GIS Based Studies in the Humanities and Social Sciences - Chpater 17

17 Evaluation of School Redistricting by the School Family System Yukio Sadahiro, Takashi Tominaga, and Saiko Sadahiro CONTENTS 17.1 Introduction................................................................................................244 17.2 Potential of GIS in Educational-Administration Research.................244 17.2.1 GIS for Analysis in Educational-Administration Research..........................................................................................244 17.2.2 GIS for Planning in Educational-Administration Research246 17.2.3 GIS for Evaluation in Educational-Administration Research..........................................................................................247 17.3 GIS for School Redistricting.....................................................................248 17.3.1 School Districting in Elementary and Lower-Secondary Education........................................................................................248 17.3.2 School Redistricting in Elementary and Lower-Secondary Education........................................................................................249 17.3.3 School-Family System...................................................................249 17.3.4 School Redistricting as a Spatial-Optimization Problem .......250 17.4 School Redistricting in Kita Ward, Tokyo .............................................251 17.4.1 Formulation of School-Redistricting Problem in Kita Ward, Tokyo...................................................................................252 17.4.2 School Redistricting Where the Average Distance from Home to School Is the Objective Function...............................256 17.4.3 School Redistricting Where the Number of Students Assigned to Different Schools Is the Objective Function.......259 17.5 Conclusion ..................................................................................................262 References.............................................................................................................262 243 Copyright © 2006 Taylor & Francis Group, LLC 244 GIS-based Studies in the Humanities and Social Sciences 17.1 Introduction Geographical Information System(GIS) is a set of tools for analyzing spatial objects and phenomena interactively in a computer environment. Since it treats geographical information, it is effective in educational administration to discuss geographical factors. For instance, we can visualize the location of schools, traffic networks, and public facilities as an integrated map. A map of schools and population distribution classified by ethnicity and race is useful for discussing the educational program desirable in each school. Calculating the average distance from home to school, we can evaluate a physical aspect of educational environment. This paper aims to present potentials of GIS in educational administration. Potential applications of GIS in educational administration are threefold: analysis, planning, and evaluation. We discuss these subjects in turn in the following sections. We then show a methodology for treating school redis-tricting in GIS with a focus on the school-family system, a new concept in school cooperation. Applying the method to a concrete example of school redistricting in Tokyo, Japan, we will show the effectiveness of GIS in edu-cational administration. In the last section, we summarize the conclusions. 17.2 Potential of GIS in Educational-Administration Research 17.2.1 GIS for Analysis in Educational-Administration Research One typical usage of GIS in educational administration is spatial analysis of the present status of education in a region. Spatial analysis usually starts with visual analysis, which is followed by statistical and mathematical anal-ysis. These steps are explained successively in the following. Visual analysis is an initial examination of spatial phenomena in GIS (MacEachren and Taylor, 1994; Nielson et al., 1997; Slocum, 1998; Gahegan, 2000). Suppose, for instance, a map showing the location of schools, the number of students, and the population distribution of Hispanics (Figure 17.1a). A spatial variation exists in the number of students among school. Some schools have very few students, while others have so many students that they may be beyond their capacity. Since a strong correlation exists between the number of students and that of Hispanics, we suppose that a sudden increase of Hispanic students may have caused lack of schools, which has lowered the quality of educational environment. If our interest lies in the regional variation in the grade of students, we may overlay a map of students with their grade on the map showing pop- Copyright © 2006 Taylor & Francis Group, LLC Evaluation of School Redistricting by the School Family System 245 (a) (b) Elementary school Major traffic road FIGURE 17.1 GIS maps for visual analysis: (a) the number of students (white circles) and the distribution of Hispanics (gray shades); (b) traffic network (broken lines) and crime rate (gray shades). ulation distribution classified by gender, age, ethnicity, and race. The quality of teachers and educational programs can also be visualized as attributes of schools to be discussed in relation to regional variation of students. Visual analysis is also useful for assessing educational environment in a region. A map indicating the location of schools and individual students is useful for assessing the regional variance in the distance from home to school. Overlaying the maps of traffic networks and topography, we can evaluate the time distance instead of physical distance. Maps showing crime occurrences and land-use patterns may also work as indicators of educa-tional environment (Figure 17.1b). Though we can do these analyses manu-ally using paper maps, GIS drastically improves the efficiency and accuracy of analysis. Visual analysis provides a lot of useful information about spatial phenom-ena. However, visual analysis is inherently subjective to some extent, because it primarily depends on the perception and evaluation of the analyst. More-over, since the result is qualitative rather than quantitative, it often fails to lead persuasive result and discussion. Consequently, visual analysis is usu-ally followed by statistical and mathematical analysis (Bailey and Gatrell, 1995; O’Sullivan and Unwin, 2002; Haining, 2003). Statistical analysis includes basic summary statistics, say, the number of students and teachers, the floor size of school buildings, the cost of maintaining educational Copyright © 2006 Taylor & Francis Group, LLC 246 GIS-based Studies in the Humanities and Social Sciences resources, both human and physical, and so forth. They are calculated for individual schools, reported by the histogram, mean, variance, the maximum and minimum values, and often represented by the size of map symbols in GIS. These descriptive measures are useful for generating research hypotheses. To test research hypotheses, statistical tests are performed. In addition to traditional statistics, spatial statistics are often used in GIS (Isaaks and Srivas-tava, 1989; Cressie, 1993; Diggle, 2003). Spatial statistics are a subfield of statistics focusing on the spatial distribution of stochastic phenomena. Whether or not the students of high grades are clustered in specific regions can be statistically tested at a given significance level. Spatial relationship between the location of schools and juvenile offenses can also be statistically evaluated. Once a hypothesis is statistically supported, mathematical models are built to represent spatial phenomena. General spatial models include spatial-regression models (Bailey and Gatrell, 1995; Fotheringham et al., 2002), geo-statistics, spatial-point processes (Stoyan and Stoyan, 1994; Diggle, 2003), spatial econometrics (Anselin, 1988; Anselin and Florax, 1995), and spatial-choice models (Ben-Akiva and Lerman, 1985; Fischer et al., 1990; Smith and Sen, 1995). These models describe spatial phenomena in a formal manner using mathematical and statistical theories. Suppose, for instance, school choice of students, a kind of spatial choice behavior. Various factors are considered to affect school choice; the distance from home to school, the quality of education and facilities, the environment around school, and so forth. To measure the weight of each factor in school choice, a discrete choice model is often utilized. Collecting the data of school choice, we can estimate the model and evaluate quantitatively the degree of influence of each factor. This helps us in understanding one aspect of human behavior in education. 17.2.2 GIS for Planning in Educational-Administration Research In educational administration, analysis is usually followed by plan making. For example, if the quality of education varies considerably among schools, a plan may have to be devised that assures all the schools of a certain quality of education. GIS can be utilized at this stage, that is, GIS supports decision-making in educational administration. One effective tool for plan making is spatial optimization, which can be implemented in GIS (Drezner, 1996; Drezner and Hamacher, 2001). Spatial optimization is a collection of mathematical techniques that derives the spatial structure of variables optimal in a certain aspect. Imagine, for instance, location planning of elementary schools in a new town. There is no existing school, and financial status permits opening two elementary schools. For simplicity, we assume that the geography of the town is homo-geneous and that the two schools provide the educational services of the same quality. In such a case, the distance from home to school is a critical Copyright © 2006 Taylor & Francis Group, LLC Evaluation of School Redistricting by the School Family System 247 factor in location planning; the average distance from home to school should be as small as possible. Spatial optimization gives a set of such locations that minimize the average distance from home to school. Spatial optimization can consider not only a single element of educational environment, such as the distance from home to school, but also various factors simultaneously. In locating schools in a region, the traffic condition of the region, ethnic and racial balance among schools, the quality of teachers and programs also have to be taken into account. Administrative system is also an important element of educational administration. These factors are represented as variables, either qualitative or quantitative, and incorporated in mathematical calculations. Besides facility location, spatial optimization includes network planning, location, and allocation of resources, shortest-path finding, and so forth. Network-planning techniques are useful for discussing the route of school buses, which is financially an important subject in educational administra-tion. Location and allocation of educational resources, including teachers and facilities for education, can also be treated as a spatial-optimization problem. Once spatial-optimization techniques are implemented in GIS, we can interactively compare alternatives for their decision-making (Lemberg and Smith, 1989; Ferland and Guénette, 1990; Armstrong et al., 1993; James, 1996). One may consider that the distance from home to school is very important and derive the optimal location of schools that minimizes the average dis-tance from home to school. Others may think that the ethnic balance among schools is critical, which gives different optimal location of schools. If spatial-optimization techniques are implemented in GIS, we can try various view-points of a problem to be solved, derive their optimal solutions, and compare them using various measures. 17.2.3 GIS for Evaluation in Educational-Administration Research After a program is executed, whether it works successfully is of great interest. To evaluate an educational program, we again use methods of spatial anal-ysis with those of policy evaluation. Take, for instance, the charter-school program. Unlike ordinary public schools, charter schools are run by nonformal organizations consisting of teachers, parents, and so forth, typically characterized by some unique edu-cational programs. Charter schools don’t have a certain district but overlap with those of ordinary schools, so that students can choose either a charter or an ordinary school. The main objective of the charter-school program is to provide students alternatives to ordinary schools, which leads to a com-petition among schools, and, consequently, improves the quality and effi-ciency of education. To evaluate the program, we need to know whether a charter school really draws students widely from its school district. Com-paring the distributions of students of charter and ordinary schools using Copyright © 2006 Taylor & Francis Group, LLC ... - tailieumienphi.vn