Learning to Think Spatially (2006) / Chapter Skim
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5 Responding to the Need for Spatial Thinking
5 Responding to the Need for Spatial Thinking
Pages 110-134
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From page 110... ...
This chapter reviews the extent to which the educational system is meeting societal needs for spatial thinkers. Sections 5.2 and 5.3 show how the increasing importance of the information technology sector is generating demands for skilled workers with spatial skills and for citizens who can use spatial tools and technologies in their everyday lives.
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From page 111... ...
. 5.3 PROVIDING SKILLED SPATIAL THINKERS A strong component of the drive for K12 educational reform since the 1989 Charlottesville Education Summit has been a concern about the capacity of the American workforce to compete successfully in a context defined by intense international competition in global markets and rapid technological change in the nature of the work process.
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From page 112... ...
The skills comprise basic skills (reading, writing, arithmetic and mathematics, speaking, and listening) , thinking skills, and the diligent application of personal qualities.
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From page 113... ...
Geospatial Technology Competency Model establishes a link between competencies -- the knowledge, skills, and abilities that an individual needs to do a job -- and roles, which are groupings of work-related competencies. Many of the technical and analytical competencies listed in the model are directly related to the process of spatial thinking.
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From page 114... ...
To what extent is that happening? 5.5 SPATIAL THINKING IN THE NATIONAL EDUCATION STANDARDS 5.5.1 The Role of Spatial Thinking in the Mathematics and Science Standards In the current educational environment one important place to look for attention to spatial thinking is in the educational standards for various disciplines.
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From page 115... ...
For example, the science standards are built around eight intellectual categories: unifying concepts and processes in science, science as inquiry, physical science, life science, Earth and space science, science and technology, science in personal and social perspectives, and the history and nature of science. For each category there is a content standard and "as a result of activities provided for all students in those grade levels, the content of the standard is to be understood or certain abilities are to be developed" (NRC, 1996, p.
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From page 116... ...
Although there is a direct connection with the discipline of history through one content standard, there is no explicit connection with either the mathematics or the science standards. Given the way geography is taught in elementary school -- as part of social stud ies -- there is a very low probability that students would enjoy the benefits of coordination between, say, mathematics and geography teaching and learning.
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From page 117... ...
RESPONDING TO THE NEED FOR SPATIAL THINKERS 117 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 continued
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From page 118... ...
The discussion of the standard goes on to make the point that "geometric modeling and spatial reasoning offer ways to interpret and describe physical environments and can be important tools in problem solving" (NCTM, 2000, p.
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From page 119... ...
So in the science standards there are standards for teaching, assessment, teacher preparation, and content, while the mathematics standards handle many of these topics in the principles. The science content standards contain six basic themes, for which standards are elaborated in each of three grade intervals (K4, 58, and 912)
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From page 120... ...
specify locations and describe spatial relationships using coordinate geometry and other representational systems, and (2) use visualization, spatial reasoning, and geometric modeling to solve problems.
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From page 121... ...
All rights reserved. FIGURE 5.2 Use visualization, spatial reasoning, and geometric modeling to solve problems.
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From page 122... ...
All rights reserved. FIGURE 5.4 Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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From page 123... ...
The geometry standard for middle school and high school requires students to "specify locations and describe spatial relationships using coordinate geometry and other representational systems" and to engage in "visualization, spatial reasoning, and geometric modeling" (Figures 5.10 and 5.11)
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From page 124... ...
As part of the grades 912 experience, the physical science standard involves developing an understanding of the geometry of molecules. An examination of the geometry standard (Figure 5.14)
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From page 125... ...
In the pre-K2 standards, students are asked to apply transformations and to use symmetry to analyze mathematical situations, skills that could again be useful in describing molecular structures. However, in sharp contrast to the strong links between K4 mathematics and science, the necessary concepts in geometry are not introduced concurrently with science content that might use them.
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From page 126... ...
SOURCE: NCTM, 2000. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics.
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From page 127... ...
RESPONDING TO THE NEED FOR SPATIAL THINKERS 127 FIGURE 5.7 Guide to the content standard for physical science for grades K4.
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128 LEARNING TO THINK SPATIALLY FIGURE 5.8 Guide to the content standard for physical science in grades 912.
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From page 129... ...
In the first case, that of grades 912 chemistry, the spatial thinking concepts that would allow the student to grasp the structure of atoms and molecules are introduced well ahead of need; therefore both students and teachers may not recall the relevant material from earlier grades. In the second case, that of the Earth and space science standard, other than the discussion of coordinate geometry, the committee could not find anything in the mathematics standards that supported the complex spatial thinking process associated with the description of the motion of fluids (wind and ocean currents)
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From page 130... ...
Finally, the science standards seem to presume a very sophisticated skill set in spatial thinking, reasoning, and representation, and it is unclear where in the education system that skill set has been developed. To the extent that spatial thinking skills are explicitly taught, the process occurs under the rubric of geometry, which is only one of ten standards that are to be met by mathematics teaching and learning.
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From page 131... ...
SOURCE: NCTM, 2000. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics.
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From page 132... ...
All rights reserved. FIGURE 5.13 Geometry Standard: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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From page 133... ...
SOURCE: NCTM, 2000. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics.
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From page 134... ...
The breadth and variety of spatial thinking and of spatial thinkers pose an educational challenge. How can we design instructional programs to fit such a rich, diverse, complex, and intriguing set of learning tasks and domains?
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