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## Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum (2006) Board on Earth Sciences and Resources (BESR)

### Citation Manager

. "5 Responding to the Need for Spatial Thinking." Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum. Washington, DC: The National Academies Press, 2006.

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Learning To Think Spatially

TABLE 5.2 Table of Standards and Expectations for School Mathematics

 Number and operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems Understand meanings of operations and how they relate to one another Compute fluently and make reasonable estimates Algebra Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement Apply appropriate techniques, tools, and formulas to determine measurements Data analysis and probability Formulate questions that can be addressed with data, and collect, organize, and display relevant data to answer them Select and use appropriate statistical methods to analyze data Develop and evaluate inferences and predictions that are based on data Understand and apply basic concepts of probability Problem solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Reasoning and proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof Communication Organize and consolidate mathematical thinking through communication Communicate mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely
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 Front Matter (R1-R18) Executive Summary (1-10) 1 Introduction (11-22) PART I: THE NATURE AND FUNCTIONS OF SPATIAL THINKING --2 The Nature of Spatial Thinking (23-48) 3 Spatial Thinking in Everyday Life, at Work, and in Science (49-93) 4 Teaching and Learning About Spatial Thinking (94-109) 5 Responding to the Need for Spatial Thinking (110-134) 6 Tools for Thought: The Concept of a Support System (135-152) PART II: SUPPORT FOR SPATIAL THINKING--7 High-Tech Support Systems for Spatial Thinking (153-165) 8 An Assessment of GIS as a System for Supporting Spatial Thinking in the K-12 Context (166-216) 9 GIS as a Support System for Spatial Thinking (217-226) PART III: SUPPORTING SPATIAL THINKING IN THE FUTURE--10 Conclusions and Recommendations (227-236) 11 The Spatial Thinker (237-242) References (243-256) Appendix A Biographical Sketches of Committee Members and Staff (257-263) Appendix B Oral Presentations and Written Statements (264-265) Appendix C Individual Differences in Spatial Thinking: The Effects of Age, Development, and Sex (266-280) Appendix D The Role of Spatial Representations in Learning, Problem Solving, and Transfer (281-284) Appendix E Software Descriptions and Resources (285-286) Appendix F What Is GIScience? (287-288) Appendix G The Introduction of GIS into K–12 Education (289-292) Appendix H Seasonal Differences: A Customized Eighth-Grade GIS Module (293-297) Appendix I List of Acronyms (298-300) Index (301-314)