SpatialSTEM: A Mathematical Structure for Teaching Fundamental Concepts in Spatial Reasoning, Map Analysis and Modeling

Joseph K. Berry

Adjunct Faculty in Geosciences, University of Denver

Adjunct Faculty in Natural Resources, Colorado State University

Principal, Berry & Associates // Spatial Information Systems, Fort Collins, Colorado

Email: jkberry@du.edu — Website: www.innovativegis.com/basis/

Background:

The online materials listed below support a SpatialSTEM approach for understanding and teaching map analysis and modeling fundamentals within a mathematical/statistical context that resonates with science, technology, engineering and math/stat communities. The premise is that “maps are numbers first and foremost, pictures later” and we do mathematical things to mapped data for insight and better understanding of spatial patterns and relationships within decision-making contexts …from Where is What graphical inventories to a Why, So What and What If problem solving environment— thinking with maps.

The goal is to get the STEM communities to infuse direct consideration of map analysis and modeling techniques into their teaching, research and professional applications, as an alternative to traditional spatially-aggregated math/stat procedures that assume uniform or random distribution in geographic space.

Keywords: GIS modeling, grid-based map analysis, spatial analysis, spatial statistics, map algebra, map-ematics

Readings and Materials:

- Seminar Description — handout describing 50 minute General Seminar introducing the idea of SpatialSTEM for teaching spatial reasoning, map analysis and modeling fundamentals within a mathematical/statistical framework that resonates with science, technology, engineering and math/stat communities

- Seminar PowerPoint — PowerPoint slide deck supporting the seminar with presentation notes accompanying each slide and a final slide with online links to further readings organized by slide# topics

- Making a Case for SpatialSTEM — short white paper providing an overview of a SpatialSTEM framework for grid-based map analysis and modeling concepts and procedures as direct spatial extensions of traditional mathematics and statistics

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- Workshop Description — handout describing a six contact hour Workshop (3 sessions of 2 hours each) developing the underlying theory, practice and application of spatial data analysis and reasoning skills for college-level instructors in science, technology, engineering and math programs

- Workshop Workbook (in preparation) — participants receive a workshop workbook, extensive set of links to online readings, PowerPoint slide sets, MapCalc Learner software, databases and example application models that they can “tweak” for use in their classes. All materials are royalty free and can be edited and freely disseminated

- Workshop PowerPoints (in preparation) — PowerPoint slide deck supporting workshop sessions 1 and 2 with presentation notes accompanying each slide and a final slide with online links to further readings organized by slide# topics

- 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

- 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 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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- 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

- 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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