SpatialSTEM: A Mathematical/Statistical Framework for Understanding and
Communicating Gridbased 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: jkberry@du.edu
or jberry@innovativegis.com — Website: www.innovativegis.com/basis/
Premise: There is a “mapematics” 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 “mapematics”
extending traditional quantitative analysis operations to mapped data as a
means to better understand spatial patterns and relationships. The approach
focuses on gridbased analytical tools used in spatial reasoning by nonGIS
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 spatiallyaggregated math/stat procedures that
assume uniform or random distribution of variables in geographic space. The
recasting of gridbased 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 royaltyfree
teaching materials.
KEYWORDS:
GIS modeling, map analysis, spatial analysis,
spatial statistics, STEM education
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Related
Readings and Materials:

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

A
Math/Stat Framework for Map Analysis, 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 gridbased 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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SpatialSTEM:
a math/stat framework for gridbased map analysis and modeling — Topic
30 in the online book Beyond Mapping, a compilation of ten Beyond Mapping
columns appearing in GeoWorld, 201213 describing the SpatialSTEM approach..

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

Math/Stat
Classification of Spatial Analysis and Spatial Statistics Operations (MapCalc
by Basis) — white paper listing MapCalc operations by traditional
mathematics and statistics categories

Math/Stat
Classification of Spatial Analysis and Spatial Statistics Tools (Spatial
Analyst by Esri) — white paper listing Spatial Analyst module operations by
traditional mathematics and statistics categories
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