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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.