Learning to Think Spatially (2006) / Chapter Skim
Currently Skimming:
3 Spatial Thinking in Everyday Life, at Work, and in Science
3 Spatial Thinking in Everyday Life, at Work, and in Science
Pages 49-93
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 49... ...
. 3.2 SPATIAL THINKING IN EVERYDAY LIFE In March 2003, Mark Wegner and Deborah Girasek published a study in Pediatrics on the readability of printed instructions for car safety seat (CSS)
|
From page 50... ...
Imagine solving the problems of everyday life. A phone call in late August to a daughter on a study-abroad program in Europe requires, among other things, working out the right time to call.
|
From page 51... ...
The costume for the middle daughter's school play has to be cut from fabric, fitted, and sewn by tomorrow's dress rehearsal. Everyday life is impregnated with tasks that, on the surface, are routine and trivial.
|
From page 52... ...
All tasks involve complex sequences of operations: finding the clock times of the two places and subtracting the right one to work out the time difference; choosing boxes of the right size for the space available, orienting and rotating them, and stacking them; rotating parts, twisting parts, and tightening fastenings; breaking an operation into discrete parts and demonstrating and explaining the operations; making a loop with one lace, putting the other part of the shoe lace over the top of the loop, and so forth. Some of the tasks can be taught formally, such as map reading, whereas others, such as dress making, are no longer taught formally in schools, and still others, such as tying shoelaces, are learned informally as part of everyday life.
|
From page 53... ...
Skilled radiologists are no better than novices at recognizing skin diseases that dermatologists are expert in diagnosing or plant diseases that botanists excel at discerning. Expertise in pattern recognition is domain specific.
|
From page 54... ...
. Expertise in dealing with three-dimensional representations is, like pattern recognition, also domain specific.
|
From page 55... ...
Novices or people low in spatial ability can also understand the structural relations among the parts of a device, but they have difficulty anticipating its behavior or function. Teaching this spatial thinking skill is part of the process of turning novices into experts in everyday life, in the workplace, and in science.
|
From page 56... ...
3.5 SPATIAL THINKING IN ASTRONOMY 3.5.1 From the Celestial Sphere to the Structure of the Universe The process of moving from the human wonder at the glory of the night sky to a scientific understanding of the structure and evolution of the universe is a remarkable story, made possible to a significant degree by insights and inferences generated by spatial thinkers. The fundamental problem in astronomy is that it has a limited set of basic measurements from which to work.
|
From page 57... ...
They did so by converting data about energy into representations, often graphic, that allowed them to draw inferences about the physics of the stars and the cosmos. Spatial thinking is so pervasive in astronomy that in our illustrative story, we will further restrict the discussion to some of the key steps that built up a cosmic distance scale and enabled us to place objects in space, and eventually in time, with increasing precision.
|
From page 58... ...
with an origin at the center of Earth and measured the relative orientation of sunlight as it struck Earth. The key to his spatial analysis was the measurement of angles relative to a plane perpendicular to a radius to the center of Earth, an absolute measure of direction (Figure 3.2)
|
From page 59... ...
The Ptolemaic universe, the dominant geocentric cosmology for many centuries, is a spatialization of a method used to predict the position of various celestial objects, such as the Moon and the planets that appeared to move against the backdrop of the fixed stars. In general, the "fixed stars" tended to retain their positions with respect to one another on an imaginary "celestial sphere," which appeared to turn slowly around Earth, making one circuit every 24 hours.
|
From page 60... ...
3.5.5 Next Steps: Distances Beyond the Solar System The next step in building a picture of the universe depended on creating a distance scale that could accommodate distances beyond the solar system. The key method for doing so involved the concept of astronomical parallax (Figure 3.6)
|
From page 61... ...
FIGURE 3.5 Retrograde motion. In modern heliocentric theory, the relative motions of the planets around the Sun causes the outer planets, those further away from the Sun than Earth, to appear to move backwards relative to the fixed stars on a regular basis.
|
From page 62... ...
. This diagram plotted absolute magnitude against the newly identified spectral type of nearby stars.
|
From page 63... ...
Developed independently by the two astronomers for whom it is named, the H-R diagram shows absolute magnitude versus spectral type. Since the spectral type is a surrogate for temperature, hot blue stars are found on the left of the diagram and cool red stars on the right.
|
From page 64... ...
. This approach was made possible by Leavitt's observation in 1911 that the period of a particular class of pulsating stars is an excellent predictor of its average absolute magnitude.
|
From page 65... ...
. So even in our description of the far reaches of the universe, the distance scale is tied to the distance from Earth to the Sun.
|
From page 66... ...
Recalling from Figure 3.9 that the magnitude scale is a logarithmic scale of luminosity and that stars whose absolute magnitude differs by 5 differ in intrinsic luminosity by a factor of 100, we can calculate the distance to the star. The average apparent magnitude (visual magnitude in the figure)
|
From page 67... ...
a careful and systematic observation of the heavens and (2) a series of intellectual breakthroughs achieved by some of the finest spatial thinkers in the history of science.
|
From page 68... ...
Thinking spatially by geoscientists and geoscience students involves, among other things, · describing the shape of an object, rigorously and unambiguously; · identifying or classifying an object by its shape; · ascribing meaning to the shape of a natural object; · recognizing a shape or pattern amid a cluttered or noisy background;
|
From page 69... ...
Faced with the huge range of objects found in nature, mineralogists, petrologists, geomorphologists, structural geologists, sedimentologists, zoologists, and botantists had to begin by agreeing upon words, measurements, and concepts with which to describe these natural objects. Given a collection of objects that intuitively seem related in some way, what should you observe, and what should you measure, in order to capture the shape of each object?
|
From page 70... ...
In some cases, these descriptive techniques call upon projective and Euclidean spatial skills that many learners find extremely difficult. For example, when structural geologists collect data on which to apply their fold classification system, they record the vector that is perpendicular to the surface of the fold at many points on the fold, mentally extend those vectors until they intersect an imaginary hemisphere beneath the fold, and convey this information as points on a lower-hemisphere equal-area projection diagram.
|
From page 71... ...
. However, individual grains of the same mineralogy and individual fossils of the same species are not identical, but tend to share certain diagnostic properties (e.g., plagioclase grains tend to be much longer than they are wide, whereas olivine grains tend to be roughly as long as they are wide)
|
From page 72... ...
Ascribing Meaning to the Shape of a Natural Object The shape of a natural object found in situ (including its size and orientation) carries clues about its history and formative processes.
|
From page 73... ...
Reprinted by permission of Pearson Education, Inc., Upper Saddle River, N.J. FIGURE 3.18 Ascribing meaning to the shape of a natural object: Siccar Point.
|
From page 74... ...
Similarly, the grain-size distribution of sedimentary particles tells sedimentologists about the velocity of an ancient river; it takes a higher energy flow to carry gravel rather than sand. To summarize from these examples, the shape of a natural object can be influenced by (1)
|
From page 75... ...
The novice generally begins by applying learned rules of thumb. At the expert level, this thought process involves reasoning from first principles about the connection among form, function, and history and doing so in the context of an expert knowledge base about the normal characteristics of the class of objects under study.
|
From page 76... ...
Visualizing a Three-Dimensional Object, Structure, or Process by Examining Observations Collected in One or Two Dimensions Physical oceanographers measure the temperature and salinity of seawater by lowering an instrument package on a wire vertically down from a ship and recording the temperature, conductivity, and pressure at the instrument. Thousands of vertical conductivity-temperature-depth profiles have been combined to create our current understanding of the three-dimensional interfingering of the water masses of the world's oceans.
|
From page 77... ...
. This technique requires Euclidean spatial skills (see Appendix C)
|
From page 78... ...
SOURCE: Rehault et al., 1987. FIGURE 3.24 Visualizing a three-dimensional object, structure, or process by examining observations collected in one or two dimensions.
|
From page 79... ...
As with Marie Tharp, Smith made his map before the causal processes that underlay the observations on his map were understood, and he worked from incomplete data, primarily outcrops revealed in canal cuts. As with Marie Tharp's map, Smith's map stands up very well to comparison with modern maps.
|
From page 80... ...
The simplistic notion is that one collects a mass of data about the distribution of some property or process, combines the data into a mental picture or computer-aided visualization, and then interprets it. This may understate and underestimate the skill of a spatial thinker.
|
From page 81... ...
Thinking about eroded terrains requires the ability to envision negative spaces, the shape and internal structure of the material that is no longer present. Using Spatial Thinking to Think About Time It is common in thinking about Earth to find that variation or progression through space is closely connected with variation or progression through time.
|
From page 82... ...
Physical oceanographers deal in "T-S" diagrams, where T is the temperature and S the salinity of water mass. Temperature and salinity together control the density of the water mass, and density in turn controls whether the water mass will sink relative to other water masses in the same ocean.
|
From page 83... ...
Finally, geoscientists can use spatial thinking processes as a short-cut, metaphor, or mental crutch to think about processes or properties that are distributed across some dimension other than physical space. 3.7 THINKING SPATIALLY IN GEOSCIENCE: THE SEAFLOOR MAPS OF MARIE THARP 3.7.1 Introduction: Seafloor Mapping Marie Tharp (1920)
|
From page 84... ...
Tharp's decades-long effort involved synthesizing vast amounts of spatial data, visualizing what was previously unseen, and interpreting spatial observations in terms of causal processes. Marie Tharp worked at the Lamont-Doherty Earth Observatory of Columbia University in the research group of Professor Bruce Heezen.
|
From page 85... ...
Copyright by Marie Tharp 1977/2003. Reproduced by permission of the Marie Tharp Oceanographic Cartography, One Washington Ave., South Nyack, New York 10960.
|
From page 86... ...
Nowadays, such tasks would be supported by a tool such as GIS. 3.7.3 The Importance of Marie Tharp's Work Prior to the work of Heezen, Tharp, and a handful of contemporaries at other major oceanographic institutions, most geoscientists did not think at all about the seafloor.
|
From page 87... ...
A skilled spatial thinker is capable of detecting spatial patterns and regularities from a sparse, discontinuous, and error-laden data set. Even today, it would be a challenge for a geoscientist, knowledgeable about the processes that shape seafloor morphology, to generate sensible seafloor contours from the scattered ship tracks that Tharp had available.
|
From page 88... ...
By having one of her helpers plot earthquake epicenter locations at the same spatial scale as her bathymetric maps, Tharp was able to extrapolate the location of the mid-ocean ridge axis to regions for which there was no bathymetric coverage available. A skilled spatial thinker must be capable of holding large amounts of spatial information in mind at one time and browsing through these data.
|
From page 89... ...
3.8.2 The Roots of Walter Christaller's Work Three sets of formative influences shaped Christaller's work: those derived from his childhood, from his career, and from the intellectual context in which he worked. One of the formative influences in his childhood was the gift of an atlas from an aunt, a gift suggested by Christaller's mother: "My aunt was quite disappointed that she `just' sent a `useful' gift, and not something to play with, which would really make one happy" (Christaller, 1972, p.
|
From page 90... ...
The young Christaller exemplifies the development of a spatial thinker: he was fascinated by maps and data and patterns, emboldened to imagine and depict alternative worlds, grounded in the description and explanation of actual worlds, and prompted to ask questions about existing patterns and relationships. His career shows both the power of these childhood formative influences and the effects of persistence, constraint, and opportunity.
|
From page 91... ...
In his work, we can see a variety of complementary approaches: space as in graphics, space as in the description and analysis of patterns, space as in a structure for a model, and space as in algebraic relations in the form of hierarchies. The observational component drew on the formative influences of his childhood.
|
From page 92... ...
." After arraying the values into size classes: "I was able to mark in the central places in South Germany, according to their significance as central places, on a map, to measure the distances among them, and to determine their rank in the hierarchy of their `complementary areas' which belonged to them (i.e., of their surrounding territory) ." At this point, the mapped patterns and the theoretical patterns intersect in a brilliant exercise in spatial thinking.
|
From page 93... ...
There are three messages about the role of spatial thinking in everyday life, at work, and in science. The first is the pervasiveness, power, and flexibility of the process of spatial thinking: successful problem solving in many contexts depends to a significant degree upon spatial thinking.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.