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Secondary school allocation optimization towards equal access: A case study on Shijingshan District, Beijing
DAI Teqi,, LIAO Cong,, HU Ke, ZHANG Wenxin, LIU Zhengbing
School of Geography, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
Abstract

Spatial optimization is an important research area in geography. Most research on spatial optimization of education resource in this field is concerned with spatial efficiency, while the public is more concerned with spatial equity. In recent years, random allocation has been tested in some places, but the optimization models on the random allocation of schools have not been well formulated and developed. In China, to improve the spatial equity of education, a newly proposed reform tries to use lottery for school admission, namely "allocating several schools to one school district". However, there is little literature on how to implement the new school allocation, its impacts on school distance and educational equity. This paper constructs a quadratic programming model to minimize the variance of all students' expected values on educational quality under constraints of the maximum distance and schools' capacities. Then, Shijingshan District in Beijing is taken as a case area. The result indicates that the new allocation model can significantly improve the spatial equity of educational resources compared with the way of allocating students to the nearby school. The variance of the former decreases by 99%. Over 2/3 of the communities benefit from our model of maximum spatial equality, whose expected values of educational quality will increase. The ratio of benefit students is also about 2/3. On the other hand, the distance cost of school commuting is also significant. The average school distance increases by 3.99 times. However, it is still less than 5 km, which is commonly set as maximum distance to school. Moreover, it is also less than the survey school distance in the study area. When the parameter of the maximum distance in the model increases from 5 km to 8 km, the improvement of the variance of expected value of educational quality obeys the law of exponential growth, and the average distance increase obeys the law of arithmetic growth. When it is set at 7 km, the variance of expected value of educational quality approaches zero. It can be regarded as a state of absolute equal opportunity for every student which is usually thought to be hard or impossible to realize. Based on the results, the policy implication for China's school admission system is discussed.

Keyword: educational equity; school district; spatial optimization; quadratic program; random allocation; Shijingshan District; Beijing;
1 引言

2 研究方法
2.1 指标定义

2.2 公平导向的“多校划片”模型构建

$Min ∑ i = 1 m N i ( A i - a ) 2$ （1）

s.t.

$A i = ∑ j = 1 n ( Y ij X ij Q j ) / N i$ （2）

$∑ j = 1 n Y ij X ij = N i$ （3）

$∑ i = 1 m Y ij X ij = S j$ （4）

$S j > C min$ （5）

$S j < C max$ （6）

$d ij × Y ij ≤ D max$ （7）

$0 ≤ X ij ≤ N i$ （8）

2.3 “就近入学”情景的模型构建

$Min ∑ i = 1 m ∑ j = 1 n N i d ij L ij$ （9）

s.t.

$∑ L ij = 1$ （10）

$d ij × L ij ≤ D max$ （11）

$S j = ∑ i = 1 n N i L ij$ （12）

$S j ≤ C max$ （13）

$S j ≥ C min$ （14）

3 研究区域和数据来源

 Figure Option 图1 研究区概况 Fig. 1 Overview of the study area

4 结果与分析
4.1 “就近入学”情景

 Figure Option 图2 北京石景山区“就近入学”空间配置 Fig. 2 Spatial allocation of schools in the scenario of "nearby enrollment" in Shijingshan District, Beijing

4.2 公平最大化的“多校划片”情景

 Figure Option 图3 北京石景山区“多校划片”空间配置 Fig. 3 Spatial allocation of schools in the scenario of "Duoxiaohuapian" in Shijingshan District, Beijing

 Figure Option 图4 北京石景山区“多校划片”下教育质量及上学距离变化 Fig. 4 Changes of educational quality and school distance in each community in Shijingshan District, Beijing

4.3 公平最大化情景下最大距离参数与教育公平的关系

 Figure Option 图5 距离与教育公平的关系 Fig. 5 The tradeoff between distance and educational quality

 Figure Option 图6 北京石景山区不同最大上学距离约束下上学距离超过5 km的小区分布 Fig. 6 Distributions of communities with the distance over 5 km under different values of parameters Dmax

5 结论与讨论

（1）与就近入学相比,公平最大化的“多校划片”可以显著提高教育空间公平,但也会付出明显的距离代价。当最大上学距离不超过5 km时,各个小区教育质量的方差仅为0.070,比就近入学情景降低了99%;平均上学距离则增加到3.99倍,达到3.20 km,这一距离符合一般的上学距离要求,是可以接受的。

（2）公平最大化的“多校划片”带来的损益的空间分布是显著不均衡的。总体而言,多数地区和人口的教育质量预期值会比“就近入学”得到改善,其中教育质量预期值增加的小区占总数的64.84%,学生人数则占总数的62.93%;这些小区主要分布在学校质量评分较低的学校附近。

（3）公平最大化的“多校划片”模型下,最大上学距离约束的放松可以显著提升教育质量的空间公平,直至实现教育机会空间均等化。当最大上学距离增加到7 km时,得到的方差近似为0,基本实现了教育质量预期值的空间均等化,此时平均上学距离为3.70 km。随着最大上学距离的增加,空间公平的改善近似指数增长,而距离代价近似算术增长,公平的改善速度更快。具体地,最大上学距离从5 km开始增加到8 km,每增加1 km,各小区教育质量方差平均下降96%,平均上学距离平均增长0.40 km,超过5 km的较长上学距离人数平均增加197人。按边际增量看,当最大上学距离约束为6 km时,上学距离过长的人口总数最小,仅有50人,而公平性提高最显著,是本文推荐的决策点。

The authors have declared that no competing interests exist.

Reference