query user interface,   35 2.8   Three modules of the Personal Guidance System,   38 2.9   Representations can be brought into direct contact with the real world using wearable computers,   39 3.1   A set of instructions for installing a ceiling fan,   51 3.2   Eratosthenes’ technique for determining the size of Earth,   58 3.3   Ptolemaic system,   60 3.4   Epicycles in the Ptolemaic system,   61 3.5   Retrograde motion,   61 3.6   Astronomical parallax,   62 3.7   The Hertzsprung-Russell (H-R) diagram,   63 3.8   Map of the solar neighborhood,   65 3.9   The period-luminosity diagram for the Cepheids,   66 3.10   The characteristic light curve of a Cepheid variable,   66 3.11   Cepheids in the Andromeda galaxy,   67 3.12   The redshift distance relationship,   68 3.13   Describing the shapes of natural objects, rigorously and unambiguously: stereograms of crystals,   69 3.14   Describing the shapes of natural objects, rigorously and unambiguously: classification of folds,   70 3.15   Diagrammatic representation of equal-area projection of various fabric elements,   71 3.16   Flow chart for identifying minerals,   72 3.17   Ascribing meaning to the shape of a natural object: jigsaw-like fit of the coastlines of Africa and South America,   73 3.18   Ascribing meaning to the shape of a natural object: Siccar Point,   73 3.19   Ascribing meaning to the shape of a natural object: distribution of modern species of planktonic foraminifera,   74 3.20   Ascribing meaning to the shape of a natural object: carbonate-shelled microfossils,   75 3.21   Ascribing meaning to the shape of a natural object: the shape and orientation of the mineral grain in this photomicrograph are interpreted as evidence that the rock has undergone shearing,   76 3.22   Ascribing meaning to the shape of a natural object: reasoning from first principles,   77 3.23   Recognizing a shape or pattern amid a cluttered, noisy background,   78 3.24   Visualizing a three-dimensional object, structure, or process by examining observations collected in one or two dimensions,   78 3.25   Describing the position and orientation of objects in the real world relative to a coordinate system anchored to Earth,   79 3.26   William Smith’s geological map of England and Wales,   80 3.27   Mentally manipulating a volume by folding, faulting, and eroding: geometry of the lower duplex at Hénaux,   81 3.28   Marie Tharp in 1960,   83 3.29   Tharp’s original hand contouring of a portion of the mid-Atlantic ridge,   85 3.30   World ocean floor panorama,   85 3.31   Diagram of central places in southern Germany,   89

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Learning To Think Spatially 3.32   Diagram of a classic central place system,   91 4.1   A sample mental rotation task,   99 5.1   Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   121 5.2   Use visualization, spatial reasoning, and geometric modeling to solve problems,   121 5.3   Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   122 5.4   Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   122 5.5   Use visualization, spatial reasoning, and geometric modeling to solve problems: developing spatial thinking,   125 5.6   Use visualization, spatial reasoning, and geometric modeling to solve problems: building additional spatial thinking skills,   126 5.7   Guide to the content standard for physical science for grades K–4,   127 5.8   Guide to the content standard for physical science in grades 9–12,   128 5.9   Guide to the content standard for Earth science in grades 9–12,   129 5.10   Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   130 5.11   Use visualization, spatial reasoning, and geometric modeling to solve problems,   131 5.12   Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   132 5.13   Geometry Standard: Specify locations and describe spatial relationships using coordinate geometry and other representational systems,   132 5.14   Use visualization, spatial reasoning, and geometric modeling to solve problems,   133 6.1   Using a calculator to solve a mathematical problem,   136 6.2   A Puluwatan canoe,   137 6.3   A mattang stick chart,   138 6.4   Representation of the Etak method, a system for tracking position at sea,   139 6.5   The dangers of an inappropriate map projection,   146 7.1   Components of a GIS,   160 7.2   A raster-based map of Santa Barbara County,   161 7.3   Map of the United States recorded on a vector GIS of polygons, lines, and points,   161 7.4   A geographic information system,   162 7.5   Geographical data can be divided into geometric data and attribute data,   162 7.6   Attribute data consist of qualitative or quantitative data,   163 7.7   Phases in the scientific method,   164 8.1   Six graphic variables that can be used to symbolize geographic phenomena,   170 8.2   Two screenshots from Earthviewer,   172 8.3   The WIMP (windows, icons, menus, pointers) environment for computing,   174 8.4   Multistage analysis in a pictorially based GIS,   178 8.5   Trees conflicting with utility lines,   180 8.6   Hazardous trees: trees in poor or dying condition,   181 8.7   A screen display from a user-built map generated from Level 4 of ArcVoyager,   185 8.8   ArcView digitizing,   186

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Learning To Think Spatially 8.9   “On-screen” representation of a haptic choropleth map of southern California,   189 8.10   ArcView Quick Reference Graphical User Interface,   190 8.11   On or off themes: adding a theme in ArcView 3,   194 8.12   Active and inactive themes: one active theme,   195 8.13   Active and inactive themes: two active themes,   195 8.14   Logical queries: query window in ArcView 3,   196 8.15   Logical queries: query windows in ArcView 8,   197 8.16   Logical queries: select by theme,   197 8.17   Zooming in: ArcView 3 zooming tool,   198 8.18   Zooming in: standard procedure for defining a box to create a rescaled map,   199 8.19   Zooming in: what happens when a user clicks in a site and accidentally wiggles before releasing the mouse?,   199 8.20   Teachers’ feelings of preparedness to incorporate digital content into their classrooms,   208 8.21   Browsing the DLESE library for educational resources by subject,   210 8.22   A page from ESRI’s Geography Network web site from which users can access a huge collection of geospatial datasets,   211 9.1   The U.S. map, showing average annual precipitation superimposed on county and state boundaries, is based on a built-in project in ESRI’s ArcExplorer Java Edition for Education,   223 9.2   This map of elevation and earthquakes, superimposed on state borders, is part of a project generated by ESRI’s ArcView 9,   224 9.3   An oblique perspective view of North America showing earthquakes (greater than 3.0 on the Richter scale),   225 9.4   A frame, showing Mount Everest, from a QuickTime video file exported from ArcGlobe,   226 10.1   Timetable for implementing Recommendations 2–6,   236 11.1   Map of infant mortality rates,   238 11.2   Maps of variables affecting infant mortality,   239 C.1   Shadow projection drawing tasks,   275 H.1   Map of South Asia with countries, rivers, and major cities named with graphs contrasting total and annual rainfall for Bombay and Mangalore,   294 H.2   Map of South Asia with countries, rivers, and annual precipitation,   295 H.3   Map of South Asia with countries, rivers, and types of agriculture,   296 H.4   Map of South Asia with countries, rivers, and population density,   297 LIST OF TABLES 5.1   The Geospatial Technology Competency Model,   113 5.2   Table of Standards and Expectations for School Mathematics,   117 7.1   Comparison of the Current Capabilities of High-Tech Systems That Can Support Spatial Thinking,   158

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Learning To Think Spatially 8.1   Major GIS Software Products Used in K–12 Education,   167 8.2   Potential GIS Database Volumes for Some Typical Applications,   168 8.3   Assessment of the Capacity of GIS to Spatialize, Visualize, and Perform Functions,   176 8.4   Assessment of the Design of GIS to Meet Educational Goals,   183 8.5   Assessment of GIS in Terms of Its Appropriateness to Meet Student Needs,   192 8.6   Computational Requirements for Idrisi and ArcView Software,   201 8.7   Assessment of GIS to Match the Educational Context,   203 8.8   Assessment of Programs for the Implementation of GIS as a Support System,   213