Locating and Measuring Spatial Thinking

"...spatial thinking is pervasive: it is vital across a wide range of domains of practical and scientific knowledge, yet it is underrecognized, undervalued, underappreciated and underinstructed" — from the 2006 NRC report, Learning to Think Spatially

"...we know that spatial cognition is malleable, and that spatial thinking can be improved by effective technology and education. But as the NRC report points out, we still don't know exactly how to infuse spatial thinking throughout the curriculum..." — N. Newcombe (2006) A Plea for Spatial Literacy

[unpublished manuscript: Grossner and Montello (2010). Locating and Measuring Spatial Thinking in Text Corpora. PDF (right-click & download if there's a problem)]

At the University of California, Santa Barbara's Center for Spatial Studies we’ve recently undertaken to develop methods for locating and measuring spatial thinking in text collections, with a few goals in mind. The first is quantifying just how pervasive spatial thinking is, differentially, in many STEM knowledge domains. We expect to demonstrate a breadth that will strengthen the case being made to educators and funding agencies for expanded and more explicit instruction in spatial thinking. The second goal is locating evidence of spatial analytic reasoning in existing published educational standards—or the lack thereof. Finally, we expect that identifying a broad range of highly spatial exemplar research projects will assist in developing educational goals generalized across many disciplines, as well as specific curricula and lesson plans. This work will be detailed in a forthcoming paper, but this blog seems a reasonable venue to share the plan of work and interim results.

Briefly, the steps taken so far include:

• Developed a preliminary dictionary of 120 terms for spatial concepts considered ‘core,’ or ‘fundamental’ from several disciplinary perspectives.
• Performed a simple measure of ‘spatial term density’ (count of dictionary terms/number of words in a document) on approximately 200,000 NSF award abstracts as well as several collections of ‘Standard English’ text. This is referred to as the density10 measure below.
• Conducted an experimental survey, asking a relatively 'spatially expert’ population to rate twenty selected NSF abstracts for "the degree to which they entail spatial analytic reasoning," on a scale of 0-100
• Based on that experiment’s results, adjusted the computational measure with some weighting of the simple term counts. The resulting index of spatiality (IOS) produces a rank correlation of 0.743 with the human judgment of the 20 abstracts considered.
• Applied the new IOS measure to the NSF and Standard English corpora, as well as a set of college course descriptions.

It's important to note that the term list used was designed to locate spatial analytic reasoning. Spatial terms are often used metaphorically, and many, such as 'form' or 'map' are polysemous. Many other inquiries into spatial language use are possible and some interesting theoretical questions can be asked, not least whether the use of spatial metaphors for reasoning about non-spatial phenomena constitutes spatial reasoning. For example the 'distance' between concepts or points of view. But we start with STEM.

NSF Abstracts

The figure below illustrates a preliminary result, the degree of spatial analytic reasoning, according to our IOS measure, in ~185,000 funded projects for 34 divisions within eight directorates at NSF between 1988 and mid-2009 [mouse over boxes for division names]. The size of boxes corresponds to funding dollars; the color to quintiles of ‘spatiality,’ with the darker, redder values indicating the presence of more spatial analytic language.

A couple of things stand out. We would expect the geosciences (GEO) to be closely associated with spatial thinking, but we might not expect the mathematical and physical sciences (MPS) to be more so (mean IOS of 0.365 vs. 0.333), or that the computational sciences (CISE) are very nearly equally so (IOS = 0.032). Secondly, given the broad application of spatial thinking in STEM fields, we might hope to see more spatial language in education-related projects (EHR, 0.021).

College Course Descriptions

We gathered the course descriptions from 56 academic departments in the 2008-09 UC Santa Barbara catalog and calculated an average density10 measure for each. These were averaged in turn across groups corresponding largely to colleges: Engineering, Science and Math, Environmental Sciences and Management, Social Sciences, Humanities, Education and Interdisciplinary Studies. Results appear in the figure below.

A Baseline

The values produced by this Index of Spatiality (IOS) are a useful relative measure, but become more meaningful when applied to ‘standard English.’ To create a baseline, we measured several text collections of ‘standard English,’ including: 2615 featured Wikipedia articles (Wiki2615, 10.2 million words); the ‘academic’ subset of the Corpus of Contemporary American English (COCA, 79.3 million words); several works of literature (Austen, Carroll, Melville, Whitman, 733,000 words); and 48 campaign speeches from the 2008 US presidential election cycle (81,000 words).

Note that the figure below shows results for various corpora using the original spatial term density calculation (density10). The improved IOS measure applied to NSF abstracts above is not appropriate for large text collections like COCA and the Wikipedia corpus; its weighting scheme was designed for individual, smaller documents (like abstracts or course descriptions) where a single cohesive topic is described. The narrow difference in results between the density10 and IOS measures (0.728 versus 0.742 correlation with human subjects' judgments) makes the comparison below relevant.

The average spatial term density for all NSF abstracts (0.0306) is roughly triple that for the very large corpus of standard "academic" English (COCA-Acad). Even the lowest value for NSF divisions, EHR (Education and Human Resources) is double that of COCA-Acad. Course descriptions for UCSB departments in engineering, 'hard science' and mathematics departments use decidedly, and unsurprisingly, more spatial analytic language.

Discussion and Further Steps

As it stands the IOS measure is already useful for demonstrating pervasiveness of spatial thinking in advanced scientific research, and for one of the educational goals mentioned above, namely locating varied exemplars.We'll try IOS for locating spatial analytic reasoning in published educational standards, but it seems likely the term dictionary will have to be adjusted. In fact it's easy to imagine vocabularies corresponding to various perspectives on the issue: scientists' highly technical research abstracts, educators' learning goals and objectives, and the high level course descriptions written for prospective students.

We do plan to further improve the IOS measure by reducing the number of terms and improving the weighting system. We'll also experiment with adding more sophisticated computational linguistics measures, such as term co-occurence and dispersion within documents.

The 120 Terms

The terms listed below (stemmed) comprised our initial list. They come from the set of spatial terms gathered from twenty documents in eight fields for teachspatial.org, two textbooks on spatial analysis and a glossary of topological terms. The ten most frequent of these in the NSF corpus are in bold. The #1 term, 'structure' appeared 1 1/2 times as frequently as the next most common, 'area.' Comments about this list are welcome. Note, in retrospect I have my own problems with it!

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