summarized and visualized in Figure 1. IOS. NSF DIRECTORATE. 0.033 ... sciences (CISE) to be nearly equal (IOS = 0.028). .... Information Age Publishing.
Locating and Measuring Spatial Thinking in Text Corpora Karl E. Grossner1 and Daniel R. Montello2 1, 2
1
Department of Geography, University of California, Santa Barbara, CA US {1karlg, 2montello}@geog.ucsb.edu
INTRODUCTION
We report results to date on a long-term project the purpose of which is to increase awareness of the importance of spatial literacy in academic fields, especially so-called STEM (science, technology, engineering, and mathematics) fields, and to discover ways to “infuse spatial thinking throughout the curriculum” (Newcombe 2006). Steps taken to date include: 1) identifying core spatial concepts in multiple disciplines, 2) organizing them usefully, 3) measuring the density of spatial analytic terms in 21 years of U.S. National Science Foundation (NSF) research abstracts, and 4) grounding the measure of term density in an empirical survey with human respondents.
2
IDENTIFYING SPATIAL CONCEPTS
We have undertaken to identify those spatial concepts that might be considered ‘core’ or ‘fundamental’ from several disciplinary perspectives. To date, 20 articles and books (Appendix A) have been examined as source material, representing eight disciplines: geography (10 sources), psychology (3), architectural and urban design (2), earth science (1), social science (1), science education (1), mathematics (1), and philosophy (1). These authors have noted the centrality of spatial thinking in their fields and have attempted to delineate it; they do not reflect all considerations of spatiality for their respective fields. We gathered 185 distinct terms from these texts. Of those, 50 were listed by multiple authors, resulting in a total of 301 assertions and definitional text excerpts.
3
ORGANIZING FRAMEWORKS
Many of the 185 concept terms are near-synonyms or otherwise closely related. In our digital compendium 1 we have purposely not merged them, in order to maintain all definitional distinctions made by their authors. Further analysis began with some basic classification. The recent research report entitled “Learning to Think Spatially” (NRC 2006) proposed several conceptual frameworks for understanding spatial thinking in academic disciplines. Our analysis has shown that two of these can be joined, extending the Elements of Spatial Thinking to form an integrative matrix that reflects three categories of discipline-specific topics important to committee members: basic cognitive processing, navigation in the world, and spatial analysis. This was borne out by successfully locating the core spatial concepts within that matrix, as depicted in this poster. That process led to narrowing the scope of our search, from ‘spatial thinking’ broadly to evidence of ‘spatial analytic reasoning,’ and informed creation of the lexicon discussed in §4.
4
NSF ABSTRACTS
We assembled a corpus of titles and abstracts for 194,998 projects funded by the NSF between 1989 and 2009. A lexicon of 120 spatial terms was created from three sources: a distillation of the 185 terms mentioned in §2, two spatial analysis textbooks, and a glossary of topological terms (Appendix B).
1
www.teachspatial.org/concepts
A measure of ‘spatial term density’ was generated for each NSF award, using a computer program written to count occurrences of each lexicon term in each abstract document, and divide the sum of those counts by the number of words in the document. Document term density values ranged from 0.00 to 0.61. These were averaged across NSF Directorates and Divisions for the 21-year period as summarized and visualized in Figure 1. IOS
NSF DIRECTORATE
0.033
MPS - Mathematical and Physical Sciences
0.030
GEO - Geosciences
0.028
CISE - Computer and Information Science and Engineering
0.028
OD - Office of the Director
0.027
ENG - Engineering
0.026
OPP - Office of Polar Programs
0.021
BIO – Biological Sciences
0.020
SBE – Social, Behavioral and Economic Sciences
0.020
EHR – Education and Human Resources
Figure 1: 'Spatial term density' in NSF research award abstracts averaged over the period 1988-2009. Darker tones indicate higher values. Rectangle size corresponds to funding level. For comparison with ‘standard English,’ the same lexicon was used to rate the spatiality of several other corpora, including 2,615 Wikipedia articles, the ‘academic’ subset of the Corpus of Contemporary American English (COCA) 2, and course descriptions from 7 schools within a major university (UNIV). Results appear in Figure 2.
5
AN EMPIRICAL SURVEY WITH HUMAN RESPONDENTS
To ground the measure discussed in §4 we conducted a survey that asked participants to rate the spatiality of 20 NSF abstracts, chosen to be representative of all 8 Directorates and a range of spatial term densities. Our 70 respondents came from a sampling frame consisting of i) a university geography department’s graduate students, faculty, and research staff, ii) individuals registered on the teachspatial.org web site, and iii) members of the SILC 3 Spatial Network. This group can be considered expert, relative to the general population.
2 3
http://www.americancorpus.org/ Spatial Intelligence and Learning Center (www.silccenter.org)
DMS EHR DGE
Mathematical Sciences (Dir) Education and Human Resources (Dir) Graduate Education (Div)
UNIV: eng Engineering sci Sciences and Mathematics env int soc
Environmental Sciences and Studies Interdisciplinary Studies Social Sciences
hum
Humanities
edu
Education
Figure 2: Comparison of spatial term density in various corpora.
5.1
Results in brief
There was a rank correlation of 0.728 between our term density measure and human judgments of the spatiality of the 20 abstracts. Outliers indicated disproportionate salience given to terms appearing multiple times in documents having few other spatial term ‘hits.’ To address that, we replaced the lexicon term frequency (tf) with a weight, to produce an Index of Spatiality (IOS) for each document(d): IOS = 1+ (tf - 1) ∗ (type/token) / length(d)
(1)
The correlation with the average of human judgments improved slightly, to 0.743. There was however significant variation in the correlation of individual responses with the IOS values (between 0.816 and -0.02), indicating latent factors that bear further analysis.
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DISCUSSION AND FUTURE WORK
Our results confirm that spatial analytic reasoning is pervasive across many STEM fields. While high values were expected for the geosciences (GEO), we did not expect those for the mathematical and physical sciences (MPS) to be higher (mean IOS of 0.033 vs. 0.030), or for the computational sciences (CISE) to be nearly equal (IOS = 0.028). High values for Physics (PHY, 0.031) and Math (DMS, 0.050) reflect the extent of spatial analytic reasoning at scales from the microscopic to the cosmic. Given this disciplinary breadth, we would hope to see more spatial language in educationrelated projects (EHR, 0.020). This investigation is a step towards better understanding of how judgments of spatiality are made, and the role of spatial thinking in scientific research. We will seek to improve the IOS measure, including by incorporating collocation counts to disambiguate terms. We are also working to locate spatiality in existing published educational standards, to inform the design of explicitly spatial teaching modules.
BIBLIOGRAPHY NRC Committee on Support for Thinking Spatially: The Incorporation of Geographic Information Science Across the K-12 Curriculum (2006). Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum. Washington, DC: National Academies Press.
Newcombe, N. S. (2006). A Plea for Spatial Literacy. Chronicle of Higher Education: The Chronicle Review (52)26: B20 retrieved from http://chronicle.com/article/A-Plea-for-SpatialLiteracy/20863, 21 Jan 2010
APPENDIX A – SOURCES EXAMINED [Geography] de Smith, M., M. F. Goodchild, and P. Longley (2007). Geospatial Analysis: A comprehensive guide to principles, techniques, and software tools, 2nd Edition. London: Troubador DiBiase, D., M. DeMers, A. Johnson, K. Kemp, A. T. Luck, B. Plewe, and E. Wentz (Eds.) (2002). Geographic Information Science and Technology Body of Knowledge. Washington DC: Association of American Geographers. Gersmehl, P.J. (2005) Teaching geography. New York: Guilford Press Gersmehl, P.J., and C. A. Gersmehl (2007) Spatial thinking by young children. Neurologic evidence for early development and "educability." Journal of Geography 106:5,181-191 Golledge, R. G. (1995). Primitives of Spatial Knowledge. In Nyerges, et al. (Eds) Proceedings of the NATO Advanced Research Workshop on Cognitive Aspects of Human-Computer Interaction for Geographic Information Systems, Palma de Mallorca, Spain, March 20-25. Boston:Kluwer Academic Publishers. Golledge, R., M. Marsh, and S. Battersby (2008). Matching geographical concepts with geographic educational needs. Geographical Research, 46:1 p. 85-98 Kaufman, M. M. (2004) Using Spatial-Temporal Primitives to Improve Geographic Skills for Preservice Teachers. Journal of Geography, 103(4): 171-181 Marsh, M., R. Golledge and S. E. Battersby (2007). Geospatial Concept Understanding and Recognition in G6-College Students: A Preliminary Argument for Minimal GIS. Annals of the Association of American Geographers, 97:4, 696 — 712 Nystuen, J. D. (1963). Identification of some fundamental spatial concepts. Michigan Academy of Science, Arts, and Letters, 48, 373-384. O'Sullivan, D, and D. J. Unwin (2002). Geographic Information Analysis. Hoboken NJ: Wiley [Psychology] Newcombe, N. S. and J. Huttenlocher (2000). Making Space. Cambridge MA: MIT Press Piaget, J. and B. Inhelder (1967). A Child's Conception of Space (F. J. Langdon & J. L. Lunzer, Trans.). New York: Norton (Original work published 1948) Tversky, B. (2005). Functional Significance of Visuospatial Representations. In P. Shah and A. Miyake (Eds.) Cambridge Handbook of Visuospatial Thinking, p 1-34. Cambridge, UK: Cambridge University Press [Architectural and Urban Design] Alexander, C. (2004). The Phenomenon of Life: The Nature of Order, Book One. New York: Oxford University Press Lynch, K. (1984). Good City Form. Cambridge, MA: MIT Press [Earth Science] Kastens, K.A., and Ishikawa, T. (2006) Spatial thinking in the geosciences and cognitive sciences: A cross-disciplinary look at the intersection of the two fields, In Manduca, C.A., and Mogk, D.W., eds., Earth and Mind: How Geologists Think and Learn about the Earth; Geological Society of America Special Paper 413, p. 53-76
[Social Science (General)] Janelle, D. G. and M. F. Goodchild (in press 2009). Concepts, Principles, Tools, and Challenges in Spatially Integrated Social Science. In Nyerges, T., H. Couclelis, and R. McMaster (Eds.) GIS & Society Research. Sage Publications. [Science Education] Mathewson J. H. (2005). The visual core of science: definition and applications to education. International Journal of Science Education, 27(5): 529-548 [Mathematics] Battista, M. T. (2007). The Development of Geometric and Spatial Thinking. In F. K. Lester, Jr. (Ed.) Second Handbook of Research on Mathematics Teaching and Learning, Charlotte NC: Information Age Publishing [Philosophy/Linguistics] Johnson, M. (1990) The Body In The Mind: The Bodily Basis of Meaning, Imagination and Reason. Chicago: University of Chicago Press
APPENDIX B – LEXICON OF SPATIAL TERMS The 120 terms listed below (stemmed using the Porter algorithm) comprised our initial list. The ten found most frequently in the NSF corpus are noted. adjacency, alignment, angle, anisotropic, area (2), areal, arrangement, attraction, autocorrelation, border, boundary, branching, center, centroid, chaos, chirality, circuit, cluster, cognitive map, coil, collision, compactness, conduit, congruence, connection, container, convex, cube, deformation, dense, density, diffusion, dimension, direction, dispersion, distance, enclosure, energetics, environment (8), euclidian, flow, fluid, folding, force, form (9), geography, geometric, geometry, global, gradient, granularity, gravitation, gravity, grid, imagery, interaction (3), interlock, isomorphism, isotropic, kinetic, landmark, landscape, length, local (10), location, manifold, map, mental model, microscale, migration, morphology, motion, movement, navigation, neighbor, network (4), orientation, overlay, packing, part, path, pattern, perimeter, periphery, place, planar, point, polygon, polymorphism, position, proximity, reference frame, region (7), representation, rotation, route, rupture, scale (6), section, separation, shape, size, slope, space, space-time, spatial, spatiotemporal, spatio-temporal, stratum, structure (1), surface (5), symmetrical, symmetry, topology, transport, visual, void, volume, wave, web
