For Special Supplementary Issue of the Journal of Geography
edited by C. Shearer and D. Rutherford
In Section 4. Promising Means to Improve Geographic Literacy
"Math learning and geography education"
Word Count: 1318 in text
Figures Count:6
Table Count: 1
by
Gale Olp Ekiss, Ronald I. Dorn, Elizabeth Hinde, John Douglass, and Barbara TrapidoLurie
Arizona State University
PURPOSE OF GEOMATH PROJECT
Geography inherently integrates mathematics with virtually all areas of study (Gould
1975) — not just the mapping sciences (Bednarz and Baker 2003; Furner and Ramirez
1999). All essential elements of the National Standards explore number sense, as do such
lesson packages as Mission Geography (<missiongeography.org>), ARGUS and
ARGWorld (<www.aag.org>). Similarly, mathematics innovators constantly seek
authentic exemplars to enrich conceptual understanding (Kilpatrick and Swafford 2002).
A natural question arises as to why a full curriculum package had not been developed to
exploit a math-geography linkage. The answer is uncertain, but likely includes a number
of obstacles including: convincing the elementary educator that key math skills can be
learned using elements other than the math textbook; convincing administrators that math
scores can be improved by using cross-curriculum materials and not necessarily core
math instruction; and the open secret that those attracted to elementary school teaching
are the most likely to be poorly trained in mathematics, often translating into a phobia of
mathematics for their students (Stipek et al. 1998).
Facing the loss of geography teaching time due to the pressures of a testing system that
emphasizes reading and math (Manzo 2002), Arizona geography educators agreed at their
Annual Conference of Teacher Consultants on the need to develop a GeoMath curriculum
package focused on grades K-8. These teachers saw the trend worsening, as it has. "In
Arizona, for example, 22.5 percent of 8th graders must score at the proficient level or
higher on state math tests in 2004-05, up from 7 percent last year (Olson 2004)." Thus,
we obtained support from the National Geographic Society's Education Foundation
Grosvenor Grant program, matched by such sources as the Arizona State Department of
Education, ASUs Geography Department, and a supplement to an NSF GK-12 grant.
GEOMATH MATERIALS
The net result is a CD-based lesson package of more than 80 lessons where student
assessments include math items that mirror the style of the required high stakes test. In
other words, all of the 28 teacher authors (a mix of Arizona Geographic Alliance teacher
consultants, National Board Certified teachers, and members of the National Council of
Teachers of Mathematics) placed into their lessons core tested mathematics skills based
on mathematics standards, in addition to blending in a variety of Arizona's geography
standards reflecting the six essential elements of the National Standards. Table 1
provides a sampling of the teacher lessons.
Users access the first CD through any Internet browser and a PDF reader such as Adobe
Acrobat. Figure 1 illustrates the first set of choices on viewing lessons. Although most
teachers typically select grade level, let us assume that you are an administrator
evaluating the suitability of this package and you would select math standards of Arizona
(Figure 2) and then specific lessons that match a particular math strand (Figure 3, which
also includes this same level of detail associated with a particular geography standard and
performance objective). No matter the motivation of the user, be it math or geography, all
pathways lead to the "lesson home page" (e.g. Figure 4) that contains links to all material
needed to teach that lesson.
One of the richest aspects of the GeoMath CD rests in the creative synergism between the
teacher authors and ASUs cartography program led by Barbara Trapido-Lurie and her
enthusiastic students. Several of the specially designed GeoMath maps can be seen at the
public website of the Arizona Geographic Alliance (<alliance.la.asu.edu/azga/ and click
on maps). Each of the maps went through several changes of teacher vision and
cartographic design and redesign after receiving iterative feedback.
CRAFTING THE PROGRAM
We have been asked, a number of times, how a state alliance organized such an endeavor.
This short-article format cannot present all of the steps involved in recruitment of
teachers, iterations of workshops to develop and revise lessons, piloting, evaluation, and
CD development. The CD itself includes a section on the dozens of individuals involved
in crafting the program. We isolate the key elements of crafting down to the following
factors that were required:
• a single individual who minds the store and keeps all deadlines firmly impressed on the
minds of lesson authors
• a single individual who compiles revisions and materials (this person can change, but
only 1 person should compile at one time)
• a single individual coordinating the cartography
• a single individual editing the lesson materials for conformity prior to and after lesson
piloting
• a single individual organizing CD construction
• a single person collecting updates to the CD (we are currently at the seventh revision
and the third public revision, GeoMath version 1.3)
The single largest difficulty in crafting the program comes when states inevitably change
their standards. Since the inception of the program, math standards have changed twice
and geography standards are in the process of undergoing a revision. Hence, we are in
the process of planning a computerized system to automate lesson updates (a) when
standards change in the future; and (b) to be able to translate our lessons into other state
standards as part of some future national GeoMath lesson bank.
EVALUATION
The preliminary evaluation of GeoMath lessons was based on two strategies. First, we
simply asked the piloting teachers the percent of their students that mastered (defined by
80% performance) the geography performance objectives and the math performance
objectives. Figure 5 reveals that about half of the piloting classrooms had 80% or more
of their students mastering the geography standards, while only one-fifth of the
classrooms were unable to reach a mastery level in half of the students.
Our math evaluation strategy also asked piloting teachers to give a pre-test and then the
same test again 30 days after teaching the lesson. A detailed presentation of our findings
has been submitted to this journal as a separate article, and thus we present an overview
of our findings in Figure 6. Across all grade levels, the average revealed improvement in
math performance a month after the lesson was taught, and only 13 classrooms saw a
decline in math scores.
We also found a change in elementary teacher attitude towards math in a quarter of the
113 piloting teachers. All but two of the teachers who changed their attitude towards
math, after piloting a GeoMath lesson, reported an increased level of comfort. Informal
discussions reveal two general types of explanations. First, there is a realization that
math can be fun and tied to curriculum that they enjoy teaching (geography). Second,
there is a feeling that the teachers can step beyond the math textbook. In other words, so
many good elementary teachers enjoy the creative process that takes place in so much of
the curriculum other than math. GeoMath lessons exemplify how to exert that same
creativity over math. Thus, just focusing on controlled testing of students may be barking
up the wrong strategic tree. The phobia of math by elementary teachers often results in
fears of math by their students (Stipek et al. 1998). A very powerful policy motivation
could be to take a program like GeoMath to systematically foster an improvement in
elementary teacher attitudes towards math.
CONCLUSION
The No Child Left Behind legislation created a downward spiral for K-8 geographic
education in Arizona. The Teacher Consultants of the Arizona Geographic Alliance
developed a plan to convince administrators of the value of geography in preparing for
the high stakes testing. First, they envisioned a package of GeoLiteracy lessons and
associated activities that co-teach explicit tested language arts skills and geography
standards (see Hinde et al. this issue). Second, the envisioned a parallel package of
GeoMath. Piloted in more than a hundred K-8 classrooms across Arizona mirroring
Arizona's socioeconomic student body, preliminary evaluation data suggest that GeoMath
lessons improve understanding of geography while increasing performance in math skills,
as well as increasing the math comfort level of a fourth of the elementary school teachers
piloting the lessons.
NOTES
1. Acknowledgement. This research was supported by a National Geographic Society
Grosvenor Grant with cost-sharing from the Arizona Department of Education and NSF
GK-12 Grant DGE 0086465, and ASUs Geography Department.
REFERENCES
Bednarz, S.W., and T.R. Baker. 2003. Special Issue on Research on GIS in Education,
Journal of Geography 102 (6):231-291.
Furner, J.M., and M. Ramirez. 1999. Making connections: using GIS to integrate
mathematics and science, TechTrends 43 (4):34-39.
Gould, P. 1975. Mathematics in geography: Conceptual revolution or new tool,
International Social Science Journal 27:303-327.
Kilpatrick, J., and J. Swafford, eds. 2002. Helping children learn mathematics.
Washington D.C.: National Research Council.
Manzo, K.K. 2002. Concentration on reading, math troubles social studies educators,
Education Week on the Web, April 5 Edition <www.edweek.org> 21 (23).
Olson, L. 2004. Taking Root, Education Week on the Web, December 8 Edition
<www.edweek.org> 24 (15)
Stipek, D.J., K.B. Givvin, J.M. Salmon, and V.L. MacGyvers, V.L. 1998. Teachers'
beliefs and practices related to mathematics instruction, Teaching and Teacher
Education 17: 213-226.
Table 1. Sampling of the more than 80 GeoMath lessons. The bold lesson names indicate
lesson titles that can be accessed with complete materials at
<alliance.la.asu.edu/geomath/general.html>
Grade
Title
Description
K-1
Shape of My World:
Mapping a Classroom
Students identify basic shapes in the classroom and make a map
showing where major furniture and classroom features.
2-3
Don't be such a drip:
Water conservation
Students learn to draw conclusions from graphs, while they
discover the importance of water conservation
3
Relying on the Desert:
Plants used by Hohokam
Students learn how Hohokam people used natural resources to
survive in a desert, while developing data analysis skills
4-5
Now you see them... now
you don't: Movement in
and out of Arizona
Students study the movement of people through data analysis of
the census.
4-5
Grand Canyon: A River
Rafting Trip
On a Journey through the Grand Canyon, students practice
finding elevations on a topographical map and determine
measures of central tendency.
5-8
In the wake of Columbus:
Decline of native peoples
Students learn of the catastrophic population decline among
Native Americans associated with the Columbian contact, while
practicing measurement and graphing skills.
6-8
Can You Hear Me Now?
How a Country's
Wealth Influences
Communication
Students make and solve problems using scatter plots created by
using data from a variety of countries. These data will help
students explore relationships between different countries and
how their citizens get information using popular culture items
such as, TVs, cell phones, and the Internet.
6-8
Marvelous Moroccan
Mosaics: Patterns in Zillij
Students learn about the centuries-old craft of Zillij and use it to
understand geometric shapes and tessellations
6-8
Where did the lake go?
The drying up of Lake
Chad
Students explore the rate of change of Lake Chad, as they learn
about interactions between people and environmental change.