SpatialSTEM: A Mathematical/Statistical Framework for Understanding and Communicating Grid-based Map Analysis

Presented at ASPRS 2013 Annual Conference, Baltimore, Maryland, March 28, 2013

Joseph K. Berry, Keck Scholar in Geosciences, Department of Geography, University of Denver

Email: Website: www.innovativegis.com/basis/

Premise: There is a “map-ematics” that extends traditional math/stat concepts and procedures for the quantitative analysis of map variables (spatial data)

Supporting materials posted online: Paper (13 pages) — Handout (1 page) — PowerPoint slide set (7MB).

Abstract

A SpatialSTEM approach is described for understanding and communicating spatial reasoning, map analysis and modeling fundamentals within the traditional mathematical/statistical framework that resonates with science, technology, engineering and math/stat communities. The premise is that “modern maps are numbers first, pictures later” and that there is a comprehensive “map-ematics” extending traditional quantitative analysis operations to mapped data as a means to better understand spatial patterns and relationships. The approach focuses on grid-based analytical tools used in spatial reasoning by non-GIS communities instead of traditional “GIS mechanics” of data acquisition, storage, retrieval, query and display of map features directed toward GIS specialists. The goal is to get the STEM communities to “think analytically with maps” and infuse direct consideration of spatial relationships into their endeavors, as an alternative to traditional spatially-aggregated math/stat procedures that assume uniform or random distribution of variables in geographic space. The recasting of grid-based Spatial Analysis and Spatial Statistics operations into the traditional quantitative analysis framework provides a familiar conceptual foothold that cuts across most STEM disciplines and applications. For example, the calculation of slope and aspect in terrain analysis is actually a spatial extension of the mathematical derivative with numerous applications outside of traditional mapping, such as calculating the slope of a barometric surface to derive a map of wind speed (high winds where pressure is rapidly changing), while its aspect map identifies wind direction. Or the extension of traditional correlation to “localized correlation” that maps the level of dependency between two map variables by successively solving the standard statistical correlation equation within a roving window to identify where the map variables are highly correlated, and where they are not. This paper outlines the spatialSTEM framework, provides several examples of extended mat/stat operations, lists further online references and links to royalty-free teaching materials.

KEYWORDS: GIS modeling, map analysis, spatial analysis, spatial statistics, STEM education

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-         SpatialSTEM: Extending Traditional Mathematics and Statistics to Grid-based Map Analysis and Modeling — white paper describing an innovative approach for teaching map analysis and modeling fundamentals within a mathematical/statistical context

-         Topic 30 in the online book Beyond Mapping III — book chapter describing the SpatialSTEM framework for understanding and teaching map analysis and modeling fundamentals as direct extensions of traditional mathematical/statistical concepts and procedures

-         Further Readings  a comprehensive appendix to the SpatialSTEM “extension” paper with URL links to over 125 additional readings on the grid-based map analysis/modeling concepts, terminology, considerations and procedures described in the papers on SpatialSTEM

-         Beyond Mapping III  an online book by J.K. Berry containing Introduction, 28 Chapters and Epilog as a compilation of the popular Beyond Mapping columns published in GeoWorld magazine from 1996 through present (click for a Chronological Listing with links of BM columns from 1989 through present)

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-          Topic 30 in the online book Beyond Mapping, a compilation of ten Beyond Mapping columns appearing in GeoWorld, 2012-13 describing the SpatialSTEM approach..

-         Royalty Free Teaching Materials  links to instructional materials to include lecture PowerPoints, readings, exercises and MapCalc software for grid-based map analysis and modeling supporting a variety of teaching environments

-         white paper listing MapCalc operations by traditional mathematics and statistics categories

-         white paper listing Spatial Analyst module operations by traditional mathematics and statistics categories

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