Kéyah Math

by Steven Semken (Arizona State University)

Kéyah Math (KM) is a freely accessible set of versatile fully online activities for application of basic mathematics to geoscience, all of which are situated in geologically interesting and culturally significant places in the Southwestern United States. These place-based exercises are available to enhance any undergraduate geoscience course, and may be of particular interest to students and teachers with cultural ties to the Southwest, including American Indian and Hispanic students and teachers.

Kéyah is the Dine (Navajo) word for homeland, literally meaning that which is connected to one beneath one's feet. The name signifies the connection to Southwest places and that the project was initiated on the Navajo Nation. KM was developed by a collaborative group of geoscientists, mathematicians, and teachers from Arizona State University, Diné College, Fort Lewis College, San Juan College, Kennesaw State University, and several K-12 school districts in the Four Corners region, and was supported by a grant from the National Science Foundation Opportunities for Enhancing Diversity in the Geosciences Program. The principal investigators were Steven Semken, Christopher Schaufele, Nancy Zumoff, and the late Andrew Becenti. KM can be thought of as a Southwest-based, geoscience-focused spinoff of the widely used Earth Math materials (earthmath.kennesaw.edu) developed by Schaufele and Zumoff to teach mathematics using quantitative examples from environmental science.

KM activities (grouped into fourteen modules) are typically not found in introductory geoscience textbooks, nor are they readily available commercially in ancillary materials. They draw on data-rich examples from the geological and cultural landscapes of the Southwest, including the lands of several American Indian nations. Indigenous cultural and scientific experts participated directly in the development and assessment of these materials. The versatility and accessibility of the fourteen KM modules enable any number of them to be integrated into any basic Earth science or geology course at any level, regardless of the textbook or laboratory manual used. The modules are accompanied by online applets that can be used to do all of the mathematics needed to solve the problems posed. Students have the option of using the applets or their own graphing calculator.

The fourteen modules address five levels of mathematical content and are partitioned among seven topics:

Level 0 Module: Demonstration of the Kéyah Math format and use of online tools

1. Age of The Universe

Level 1 Module Pre-algebra; arithmetic; substitution into formulas; computation; simple geometry

1. Stream Flow in the Animas River

Level 2 Modules: Algebra with equations (not functions); solving equations; reading graphs; geometry

1. Volcanic Ejecta from Sunset Crater
2. Snow Melt and Stream Flow in the Animas River
3. Measuring the Size of the Earth from Arizona
4. The Epicenter of a Southwestern Earthquake
5. Impact Processes at Meteor Crater
6. Ages of Rocks and the Earth

Level 3 Modules: Algebra with functions; evaluating algebraic functions; solving equations; graphing

1. Mass and Density of the Earth
2. Layers of the Earth
3. Size, Mass, and Density of the Earth

Level 4 Modules: Pre-calculus; algebraic and exponential functions; evaluation; graphing; geometry

1. Geochronology in the San Juan Mountains
2. Impact Processes at Meteor Crater (Advanced)

Instructions and instructor's reference materials are posted online. The solutions to the module problems are password-protected on the site, and an instructor can readily obtain the passwords from the development team via a link that is posted on the main menu. This same link enables users to contact the developers with questions or comments, which are always welcomed!