Keyah Math Project

Project Description:
The Kéyah Math Project has developed a series of versatile online activities in mathematical geoscience, using the natural and cultural landscapes of the Southwest United States as context and setting. 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-- it literally means that which is connected to one beneath one's feet. We use this name to emphasize the connection to Southwest places.

Fourteen activities address five levels of mathematical content and are partitioned among seven topics. (Note that one of these--Age of the Universe-- is a demonstration of the Kéyah Math format and is identified as Level Zero.) Kéyah Math activities 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 Southwestern United States, including the lands of several American Indian nations. Indigenous cultural and scientific experts have participated directly in the development of these activities. The versatility and accessibility of these activities will 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 Kéyah Math team plans to continue developing place-based quantitative geoscience activities, and welcomes your comments and recommendations (via the Contact Team link at left).

Pedagogical Concerns:
Recommendations of the Greater Geoscience-Education Community:
In 1996, the National Science Foundation published the "George Report," a comprehensive review of undergraduate education in all areas of science, technology, engineering, and mathematics (George et al., 1996) that in turn inspired communities of educators in the various disciplines to conduct their own reviews.
Later that same year, in response to the "George Report," the Shaping the Future conference on innovation in undergraduate Earth science education (Ireton et al., 1997), also sponsored by NSF, was convened by the American Geophysical Union and the Keck Geology Consortium.

A panel at this conference addressed the question of increasing diversity, recruitment, and retention of students in the Earth and space sciences. The foremost recommendation of this Diversity Panel (which included the PI of this project), to college and university instructors, echoes the sentiments of Native educators discussed above:
"Place Earth system science principles and problem-solving methods in the context of the local environment, which helps students connect the relevance of Earth system science to their lives." (Ridgway et al., 1997).
The place-based, culturally-responsive framework of the Kéyah Math modules is fully concordant with this recommendation.

The recent report, Blueprint for Change (Barstow et al., 2002), the proceedings of a major recent NSF-funded workshop in geoscience education reform involving a diverse group of educators (including the PI of this project), also lists a number of recommendations for improving curricula and instructional materials. These, though formally addressed to the K-12 community, are equally relevant at the lower-division undergraduate level. The proposed Kéyah Math project responds directly to several of these recommendations, specifically that new curricula and instructional materials should:
  • Engage students by means of "dynamic learning opportunities that are relevant to students' lives and communities;
  • "Be inquiry-based;
  • "Illustrate how Earth and space science reflects the contributions of and is relevant to diverse populations;
  • "Provide a forum for the development of skills in math." (Barstow et al., 2002)


  • Benefits of Using Kéyah Math:
    Results of the project evaluation show:
    1. Kéyah Math bolsters the interest and capabilities of all students in the geosciences through the use of scientific inquiry and current scientific data.
    2. Kéyah Math attracts the interest of Native American students in particular, through the use of data and case studies taken from familiar, culturally-significant localities and contemporary issues of significance to their communities.
    3. Kéyah Math improves the quantitative skills of Native American and other minority science students at an early stage in their undergraduate programs, better preparing them for professional careers in the geosciences.
    4. Kéyah Math enhances the global infrastructure for geoscience education through universal web-based dissemination.

    Download the full evaluation report (.doc)


    Using the Kéyah Math Modules

    The specific modules and their mathematical levels are given in the tables below. Table 1 provides an organization of the modules themselves, while Table 2 shows the requisite mathematics per level. The instructor's guide gives detailed information about the use of the materials.
    Instructor's Guide: http://keyah.asu.edu/InstructorsGuide.doc (coming soon)

    Table 1. Organization of Kéyah Math Modules

    Topic Mathematical Level Module Name
    Demonstration of Kéyah Math Format Level 0 Age of the Universe
    Stream Flow Level 1 Stream Flow for the Animas River
    Stream Flow Level 2 Snow Melt & Stream Flow for the Animus River
    Earthquakes Level 2 Location of the Epicenter of an Earthquake
    Volcanic Processes Level 2 Sunset Crater
    Age of the Earth Level 2+ Age of the Earth
    Age of the Earth Level 4 Age of the Earth
    Impact Processes Level 2 Meteor Crater
    Impact Processes Level 4 Age of the Earth
    How Big is the Earth? Level 2 The Size of the Earth, Estimated in Arizona
    How Big is the Earth? Level 3 Mass & Density of the Earth and Size, Mass, & Density of the Earth
    Layers of the Earth Level 3 Layers of the Earth


    Table 2. Requisite Mathematics per Level

    Level Mathematical Topic
    Level 1 Pre-Algebra, Substitution into Formulas, Computation, Simple Geometry
    Level 2 Algebra with Equations (not Functions), Solving Equations, Reading Graphs, Geometry
    Level 3 Algebra with Functions, Evaluating Algebraic Functions, Solving Equations, Graphing
    Level 4 Pre-Calculus, Algebraic & Exponential Functions, Evaluation, Graphing, Geometry